Grade 5 Unit 1 2011-2012 FINAL

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Grade 5 Unit 1 Indicators 6 weeks of instruction

These are the grade level objectives that my students were exposed to last year:

All objectives in this column will be assessed on post-assessments and MSA:

My students achieved the assessed objectives. So, now I will explore:

Knowledge of Algebra: Patterns and Functions

1.A.1.a(4) Represent or analyze numeric patterns using skip counting AL: Use patterns of 3, 4, 6, 7, 8, or 9 starting with any whole number (0-100)

1.A.1.a(5) Interpret and write a rule for a one operation (+, -, x, ÷ with no remainders) function table AL: Use whole numbers (0-1000) or decimals with no more than 2 decimal places (0-1,000)

1.A.1.a(6) Identify and describe sequence represented by a physical model or in a function table

1.A.1.b(4) Create a one operation (+ or -) function table to solve a real world problem

1.A.1.b(5) Create a one operation (+, -, x, ÷ with no remainders) function table to solve a real world problem 1.A.1.b(6) Interpret and write a rule for a one-operation (+, -, x, ÷ without remainders) function table AL: Use whole numbers or decimals with no more than 2 decimal places (0-1,000)

1.A.1.c(4) Complete a function table using a one operation (+, -, x, ÷ with no remainders) rule AL: Use whole numbers (0-50)

1.A.1.c (5) Complete a one-operation function table AL: Use whole numbers with +, -, x, ÷ (with no remainders) or use decimals with no more than two decimal places with +, – (0-200)

1.A.1.c(6) Complete a function table with a given two-operation rule AL: Use the operations (+, -, x), numbers no more than 10 in the rule and whole numbers (0-50)

1.A.1.d(4) Describe the relationship that generates a one operation rule

1.A.1.d(5) Apply a given two operation rule for a pattern AL: Use two operations (+, -, x) and whole numbers (0-100)

1.A.2.a(4) Generate a rule for the next level of the growing pattern AL: Use at least 3 levels but no more than 5 levels 1.A.2.b(4) Generate a rule for a repeating pattern AL: Use no more than 4 objects in the core of the pattern

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Knowledge of Algebra: Expressions, Equations, and Inequalities

1.B.1.a(4) Represent numeric quantities using operational symbols(+, -, x, ÷ with no remainders) AL: Use whole numbers (0-100)

1.B.1.a(5) Represent unknown quantities with one unknown and one operation (+, -, x, ÷ with no remainders) AL: Use whole numbers (0-100) or money ($0-100)

1.B.1.a(6) Write an algebraic expression to represent unknown quantities AL: Use one unknown and one operation (+, -) with whole numbers, fractions with denominators as factors of 24, or decimals with no more than two decimal places (0-200)

1.B.1.b(4) Determine equivalent expressions AL: Use whole numbers (0-100)

1.B.1.b(5) Determine the value of algebraic expressions with one unknown and one-operation AL: Use +, - with whole numbers (0-1000) or x, ÷ (with no remainders) whole numbers (0-100) and the number for the unknown is no more than 9

1.B.1.b(6) Evaluate an algebraic expression AL: Use one unknown and one-operation (+, -) with whole numbers (0-200), fractions with denominators as factors of 24 (0-50), or decimals with no more than two decimal places (0-50)

1.B.1.c(5) Use parenthesis to evaluate a numeric expression 1.B.1.c(6) Evaluate numeric expressions using the order of operations AL: Use no more than 4 operations (+, -, x, ÷ with no remainders) with or without 1 set of parentheses or a division bar and whole numbers (0-100)

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Knowledge of Algebra: Expressions, Equations, and Inequalities (continued)

1.B.2.a(4) Represent relationships using relational symbols (<, >, =) and operational symbols (+, -, x, ÷) on either side AL: Use operational symbols (+, -, x) and whole numbers (0-200)

1.B.2.a(5) Represent relationships using relational symbols (<, >, =) and one operational symbols (+, -, x, ÷ with no remainders) on either side AL: Use whole numbers (0-400)

1.B.2.a(6) Identify and write equations and inequalities to represent relationships AL: Use a variable, the appropriate relational symbols (<, >, =), and one operational symbol (+, -, x, ÷) on either side and use fractions with denominators as factors of 24 (0-50) or decimals with no more than two decimal places (0-200)

1.B.2.b(4) Find the unknown in an equation with one operation AL: Use multiplication and whole numbers (0-81)

1.B.2.b(5) Find the unknown in an equation use one operation (+, -, x, ÷ with no remainders) AL: Use whole numbers (0-2000)

1.B.2.b(6) Determine the unknown in a linear equation AL: Use one operation (+, -, x, ÷ with no remainders) and positive whole number coefficients using decimals with no more than two decimal places (0-100)

Knowledge of Numeric and Graphic Representations of Relationships

1.C.1.b(4) Identify positions in a coordinate plane AL: Use the first quadrant and ordered pairs of whole numbers (0-20)

1.C.1.b(5) Create a graph in a coordinate plane AL: Use the first quadrant and ordered pairs of whole numbers (0-50)

1.C.1.b(6) Graph ordered pairs in a coordinate plane AL: Use no more than 3 ordered pairs of integers (-20 to 20) or no more than 3 ordered pairs of fractions/mixed numbers with denominators of 2 (-10 to 10)

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Knowledge of Number Theory

6.B.1.a Identify or describe numbers as prime or composite AL: Use whole numbers (0-100)

6.B.1.a(6) Determine prime factorizations for whole numbers and express them using exponential form

6.B.1.a(4) Identify and use divisibility rules AL: Use the rules for 2, 5, or 10 with whole numbers (0-1,000)

6.B.1.b(5) Identify and use divisibility rules AL: Use the rules for 2, 3, 5, 9, or 10 with whole numbers (0-10,000)

6.B.1.b(4) Identify factors AL: Use whole numbers (0-24)

*6.B.1.c(5) Identify the greatest common factor AL: Use 2 numbers whose GCF is no more than 10 and whole numbers (0-100)

6.B.1.c(4) Identify multiples AL: Use the first 5 multiples of any single digit whole number

*6.B.1.d(5) Identify a common multiple and the least common multiple AL: Use no more than 4 single digit whole numbers

Knowledge of Computation (Whole Number)

6.C.1.c(4) Multiply whole numbers AL: Use a 1-digit factor by up to a 3-digit factor using whole numbers (0-1000)

6.C.1.a(5) Multiply whole numbers AL: Use a 3-digit factor by another factor with no more than 2-digits and whole numbers (0 - 10,000)

6.C.1.b(6) Multiply fractions and mixed numbers and express in simplest form AL: Use denominators as factors of 24 not including 24 (0-20) 6.C.1.c(6) Multiply decimals AL: Use a decimal with no more than 3 digits multiplied by a 2-digit (0-1000)

6.C.1.d(4) Divide whole numbers AL: Use up to a 3-digit dividend by a 1-digit and whole numbers with no remainders (0-999)

6.C.1.b(5) Divide whole numbers AL: Use a dividend with no more than a 4-digits by a 2-digit divisor and whole numbers (0 – 9999)

6.C.1.d(6) Divide Decimals AL: Use a decimal with no more than 5 digits divided by a whole number with no more than 2 digits without annexing zeros (0-1000)

6.C.1.c(5) Interpret quotients and remainders mathematically and in the context of a problem AL: Use dividend with no more than a 3-digits by a 1 or 2 digit divisor and whole numbers (0 – 999)

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Measurement: Time

3.C.1.c(4) Determine start time, elapsed time, and end time AL: Use hour and half hour intervals

3.C.2.a(5) Determine start, elapsed, and end time AL: Use the nearest minute

3.C.2.b(4) Determine equivalent units of time

3.C.2.b Determine equivalent units of measurement AL: Use seconds, minutes, and hours or pints, quarts, and gallons

Algebra “Big Ideas”

The concepts of number and variable and their symbolic representation and

manipulation are central to the understanding of arithmetic, its generalization in algebra, and the application of mathematics in the real world.

Algebra is a useful tool for generalizing arithmetic and representing patterns in our world.

Symbolism, especially involving equality and variables, must be well understood conceptually for students to be successful in mathematics, particularly algebra.

Methods we use to compute and the structures in our number system can and should be generalized. For example, the generalization that a + b = b + a tells us that 83 + 27 = 27 + 83 without computing the sums on each side of the equal sign.

Patterns, both repeating and growing, can be recognized, extended, and generalized. Patterns are found in physical and geometric situations as well as in numbers.

Variables are symbols that take the place of numbers or ranges of numbers.

Equations and inequalities are used to express relationships between two quantities.

Functions in K-8 mathematics describe in concrete ways the notion that for every input there is a unique output.

Adapted from:

• Teaching Student-Centered Mathematics Grades 3-5, Van de Walle and Lovin.

• Elementary and Middle School Mathematics: Teaching Developmentally, Van de Walle , Karp, Bay-Williams.

• Curriculum Focal Points, NCTM.

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Potential Algebra Focus Questions

How do patterns help in counting and/or computation? What patterns do you notice in the numbers when skip counting? How can patterns be generalized? Why do we use variables? How is an equation like a balance scale? What strategies can be used to find the unknown in an equation? Why do we represent a quantity in multiple ways? How can we use numbers and symbols to represent relationships in the real world? What is the relationship between patterns and functions? How can we use algebraic expressions to represent a real world situation? How can we identify and describe patterns? What can be learned from studying patterns? How can relationships be expressed symbolically?

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Computation “Big Ideas”

Flexible methods of computation involve taking apart and combining numbers in a wide variety of ways. Most of the partitions of numbers are based on place value or “compatible” numbers—number pairs that work easily together, such as 25 and 75.

Invented strategies are flexible methods of computing that vary with the numbers and the situation. Successful use of the strategies requires that they be understood by the one who is using them—hence the term invented. Strategies may be invented by a peer or the class as a whole; they may even be suggested by the teacher. However, they must be constructed by the student.

Flexible methods for computation require a good understanding of the operations and properties of the operations. How the operations are related—addition to subtraction—is also an important ingredient.

The traditional algorithms are clever strategies for computing that have been developed over time. Each is based on performing the operation on one place value at a time. Each is based on performing the operation on one place value at a time with transitions to an adjacent position (trades, regrouping, “borrows,” or “carries”). These algorithms work for all numbers but are often far from the most efficient or useful methods for computing.

Students develop their understanding of numbers by building their facility with mental computation (addition and subtraction in special cases, such as 2,500 + 6,000 and 9,000 – 5,000), by using computational estimation, and by performing paper-and-pencil computations.

Adapted from:

• Teaching Student-Centered Mathematics Grades 3-5, Van de Walle and Lovin.

• Elementary and Middle School Mathematics: Teaching Developmentally, Van de Walle , Karp, Bay-Williams.

• Curriculum Focal Points, NCTM.

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Potential Computation Focus Questions

What other strategies can be used to solve this problem? Is the answer you found reasonable? What strategies can be used for finding sums and differences? How can strategies help me find products and/or quotients? When is the “correct answer” not the best solution? When should you use mental computation? When should you use “paper/pencil” computation?

Multiplication and Division (Factors, Multiples) What are the mathematical properties that govern addition and multiplication?

How would you use them? How do you know if a number is divisible by ____ (insert number)? How can multiples be used to solve problems? How can the facts strategies help us compute with larger numbers? How can numbers be broken down into its smallest factors? How does the situation in the problem help me determine how to interpret the

remainder? How can multiples be used to solve problems? How can I use the array model to explain multiplication? How are repeated addition and multiplication related? How can I use what I know about repeated subtraction, equal sharing, and forming

equal groups to solve division problems? How does my knowledge about multiplication facts help me to solve problems?

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Grade 5 Unit 1 Vocabulary

Consider adding these words to the grade 5 word wall from previous grades.

Vocabulary introduced in previous grades: New grade 5 unit vocabulary:

Knowledge of Algebra, Patterns, and Functions: Expressions, Equations, and Inequalities expression (4) equation (4) unknown (4) inequality (4) relationship (4) operational (3) symbol (3) number sentence (3) greater than (1) less than (1) equal to (1) missing number (1) symbol (1) total (1) more (K) less (K) add (K) join (K) equal (K)

evaluate

Knowledge of Algebra, Patterns, and Functions: Numeric and Graphic Representations of Relationships

ordered pair (4) coordinate grid (4) number line (K)

Knowledge of Number Relationships or Computation: Number Theory factor (4) multiple (4) rules of divisibility (4) even (3) odd (3)

prime composite

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Grade 5 Unit 1 Vocabulary Continued


Knowledge of Number Relationships or Computation: Number Computation

approximate (4) factor (3) product (3) dividend (3) divisor (3) quotient (3) inverse operation (3) commutative property of multiplication (3) identify property of multiplication (3) zero property of multiplication (3) addends (2) sum (2) difference (2) multiplication (2) division (2) reasonable (2) estimate (2) equal sharing (2) array (2) counting on (1) counting back (1) making ten (1) doubles (1) doubles plus one (1) fact family (1) addition (K) subtraction (K)

remainder greatest common factor – GCF least common multiple – LCM

Knowledge of Measurement: Liquid Units quart

pint gallon

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Grade 5 Unit 1 Vocabulary Continued


Knowledge of Measurement: Time

second (3) minute (2) half-hour (1) hour (1) day (K) month (K) week (K) year (K) today (K) tomorrow (K) morning (K) afternoon (K) night (K) before (K) after

elapsed time

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evaluate

Gr. 5 Unit 1

expression

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equation

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unknown

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inequality

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relationship

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ordered pair

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coordinate plane

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prime

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composite

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factor

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multiple

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rules of divisibility Gr. 5 Unit 1

remainder

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greatest common factor Gr. 5 Unit 1

least common multiple

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approximate

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product

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quotient

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dividend

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divisor

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inverse operation Gr. 5 Unit 1

addends

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sum

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difference

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estimate

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quart

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pint

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gallon

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elapsed time

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Standard 7.0 – Building Communication Skills UUssiinngg WWoorrdd WWaallllss

When you find yourself with a brief period of time, try turning your word wall into an instructional activity.

• Give a clue, then ask students to find the word that goes with your clue.

• Ask students to find two words on the wall that go together (are connected in some way) and to justify their answers.

• Select a word wall word and ask students to work with a partner to create a quick web of all the words they can think of that go with that word.

• Ask students to define a word or use the word in a sentence to show their understanding.

• Say a sentence, but leave out a word (from the wall). Have students guess which word belongs in your sentence.

• Scramble the letters in a word. Give students a clue to its meaning and see if they can unscramble the word.

• Ask students to draw pictures or act out their understanding of a word on the wall (April’s Game).

• Share a topic with the class (e.g. multiplication) and ask students to find all of the words on that connect to your topic.

Provide students varied opportunities to interact with the words on the wall. It will build their understanding and confidence with the words.

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Washington County Public Schools

Elementary Math Grade 5

Unit 1 Pre-Assessment

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Pre-Assessment Information

Pre-assessment is part of the ongoing instruction and assessment process. Teachers need to gather data about what their students know and are able to do by concept or group of concepts. Pre-assessment:

• helps teachers plan for instruction. • yields information about options for learning. • allows teachers to anticipate differences. • respects what students already know and are able to do. • can maximize actual learning time.

The pre-assessments included in this guide are in a three column format similar to that of the grade level content maps.

Pre-Assessment Considerations: • The pre-assessments are divided into sections according to the content of the unit.

Below grade level question (Grade 4)

Above grade level question (Grade 6)

On-grade level question (Grade 5)

Gra

de L

evel

Obj

ectiv

e

1.A

.1.a

- R

ow 1

Which sequence below shows skip counting by adding 8? 5, 9, 13, 17, 21…

2, 10, 18, 26, 34…

6, 15, 24, 33, 42…

20, 23, 26, 29, 30…

Write a rule for the function table below:

x y 4 1

16 4 24 6

rule: ______________

1.A

.1.c

– R

ow 2

What is the missing number in the function table below?

x y 2 10 3 15 6 ? 8 40

? = ___________

What is the missing number in the function table below?

x y 4 5.5 7 8.5

10 ? 18 19.5

? = ___________

Paul used the following rule to make the function table below: multiply by 2 subtract 1.

x 5 6 8 10 y 9 11 15 ?

If x = 10, what is the value of y? y = __________

1.A

.1.d

- R

ow 3

The rule for a pattern is “add 2, then multiply 2.” If the pattern starts with 3, what are the first four numbers in the sequence?

3, ____, ____, ____

The rule for the function table below is subtract 3 and then multiply the difference by 6. What is the missing number?

x y 3 0 4 6 5 12 ? 24

? = ______________

1.B.

1.a

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There are 12 trucks in the parking lot. There are twice as many cars in the parking lots. Which expression names the number of cars? 2 + 12 12 - 2 2 x 12 12 ÷ 2

James plans to complete a 28 mile bike ride in 4 hours. Which expression shows how many miles he needs to ride each hour? 4 + 28 28 ÷ 4 28 - 4 28 x 4

In Mrs. Brengle’s class of 32 students one fourth of the students are in the band. Which expression shows how many students are in the band? ¼ + 32 32 ÷ ¼ ¼ x 32 32 – ¼

1.B.

1.b

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Look at the equation below.

N x 6 = 42 What value of N makes the equation correct?

N = ____

Look at the equation below.

150 ÷ N = 30 What value of N makes the equation correct?

N = _______

Whitney has a number of cookies, c. She is going to split the cookies equally with her friend. The expression below shows how many each person will get.

Evaluate the expression if c = 50.

c = ______

1.B.

2.a

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Rich buys 3 packs of 10 crayons. Julian buys 4 packs of 8 crayons. Which inequality shows the relationship between the number of crayons Rich buys and the number of crayons Julian buys? 3 x 10 < 4 x 8

3 x 10 > 4 x 8

3 + 10 < 4 + 8

3 + 10 > 4 + 8

On Monday 180 people rode the roller coaster in the morning and 152 people in the afternoon. On Tuesday 123 people rode the roller coaster in the morning and 202 people in the afternoon. Write an inequality to show the relationship between the number of people that rode the coaster on Monday and the number of people that rode the coaster on Tuesday. ________________________________

Today the number of messages left on an answering machine was ½ the number of messages (m) left yesterday. More than 8 messages were on the machine today. Which number sentence represents this relationship? ½ x m = 8

½ x m > 8

½ x m < 8

½ x m > 8

1.B.

2.b

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What number makes this equation true?

x 8 = 72

= ____

Solve for N:

N + 525 = 2,000

N = _______

Five friends spent a total of $20.25 for lunch. They solved the following equation to find p, the amount of money each should pay.

5p = 20.25

p = _______

1.C.

1.b

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Name the point that is plotted below: The point is _______________

Add a dot to the grid below so that when the points are connected they make a triangle. The point I added was: _______

Which quadrant is the point plotted in? _______ Name the coordinates of the plotted point: ______

6.B.

1.a

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George’s soccer jersey number is a prime number greater than 12 but less than 20. What number could be on his jersey? Write the number on the jersey below.

What is the prime factorization of 12? (use exponential form) _________________________

6.B.

1.b

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0 MiMi has more than 260 stickers but less than 280 stickers. The number of stickers she has is divisible by 2, 5, and 10. How many stickers does Marla have? 262

265

270

275

How many of these numbers on the sign below are divisible by 3? 0

1

2

3

6.

B.1.

c –

Row

11

What are the factors of 9? __________________________

What is the greatest common factor (GCF) or 32 and 48? __________________________

6.B.

1.d

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2

Which number is a multiple of 3 and 6? 9

24

27

33

Mrs. Reichard can divide her class into groups of 3 students or groups of 4 students. Which of the following is a possible size of her class? 22

23

24

25

WELCOME TO MATHTOWN!

Established: 1793 Elevation: 1,347 feet

Population: 8,634

6.C.

1.a

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3 In baseball there are 3 outs in an inning. If a pitcher pitched 263 innings in a season, how many batters did he get out?

The local car wash can wash 220 cars in a day. How many cars can the workers wash in a month with 31 days?

Samantha walks at a rate of 3.25 miles per hour. If she walks for 3.5 hours, how far will she travel?

6.C.

1.b

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4 Sydney has 272 pennies. She wants to divide them evenly into 4 containers. How many pennies will there be in each container?

There are 624 students at Conway Elementary. The principal plans to have 24 students in each classroom. How many classrooms will there be at Conway Elementary?

The total cost for 24 students’ admission to a museum was $598.80. What was the cost per student?

6.C.

1.c

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5

Ginger needs 340 cupcakes. The cupcakes come in packages of 24. How many packages should Ginger buy?

3.

C.2.

a –

Row

16

John started cleaning his room at the time shown below. If it took him 2 hours and 30 minutes to clean, what time did he finish?

________________________

Kiefer left for football practice at 2:35 pm. He returned home 2 hours and 30 minutes later. At what time did Kiefer return home? _________________________

3.C.

2.b

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7

A football player ran 24 yards, how many feet did he run? _____________________feet

A pitcher holds 6 pints of liquid. What amount is this equivalent to? 1 quart 2 pints

2 quarts

3 quarts

1 gallon

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Grade 5 Unit 1 Pre-Assessment Answer Key

Grade 4

Assessment Limit Level Grade 5


Assessment Limit Level 1.A.1.a Row 1

B ÷ 4

1.A.1.c Row 2

30 11.5 19

1.A.1.d Row 3

10, 24, 52 7

1.B.1.a Row 4

B C B

1.B.1.b Row 5

7 5 25

1.B.2.a Row 6

A 180 + 152 > 123 + 202 B

1.B.2.b Row 7

9 1,475 4.05

1.C.1.b Row 8

(5, 7) answers vary Quadrant III and (-4,-3)

6.B.1.a Row 9

13, 17 or 19 22 • 3

6.B.1.b Row 10

C C

6.B.1.c Row 11

1, 3, 9 16

6.B.1.d Row 12

B C

6.C.1.a Row 13

789 6,820 11.375

6.C.1.b Row 14

68 26 24.95

6.C.1.c Row 15

buy 15 packages

3.C.2.a Row 16

8:00 5:05

3.C.2.b Row 17

72 feet 3 quarts

Grade 5 Unit 1 Pre-Assessment Strategic Instruction Plan Page 1

Grade 4



Assessment Limit Level

1.A

.1.a

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1.A.1.a(4) Represent or analyze numeric patterns using skip counting AL: Use patterns of 3, 4, 6, 7, 8, or 9 starting with any whole number (0-100)

1.A.1.a(5) Interpret and write a rule for a one-operation (+, -, x, ÷ without remainders) function table AL: Use whole numbers or decimals with no more than 2 decimal places (0-1,000)

1.A.1.a(6) Identify and describe sequence represented by a physical model or in a function table

Students: Students:

Students:

1.A

.1.c

– R

ow 2

1.A.1.c(4) Complete a function table using a one operation (+, -, x, ÷ with no remainders) rule AL: Use whole numbers (0-50)

1.A.1.c(5) Complete a one-operation function table AL: Use whole numbers with +, -, x, ÷ (with no remainders) (0-200)

1.A.1.c(6) Complete a function table with a given two-operation rule AL: Use the operations (+, -, x), numbers no more than 10 in the rule and whole numbers (0-50)

Students: Students:

Students:

1.A

.1.d

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ow 3


Students: Students:

Students:


1.B.

1.a

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1.B.1.a(4) Represent numeric quantities using operational symbols(+, -, x, ÷ with no remainders) AL: Use whole numbers (0-100)

1.B.1.a(5) Represent unknown quantities with one unknown and one operation (+, -, x, ÷ with no remainders) AL: Use whole numbers (0-100) or money ($0-$100)

1.B.1.a(6) Write an algebraic expression to represent unknown quantities AL: Use one unknown and one operation (+, -) with whole numbers, fractions with denominators as factors of 24, or decimals with no more than two decimal places (0-200)

Students: Students:

Students:

1.B.

1.b

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1.B.1.b(4) Determine equivalent expressions AL: Use whole numbers (0-100)


1.B.1.b(6) Evaluate an algebraic expression AL: Use one unknown and one-operation (+, -) with whole numbers (0-200), fractions with denominators as factors of 24 (0-50), or decimals with no more than two decimal places (0-50)

Students: Students:

Students:

1.B.

2.a

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1.B.2.a(4) Represent relationships using relational symbols (<, >, =) and operational symbols (+, -, x, ÷) on either side AL: Use operational symbols (+, -, x) and whole numbers (0-200)


1.B.2.a(6) Identify and write equations and inequalities to represent relationships AL: Use a variable, the appropriate relational symbols (<, >, =), and one operational symbol (+, -, x, ÷) on either side and use fractions with denominators as factors of 24 (0-50) or decimals with no more than two decimal places (0-200)

Students: Students:

Students:


1.B.

2.b

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1.B.2.b(4) Find the unknown in an equation with one operation AL: Use multiplication and whole numbers (0-81)

1.B.2.b(5) Find the unknown in an equation using one operation (+, -, x, ÷ with no remainders) AL: Use whole numbers (0-2000)

1.B.2.b(6) Determine the unknown in a linear equation AL: Use one operation ((+, -, x, ÷ with no remainders) and positive whole number coefficients using decimals with no more than two decimal places (0-100)

Students: Students:

Students:

1.C.

1.b

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1.C.1.b(4) Identify positions in a coordinate plane AL: Use the first quadrant and ordered pairs of whole numbers (0-20)


1.C.1.b(6) Graph ordered pairs in a coordinate plane AL: Use no more than 3 ordered pairs of integers (-20 to 20) or no more than 3 ordered pairs of fractions/mixed numbers with denominators of 2 (-10 to 10)

Students: Students:

Students:

6.B.

1.a

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6.B.1.a(6) Determine prime factorizations for whole numbers and express them using exponential form

Students: Students:

Students:


6.B.

1.b

– Ro

w 1

0

6.B.1.a(4) Identify and use divisibility rules AL: Use the rules for 2, 5, or 10 with whole numbers (0-1,000)


Students: Students:

Students:

6.B.

1.c

– Ro

w 1

1

6.B.1.b(4) Identify factors AL: Use whole numbers (0-24)

6.B.1.c(5) Identify the greatest common factor AL: Use 2 numbers whose GCF is no more than 10 and whole numbers (0-100)

Students: Students:

Students:

6.B.

1.d

– R

ow 1

2

6.B.1.c(4) Identify multiples AL: Use the first 5 multiples of any single digit whole number

6.B.1.d(5) Identify a common multiple and the least common multiple AL: Use no more than 4 single digit whole numbers

Students: Students:

Students:


6.C.

1.a

– R

ow 1

3

6.C.1.c(4) Multiply whole numbers AL: Use a 1-digit factor by up to a 3-digit factor using whole numbers (0-1000)


6.C.1.c(6) Multiply decimals AL: Use a decimal with no more than 3 digits multiplied by a 2-digit (0-1000)

Students: Students:

Students:

6.C.

1.b

– Ro

w 1

4

6.C.1.d(4) Divide whole numbers AL: Use up to a 3-digit dividend by a 1-digit and whole numbers with no remainders (0-999)


6.C.1.d(6) Divide Decimals AL: Use a decimal with no more than 5 digits divided by a whole number with no more than 2 digits without annexing zeros (0-1000)

Students: Students:

Students:


6.C.

1.c

– Ro

w 1

5


Students: Students:

Students:

3.C.

2.a

– Ro

w 1

6

3.C.1.c(4) Determine start time, elapsed time, and end time AL: Use hour and half hour intervals


Students: Students:

Students:

3.C.

2.b

– R

ow 1

7

3.C.2.b(4) Determine equivalent units of time

3.C.2.b Determine equivalent units of measurement AL: Use seconds, minutes, and hours or pints, quarts, or gallons

Students: Students:

Students:

Manipulative Suggestions Grade 5 Unit 1

Manipulative Possible Connections Notes

Number Line Balances

• comparing expressions

• equivalent expressions

• solving one-step equations

Bucket Balances

• comparing expressions

• equivalent expressions

• solving one-step equations

Use a manipulative of equal weight with the bucket balance. i.e. units cubes, bear counters of the same size, etc…

Test to make sure the counters are the same weight before using with students.

Number Tiles

Use Tiles with: • Communicating with Tiles

book (SAS)

• Skillboards Book 1 (SAS)

• Skillsboards Book 2 (SAS)

• Tile Cards (see unit guide)

Each SAS has a set of 40 tiles (enough for 40 students) that teachers can borrow.

Each student needs 1 set of tiles (0-9) for activities.

Resource Books Grade 5 Unit 1

These are books that may be helpful to you in planning for this unit that your school has at least 1 copy of. If you cannot

locate this book, see your SAS.

Manipulative Author Possible Connections

Elementary & Middle School Mathematics

Van de Walle Karp

Bay-Williams

Book Location: Past Math Institute

Teachers SAS Resource Library Enrichment/Magnet

Teacher

• all unit content

All Aboard the Algebra Express

Kim Sutton

Book Location: Grade 5 Teachers

• function tables • numeric patterns

Navigating through Algebra Grades 3-5

NCTM

Book Location: SAS Resource Library

• function tables • numeric patterns • equations

• expressions

Manipulative Author Possible Connections

Beginning Weight Logic

Marcy Cook


• expressions

• equations

Do the Math

Kim Sutton


• expressions

• equations

MATHEMATICS BENCHMARK

Student: _________________________________________________

Mathematics Section 1

Grade 5 Unit 1 Page 1 GO ON

During the test, you will answer selected-response questions and constructed-response questions. Selected-response questions are questions that ask you to choose the correct answer. You may write, circle, underline, make notes, and do calculations inside the boxed area of the test question. All your calculations and notes should be written in the test booklet. Fill in only one answer bubble completely and make your mark heavy and dark. If you want to change an answer, completely erase the mark you made before making a new mark. Constructed-response questions are questions that require you to write your answer. Each constructed-response question has a Step A and a Step B. You may write, circle, underline, make notes, and do calculations inside the boxed area of the test question. Write your answers within the boxed area. Be sure to answer the question completely to show you clearly understand the question. Do not write outside the boxed area. The boxed area is your answer space. Only what you write in the answer space will be scored. You do not need to use the entire answer space.



1 Benjamin drops a ball from different heights and measures how high it bounces.

Drop Height Bounce Height

1 foot 0.5 foot

2 feet 1 foot

4 feet 2 feet

7 feet 3.5 feet

12 feet ?

If the pattern continues, what bounce height should Benjamin expect if he drops the ball from a height of 12 feet?

6 feet

5.5 feet

5 feet

4.5 feet

2 Ricky had $30. He bought a football that costs m dollars. He now has less than $10 left.

Which inequality represents this situation?

m – 30 > 10

m – 30 < 10

30 – m > 10

30 – m < 10



3 Look at the numbers on the soccer shirts below.

What do all of these numbers have in common?

They are all odd numbers.

They are all even numbers.

They are all prime numbers.

They are all composite numbers.

4 Linda is making a picture display of 120 pictures. The display area can fit 10 pictures in each row. Linda can find the number of rows (r) she will need with this equation:

10 x r = 120

Which equation could she also use to find the answer?

120 + 10 = r

120 ÷ 10 = r

120 x 10 = r

120 – 10 = r



5 Eli bought 6 gallons of milk for the soccer team. They drank 10 quarts of milk.

How many quarts of milk were left over?

2 quarts

3 quarts

12 quarts

14 quarts

6 Look at the equation below.

x + 329 = 1,000

What value of x makes this equation correct?

571

671

1,229

1,329



7 Hot dogs come in packages of 8. Rolls come in bags of 12. Mitch wants to buy the

same number of hot dogs and rolls.

What is the smallest number of hot dogs Mitch can buy?

8

12

24

32

8 The table below shows the start and the end times of a movie at a theater. Movie Times

Start Time End Time

12:25 p.m. 2:40 p.m.

2:55 p.m. 5:10 p.m.

6:50 p.m. 9:05 p.m.

9:25 p.m. 11:40 p.m.

According to the information in the table, which of the following statements is true?

The end time is exactly 2 hours 45 minutes after the start time.






9 Marci made this table to show the cost of sending some cards to her friends.

Card Price

Cost with Stamp

$1.36 $1.80

$1.99 $2.43

$2.48 $2.92

$2.82 $3.26

Step A Write a rule to represent the relationship between the price of the card and the total cost with a stamp. ___________________

Step B

10 Use what you know about function tables to explain how you know your answer is correct. Use words, numbers, and/or symbols in your explanation.



11 Rosie created a number pattern with the rule “add 2, then multiply by 2”. She

wrote down the number pattern but one number is wrong.

1, 6, 16, 32, 76

What change should be made to the pattern to correct the pattern?

Replace 32 with 36 Replace 16 with 12 Replace 76 with 80 Replace 6 with 5

12 There are 365 days in a year. The expression below names the number of days

remaining in the year if x days have passed.

365 - x

What is the value of the expression if x = 182?

123 183 283 547



13

Which number is the greatest common factor (GCF) of 32 and 40?

2 4 5 8

14 Blake gets a card stamped each time he buys a cookie at the bakery. The table

below shows the relationship between the number of stamps on his card and the number of free cookies he gets on his next visit.

Restaurant Card

Number of Stamps

Number of Free Cookies

7 1

14 2

21 3

28 4


The total number of free cookies is 6 less than the number of stamps. The total number of free cookies is 7 less than the number of stamps. The total number of free cookies is the number of stamps divided by 7.

The total number of free cookies is the number of stamps divided by 6.



15 Camryn’s grandmother said, “My age is the only prime number between 48 and

55.”

Step A What is the age of Camryn’s grandmother? ___________________

Step B

16 Use what you know about prime numbers to explain why your answer is correct. Use words, numbers, and/or symbols in your explanation.


Grade 5 Unit 1 Page 10

17 Jim’s teacher wrote the following on the board: 9 x 4 80 ÷ 2

Which symbol makes the sentence true?

> < x =

18 Jimmy created a pattern using the rule multiply by 2 and subtract 3. The first

number in his pattern is 4.

What are the next five numbers in Jimmy’s pattern?

8, 5, 10, 7, 14 5, 10, 17, 31, 59 8, 16, 32, 64, 128 5, 7, 11, 19, 35



19 Ahmed needs 336 square tiles to cover his patio. The tiles come in boxes of 12.

How many boxes of tiles does Ahmed need?

28 29 3,960 4,032

20 Mrs. Richmond drives 72 miles a day and Mr. Richmond drives 36 miles a day to

work. They both worked 22 days in August.

How many total miles did they drive to work in August?

432 792 1,584 2,376



21 Look at the triangle on the coordinate grid below.

Which of the following ordered pairs is located inside the triangle?

(3, 6)

(8, 5)

(6, 3)

(5, 8)



22 Jason has a collection of 145 trading cards. He can fit 7 cards on each page of his album.

Step A How many pages will Jason need? ___________________

Step B

23 Jason buys 5 more trading cards. Jason thinks he needs to buy 1 more album page. • Explain why Jason is correct. Use what you know about division in y our

explanation. Use words, numbers, or symbols in your explanation.



24 Shelby’s soccer schedule for September is shown below.

If Shelby attends every practice in September, what is the total number of minutes she will spend at soccer practice during the week of September 11-17?

30 min.

150 min.

210 min.

720 min.



25 Fiona won a prize at the school fair for popping a balloon that was divisible by 9. The balloon board is shown below.

Which balloon did Fiona pop?

312

504

602

701



26 Mr. Stark purchased 15 laptops for classrooms in his school.

How much money did he spend to purchase 15 laptops?

$8,985

$8,550

$8,175

$7,550

27 At the farm, 756 cantaloupes were picked this week. The cantaloupes were

shipped in boxes that held 18 cantaloupes.

How many boxes were filled?

42

40

34

32

Item Cost LCD Projector $545 Laptop $570 Desktop Computer $599

MATHEMATICS BENCHMARK

TEACHER DIRECTIONS AND ANSWER KEY

Mathematics Grade 5 Unit 1

TEACHER DIRECTIONS & ANSWER KEY Page 1

Testing Notes

Test Timing: Each section of the test should be timed as indicated in the teacher directions. If a student does not complete the test within the time limit, give them the time they need to complete the test and submit their bubble sheet with all their answers completed. The teacher should make a note to work with these students before the next assessment. Special Education: All special education students need to be given their accommodations (in IEP) for all Post-Assessments. We encourage teachers to have students working with the accommodator that they will have for MSA, if possible. Reading the Test: Students should read the test on their own, at their own pace within the time limits. Teachers, in grades 3-5, should not read the test to the class. Manipulatives: In order to model the MSA test, students should not be allowed to use any manipulative that is not listed in the test instructions. Teachers are encouraged to continue to use manipulatives during instruction. At this level, however, teachers need to work with students to transition between the concrete and pictorial levels.



Testing Materials Key

Testing Booklet

WCPS Bubble Sheet

No. 2 Pencil

Ruler cm and inches (at least 1/8 inch)

Calculator

Uni

t 1

Post

Ass

essm

ent Section Testing Time Materials

1 31 minutes

14 SR = 21 min. 2 BCR = 10 min.

2

22 minutes

8 SR = 12 min. 1 Conditional BCR = 10 min.



I am going to give you your Test Book. Do not open your Test Book until I tell you to.

Distribute the Test Books and materials. When all students have their books, continue.

Look at the front cover of your Test Book. All fifth grade Test Books have a picture of the C&O Canal at the Cushwa Basin in Williamsport, MD. If your book does not have a picture of the Cushwa Basin, please raise your hand.

Make sure all students have the appropriate Test Booklet.

Turn back to the front cover and print your first and last name on the line marked Student.

Give students time to print their first and last names on the line.

After you are told to open your Test Book, you will see one of two very important symbols at the bottom of each page in the test. The first is the STOP SIGN. When you come to this symbol at the bottom of a page in the test, you are to stop answering test questions. The other symbol you will see at the bottom of some pages is GO ON. When you come to this symbol at the bottom of a page in the test, you should go on to the next page and continue working. Open your Test Book to Section 1 on page 1. You may use any of the test materials distributed to help solve the questions. Make sure everyone has page 2 showing. Look at the directions under Section 1 and read them to yourself as I read them aloud.



During the test, you will answer selected-response questions and constructed-response questions. Selected-response questions are questions that ask you to choose the correct answer. You may write, circle, underline, make notes, and do calculations inside the boxed area of the test question. All your calculations and notes should be written in the test booklet. Fill in only one answer bubble completely and make your mark heavy and dark. If you want to change an answer, completely erase the mark you made before making a new mark. Teacher Note: Do not hand out scratch paper, just like on the MSA, students

are allowed to write everything in the booklet. We want to encourage students to use the Test Booklet for all scratch work.

Constructed-response questions are questions that require you to write your answer. Each constructed-response question has a Step A and a Step B. You may write, circle, underline, make notes, and do calculations inside the boxed area of the test question. Write your answers within the boxed area. Be sure to answer the question completely to show you clearly understand the question. Do not write outside the boxed area. The boxed area is your answer space. Only what you write in the answer space will be scored. You do not need to use the entire answer space. Are there any questions?

Pause for questions.

Please remember that during the test you may not talk to other students, and you may not share materials or look at another student’s Test Book. Also remember to read all directions and questions very carefully and to choose the best answer for each question. If you are not sure about an answer, do the best you can, but do not spend too much time on any one question. Use the space inside the boxed areas for notes and calculations. You may also use any of the test materials that were distributed to you.



You have 31 minutes to complete section 1. Now turn to page 2 in your Test Book. You will complete questions 1 through 18 and stop at the stop sign at the bottom of page 10. Take 30 seconds to preview the types of questions you will answer and find the stop sign at the bottom of page 9.

Give students just 30 seconds to preview the section. Make sure students do not have pencils in their hands for this brief preview. This is an effective test taking strategy that will help students budget their time.

Any questions? Pause for questions. You now have 31 minutes to complete questions 1 through 18. When you are finished be sure to go back and check over your work and make sure your answers are bubbled. You may begin. Give students 31 minutes to complete this section. Stop. Put your pencils down and close your Test Book.

If you had some students not finish, give them extended time but work with the students in the next unit, to help them be able to complete the section within the time limit. Pass out WCPS Scan Sheets to each student. Have each student open their booklet and transfer their answers to the bubble sheet. After students have completed their scan sheet, recollect until after section 2.



You have 22 minutes to complete section 2. Now turn to section 2 on page 11 in your Test Book. Notice the “no calculator” symbol at the top of the pages in section 2. You will not be allowed to use a calculator for this section. Be sure to show all your work on the pages of this section. You will complete questions 19 through 27 and stop at the stop sign at the bottom of page 16. Take 30 seconds to preview the types of questions you will answer and find the stop sign at the bottom of page 16.

Give students just 30 seconds to preview the section. Make sure students do not have pencils in their hands for this brief preview. This is an effective test taking strategy that will help students budget their time.

Any questions? Pause for questions. You now have 22 minutes to complete questions 19 through 27. When you are finished be sure to go back and check over your work and make sure your answers are bubbled. You may begin. Give students 22 minutes to complete this section. Stop. Put your pencils down and close your Test Book.

If you had some students not finish, give them extended time but work with the students in the next unit, to help them be able to complete the section within the time limit. Pass out WCPS Scan Sheets to each student. Have each student open their booklet and transfer their answers to the bubble sheet.



Grade 5 Unit 1 Answer Key

Problem Objective Letter Answer 1 1.A.1.c A 6 feet 2 1.B.2.a D 30 – m < 10 3 6.B.1.a D They are all composite numbers. 4 1.B.1.a B 120 ÷ 10 = r 5 3.C.2.b D 14 quarts 6 1.B.2.b B 671 7 6.B.1.d C 24 8 3.C.2.a B The end time is exactly 2 hours 15 minutes after the start time.

9 1.A.1.a BCR add 44¢ 10 7.0 BCR 11 1.A.1.d A Replace 32 with 36 12 1.B.1.b B 183 13 6.B.1.c D 8 14 1.A.1.a C The total number of free cookies is the number of stamps divided by 7.

15 6.B.1.a BCR 53 16 7.0 BCR 17 1.B.2.a B < 18 1.A.1.d D 5, 7, 11, 19, 35 19 6.C.1.b A 28 20 6.C.1.a D 2,376 21 1.C.1.b C (6,3) 22 6.C.1.c BCR 21 pages 23 7.0 BCR This question is a conditional BCR. 24 3.C.2.b B 150 min. 25 6.B.1.b B 504 26 6.C.1.a B $8,550 27 6.C.1.b A 42



1 Benjamin drops a ball from different heights and measures how high it bounces.

Drop Height Bounce Height

1 foot 0.5 feet

2 foot 1 feet

4 foot 2 feet

7 foot 3.5 feet

12 foot ?

If the pattern continues, what bounce height should Benjamin expect if he drops the ball from a height of 12 feet?

6 feet

5.5 feet

5 feet

4.5 feet

2 Ricky had $30. He bought a football that costs m dollars. He now has less than $10 left.

Which inequality represents this situation?

m – 30 > 10

m – 30 < 10

30 – m > 10

30 – m < 10

1.A.1.c (5) Complete a one-operation function table AL: Use whole numbers with +, -, x, ÷ (with no remainders) or use decimals with no more than two decimal places with +. – (0-200)




3 Look at the numbers on the soccer shirts below.

What do all of these numbers have in common?

They are all odd numbers.

They are all even numbers.

They are all prime numbers.

They are all composite numbers.

4 Linda is making a picture display of 120 pictures. The display area can fit 10 pictures in each row. Linda can find the number of rows (r) she will need with this equation:

10 x r = 120

Which equation could she also use to find the answer?

120 + 10 = r

120 ÷ 10 = r

120 x 10 = r

120 – 10 = r


1.B.1.a(5) Represent unknown quantities with one unknown and one operation (+, -, x, ÷ with no remainders) AL: Use whole numbers (0-100) or money ($0-100)



5 Eli bought 6 gallons of milk for the soccer team. They drank 10 quarts of milk.

How many quarts of milk were left over?

2 quarts

3 quarts

12 quarts

14 quarts

6 Look at the equation below.

x + 329 = 1,000

What value of x makes this equation correct?

571

671

1,229

1,329


1.B.2.b(5) Find the unknown in an equation use one operation (+, -, x, ÷ with no remainders) AL: Use whole numbers (0-2000)



7 Hot dogs come in packages of 8. Rolls come in bags of 12. Mitch wants to buy the

same number of hot dogs and rolls.

What is the smallest number of hot dogs Mitch can buy?

8

12

24

32

8 The table below shows the start and the end times of a movie at a theater. Movie Times

Start Time End Time

12:25 p.m. 2:40 p.m.

2:55 p.m. 5:10 p.m.

6:50 p.m. 9:05 p.m.

9:25 p.m. 11:40 p.m.


The end time is exactly 2hours 45 minutes after the start time.




6.B.1.d(5) Identify a common multiple and the least common multiple AL: Use no more than 4 single digit whole numbers




9 Marci made this table to show the cost of sending some cards to her friends.

Card Price

Cost with Stamp

$1.36 $1.80

$1.99 $2.43

$2.48 $2.92

$2.82 $3.26

Step A Write a rule to represent the relationship between the price of the card and the total cost with a stamp. add 44¢

Step B

10 Use what you know about function tables to explain how you know your answer is correct. Use words, numbers, and/or symbols in your explanation.


7.0 Processes of Mathematics



11 Rosie created a number pattern with the rule “add 2, then multiply by 2”. She

wrote down the number pattern but one number is wrong.

1, 6, 16, 32, 76

What change should be made to the pattern to correct the pattern?

Replace 32 with 36 Replace 16 with 12 Replace 76 with 80 Replace 6 with 5

12 There are 365 days in a year. The expression below names the number of days

remaining in the year if x days have passed.

365 - x

What is the value of the expression if x = 182?

123 183 283 547





13

Which number is the greatest common factor (GCF) of 32 and 40?

2 4 5 8

14 Blake gets a card stamped each time he buys a cookie at the bakery. The table

below shows the relationship between the number of stamps on his card and the number of free cookies he gets on his next visit.

Restaurant Card

Number of Stamps

Number of Free Cookies

7 1

14 2

21 3

28 4


The total number of free cookies is 6 less than the number of stamps. The total number of free cookies is 7 less than the number of stamps. The total number of free cookies is the number of stamps divided by 7.

The total number of free cookies is the number of stamps divided by 6.

6.B.1.c(5) Identify the greatest common factor AL: Use 2 numbers whose GCF is no more than 10 and whole numbers (0-100)




15 Camryn’s grandmother said, “My age is the only prime number between 48 and

55.”

Step A What is the age of Camryn’s grandmother? 53

Step B

16 Use what you know about prime numbers to explain why your answer is correct. Use words, numbers, and/or symbols in your explanation.





17 Jim’s teacher wrote the following on the board: 9 x 4 80 ÷ 2

Which symbol makes the sentence true?

> < x =

18 Jimmy created a pattern using the rule multiply by 2 and subtract 3. The first

number in his pattern is 4.

What are the next five numbers in Jimmy’s pattern?

8, 5, 10, 7, 14 5, 10, 17, 31, 59 8, 16, 32, 64, 128 5, 7, 11, 19, 35





19 Ahmed needs 336 square tiles to cover his patio. The tiles come in boxes of 12.

How many boxes of tiles does Ahmed need?

28 29 3,960 4,032

20 Mrs. Richmond drives 72 miles a day and Mr. Richmond drives 36 miles a day to

work. They both worked 22 days in August.

How many total miles did they drive to work in August?

432 792 1,584 2,376





21 Look at the triangle on the coordinate grid below.

Which of the following ordered pairs is located inside the triangle?

(3, 6)

(8, 5)

(6, 3)

(5, 8)




22 Jason has a collection of 145 trading cards. He can fit 7 cards on each page of his

album.

Step A How many pages will Jason need? 21 pages

Step B

23 Jason buys 5 more trading cards. Jason thinks he needs to buy 1 more album page. • Explain why Jason is correct. Use what you know about division in y our

explanation. Use words, numbers, or symbols in your explanation.





24 Shelby’s soccer schedule for September is shown below.

If Shelby attends every practice in September, what is the total number of minutes she will spend at soccer practice during the week of September 11-17?

30 min.

150 min.

210 min.

720 min.




25 Fiona won a prize at the school fair for popping a balloon that was divisible by 9. The balloon board is shown below.

Which balloon did Fiona pop?

312

504

602

701




26 Mr. Stark purchased 15 laptops for classrooms in his school.

How much money did he spend to purchase 15 laptops?

$8,985

$8,550

$8,175

$7,550

27 At the farm, 756 cantaloupes were picked this week. The cantaloupes were

shipped in boxes that held 18 cantaloupes.

How many boxes were filled?

42

40

34

32

Item Cost LCD Projector $545 Laptop $570 Desktop Computer $599



Challenge Section Overview The challenge section of the assessment was developed to assess objectives beyond students’ grade level. Challenge problems were designed to assess student’s ability to use what students’ know about unit objectives to solve more in depth problems and communicate their mathematical thinking.

• Challenge problems are optional and can be given to any student. • Challenge problems are not recorded or scored in PMI.

• Teachers may choose the problem they want students to complete. It is not

intended for students to complete all of the challenge problems in the unit guide.

• Teachers may allow students to choose the problem they complete. Student choice is often a powerful tool to motivate students.

Teachers may have students complete the problem independently, in pairs, or groups. If teachers want students to work in pairs or groups but want to see how individual students approach the problem, consider giving all students an independent amount of time to begin the problem. You will want students to include their independent thinking as a part of the final group’s response to the problem.

• Teachers should use a rubric to score student responses (possible rubrics are

included in the following pages).

• Teachers may consider having students evaluate other students’ solutions using a rubric as well as a teacher score.

• Challenge problems can often be connected to other subjects and/or topics. Teachers may certainly extend any of the problems included.

Algebra Challenge Problem

Grade 5 Unit 1

Use the numbers 1-9, no more than one time each (in each solution), to

complete the inequalities below.

• How many different solutions can you find?

• What is the largest possible sum that you could have on either side of the

inequality? How do you know?

• What is the largest possible difference you could have in the second inequality?

How do you know?


Grade 5 Unit 1

Suppose you found an old roll of 15¢ stamps. Can you use a combination of 33¢ stamps and 15¢ stamps to mail a package for exactly $1.77?

• How many different ways can you use 15¢ and 33¢ stamps to have $1.77 in postage?

• How do you know you have all the possible solutions?

• Could you have just used 33¢ stamps to have $1.77 in postage? Could you have just used 15¢ stamps to have $1.77 in postage? How do you know?


Grade 5 Unit 1

You have the following stamps in your desk.

• List all the different amounts of postage you can make with the stamps you have.

• How do you know you have all the possible solutions?

• What is the largest amount of postage you can put on an envelope with your stamps?

Measurement Challenge Problem

Grade 5 Unit 1

The human body contains approximately 6 quarts (or 5.6 liters) of blood. As part of the circulatory system, the average heart pumps about 1900 gallons of blood through it each day!

• How many gallons is that in one week? • How many gallons is that in one month? • How many gallons is that in one year? • Choose one of your answers to convert to quarts or pints.

Number Relationships Problem

Grade 5 Unit 1

Mary and Jamie spend the weekend baking 60 sugar cookies, 80 peanut butter cookies, and 100 chocolate chip cookies. They want to pack all the cookies in decorative tins to give away as gifts. Each must contain an identical assortment of cookies.

• How many should they use so that each tin has the same assortment? Explain your thinking.

• How many different solutions can you find?

Algebra Problem

Grade 5 Unit 1

On a sheet of graph paper, graph the following ordered pairs, connecting the first point to the second point, then continue connecting as each point is plotted:

(2, 1) (1, 2) (3, 2) (3, 8) (4, 8) (3, 9) (4, 10) (5, 9) (4, 8) (5, 8) (5, 2) (7, 2) (6, 1) (2, 1)

• Double each number in the ordered pairs, and graph each new point on another

sheet of graph paper. • Compare and contrast the two drawings. • Create your own simple, small drawing, and write a list of ordered pairs that

someone could plot to copy your drawing. "Scale" the drawing to a larger size by multiplying each number in the order pairs by the same factor. What scale would your object be if you divided the ordered pair numbers by the same factor?

Algebra Problem Grade 5 Unit 1 Teacher Notes

On a sheet of graph paper, graph the following ordered pairs, connecting the first point to the second point, then continue connecting as each point is plotted:

(2, 1) This is the solution to part 1 of this challenge. (1, 2) (3, 2) (3, 8) (4, 8) (3, 9) (4, 10) (5, 9) (4, 8) (5, 8) (5, 2) (7, 2) (6, 1) (2, 1)

1.A.1.a | 1

1.A.1.a Interpret and write a rule for a one operation (+, -, x, ÷ with no remainders) function table AL: Use whole numbers (0-1000) or decimals with no more than 2 decimal places (0-1,000)

Elementary and Middle School Mathematics, Seventh Edition, by John Van de Walle, Karen Karp, and Jennifer Bay-Williams, pages 269-272.

Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and Lovin, pages 52, 299-300.

Objectives 1.A.1.a and 1.A.1.c are often taught during the same lesson. The only difference is in 1.A.1.a students are to write a rule for a function table

and in 1.A.1.c they are asked to complete a function table.

1.A.1.a | 2

Resource Alignment - 1.A.1.a

Resource Title Grade Level Page Card

The Super Source Snap Cubes 4-5

30, 70, 74, 82

Color Tiles 4-5 62, 66 Pattern Blocks 4-5 78, 82

Hot Math Topics Algebraic Reasoning 5 3 N.C.T.M. Navigations Algebra 3-5 9, 27, 58

Think Tank – Computation

Brain Builders 5 5, 16 Mental Teasers 5 3 Mind Benders 5 4 Fast Figurers 5 2 Quick Thinkers 5 10

Good Questions for Math Teaching

38 3, 5

All Aboard the Algebra Express by Kim Sutton

72-102,

104-126, 128-140

Math Focus Activities by Kim Sutton

Your SAS has a copy of this book.

22-25

1.A.1.a | 3

MSDE Information – 1.A.1.a

MSDE Sample Problem

Joanne created the function machine below.

Which of these statements correctly describes the relationship between the OUT number and the IN number?

A. divide by 1 B. divide by 1.4 C. divide by 2 D. divide by 2.4

1.A.1.a | 4

Instructional Notes – 1.A.1.a

Function tables contain quantities which are related in a predictable way.

It is crucial to focus on the relationship of numbers in each row of the table, because it is the row that shows the relationship between the two quantities. You can point to a row of the table and ask, “Who can say a sentence about this row of the table? What information do the numbers in this row give us about the (insert topic of the function table)? Looking at the relationship across a row of the table lays a foundation for making general statements about how the two quantities are related.

When students believe they have the correct rule they should verify their rule by

checking it with several numbers in the function table.

Data in a function table can be graphed to look at the graphical relationship and make connections between algebra and graphing.

See the August 2010 NCTM article, from Teaching Children Mathematics, about Bella’s

thinking about functional relationships. This article may give you ideas about questions that you can ask to help students see the relationship between the input and output instead of seeing a vertical pattern in the table.

1.A.1.a | 5

1.A.1.a | 6

1.A.1.a | 7

1.A.1.a | 8

Lesson Seeds

Towers Lesson – This lesson also includes a PowerPoint which can be found in the electronic version of the unit guide.

Building Patterns – Ask students to build a function table to look at their geometric pattern. By using the function table students may be able to see that the rule is n x n.

Building Patterns III – This activity connects perimeter and functions.

Building with Chicks

What’s My Rule – Cut apart the cards and have each group complete one of these

using pattern blocks. Have each group share out their findings while the others decided whether they agree or disagree with their function rule.

Function Table Concentration – Copy the function tables on one color card stock and

the rules on another color of card stock. Pairs of students lay the function tables face up and the rules face down. On their turn students turn over a 1 minutes timer. This student then picks up a function rule and then tries to find the match within one minute. If they find the match, they may keep it. If they don’t match they lay the cards back down and the next player takes their turn. At the end of class time the student with the most matches wins. These cards may also be used to play “Old Maid” or “Go Fish” (See the directions below).

Function Table Find your Partner

1.A.1.a | 9

Function Table - Find Your Partner

Classroom Setup: Whole Class

Materials: One set of Function Table Cards

Note: Print the function table cards on one color of card stock and the rule cards on a different color of card stock. This will make it easier for students to make matches.

Directions:

1. Hand out one card to each student. 2. Have all students stand up. 3. Play some music and instruct students to walk around and trade their cards until

the music stops. 4. When you stop the music tell students to “Find the Partner” – find the person who

has the rule and missing number for your function table. 5. When students have found their partners then they should rule and the missing

numbers to make sure the match. 6. Have several pairs put their matches on the document camera and have the class

check them. 7. Play music and have students switch cards until the music stops. 8. Repeat steps 4-6.

1.A.1.a | 10

Function Table Find Your Partner

In Out 2 4 3 6 4 8 5 6 7

In Out 3 15 4 20 5 25 6 7 8

In Out 1 9 2 18 3 27 4 5 6

In Out 20 11 30 21 40 31 50 60 70

In Out 27 9 24 8 21 7 18 15 12

In Out 136 126 142 132 167 157 121 168 207

In Out 6 36 8 48 3 18 9 5 7

In Out 21 3 35 5 56 8 63 28 7

1.A.1.a | 11


In Out 37 39 88 90 15 17 34 13 71

In Out 256 276 291 311 455 475 367 888 121

In Out 333 303 444 414 555 525 666 777 888

In Out 2 8 9 36 7 28 8 4 6

In Out 15 26 18 29 13 24 21 76 43

In Out 2 16 9 72 5 40 7 4 3

In Out 986 936 476 526 354 304 352 654 259

In Out 4 20 5 25 3 15 7 6 8

1.A.1.a | 12


Rule: Multiply by 2

10, 12, 14

Rule: Multiply by 5

30, 35, 40

Rule: Multiply by 9

36, 45, 54

Rule: Subtract 9

41, 51, 61

Rule: Divide by 3

6, 5, 4

Rule: Subtract 10

111, 158, 197

Rule: Multiply by 6

54, 30, 42

Rule: Divide by 7

9, 4, 1

1.A.1.a | 13


Rule: Add 2

36, 15, 73

Rule: Add 20

387, 908, 141

Rule: Subtract 30

636, 747, 858

Rule: Multiply by 4

32, 16, 24

Rule: Add 11

32, 87, 54

Rule: Multiply by 8

56, 32, 24

Rule: Subtract 50

302, 604, 209

Rule: Multiply by 5

35, 30, 40

1.A.1.a | 14

Towers Lesson

Date

Time Grade K

MSC Curricular Connection

1.A.1.a(5) Interpret and write a rule for a one operation (+, -, x, ÷ with no remainders) function table AL: Use whole numbers (0-1000) or decimals with no more than 2 decimal places (0-1,000) 1.A.1.c (5) Complete a one-operation function table AL: Use whole numbers with +, -, x, ÷ (with no remainders) or use decimals with no more than two decimal places with +, – (0-200)

Materials

snap cubes Towers PPT (included in the Grade 5 Unit Guide Electronic Files)

Focus Question

How can patterns help us solve problems?

Vocabulary function, function table, relationship

Objective TSW use function tables to discover and continue a pattern.

BEFORE

How will I scaffold the problem/task to help students be successful with the problem/task?

1. Use the included powerpoint to begin talking and getting kids curious about

“towers”.

Introduce the problem: Many buildings have a pattern in the number of windows on each level of the tower. We need to figure out how to quickly calculate the number of windows we need to order for a building if we know how the total number of floors. Introduce this background:

• You will each need 10-12 snap cubes. • Hold up 1 snap cube. We call this a single floor in our

tower. • The single floor has a skylight and 4 windows. We say each single floor

has 5 total windows (skylights count as windows). • Take another cube to make a tower two floors high. • How many windows are on this tower? • Answer: 9 (4 on each floor and 1 skylight on

top) The task: You and your team are going to help builders be able to quickly determine the number of windows when they decide how many floors are in a building. Use the table provided and your snap cubes to investigate how many total windows are in towers of different heights.

IDEAS:

Set expectations Begin with an easier task or problem related to the During Activities.

Activate Prior Knowledge Review prior days concepts to connect new knowledge

Ensure that students understand the task or problem

Introduce vocabulary

DURING THE PROBLEM OR TASK

1. Put students into groups of 2 (pairs). 2. Students should use the snap cubes and the activity sheet to guide their

exploration and thinking.

REMINDER: Plan differentiated instruction and questions to stimulate, extend, and enrich student thinking (see page 2).

1.A.1.a | 15

AFTER

How will we wrap up the problem?

Discuss student findings. Ask questions such as:

• What patterns do you notice between the number of floors and number of windows?

• How could you determine the number of windows in a building with 75 floors without using your cubes?

• How did you know your rule was correct? How could you verify your rule?

• How does finding the pattern help us find solutions to numbers that are beyond the table?

IDEAS:

Turn and talk Think aloud with students

Share student responses/thinking/ connections

Emphasize and revisit vocabulary

Focus on justifying and evaluating results and methods

Discussion with higher order thinking questions

Extension Activities Use a similar

problem/task

ASSESSMENT

How will I formally or informally assess each student?

Extensions and Variations

To extend this lesson use the “Double Towers” Extension activity.

Consider the Common Core Practices

This lesson gives students opportunities to: Make sense of problems and persevere in solving them? Make sense of problem. Plan for and carry

out a plan to solve a problem. Reason abstractly and quantitatively? Create contexts to make sense of numeric problems. Create

numeric/algebraic representations to solve real-life problems. Construct viable arguments and critique the reasoning of others? Justifying and proving solutions.

Listening to and analyzing the reasoning of others. Model mathematics? Representing math problems concretely, pictorially, and symbolically in order to

solve them Use appropriate tools strategically? Using tools strategically (and flexibly) to solve problems. Attend to precision? Calculating accurately and efficiently. Explaining procedure/reasoning using

appropriate math vocabulary. Look for and make use of structure? Looking for relationships. Generalizing. Look for and express regularity in repeated reasoning? Looking for patterns. Checking the

reasonableness of answers.

1.A.1.a | 16

Windows in Single Towers Investigation

Number of Floors

Total number of Windows

1 5

2 9

3

4

5

6

7

8

9

10



1.A.1.a | 17

Windows in Double Towers Investigation

Number of Floors

Total number of Windows

1 8

2 14

3

4

5

6

7

8

9

10



1.A.1.a | 18

1.A.1.a | 19

1.A.1.a | 20

1.A.1.a | 21

Building Chicks

1.A.1.a | 22

1.A.1.a | 23

1.A.1.a | 24

1.A.1.a | 25

Any Concentration Game can be used to play Old Maid or Go Fish. The directions are below.

Concentration

Lay all cards face down on the table. Students will take turns choosing two cards at a time. If they make a match they

pick up the two cards and place them to the side. The next player takes a turn and follows the same procedure. The game ends when all the matches have been made.

Go Fish

Put students into groups of 2, 3 or 4. Instruct students to deal out seven cards to each player. Place the remaining cards in the center face down. The dealer begins. The dealer asks another player if they have a card to match a

card in their hand. If the player does have the card he/she surrenders it to the requester. The requester makes the match and lays the two cards to the side. If the player does not have the card, he/she says “go fish” and the requester draws a card from the center of the table.

The next player follows the same procedure. The winner is the person with the most matches at the end of the game.

Old Maid Game

Put students into groups of 3 or 4. Instruct students to deal out the cards. It is okay if some players have 1 more card

than the others. The players put all of the cards into their hand. The dealer begins. The dealer draws one card from the person on the right. If they

have a pair of cards in their hand that match they announce the match and place the matched pair on the table.

1.A.1.a | 26

The next player draws a card from the person on his/her right. If they have a pair of cards in their hand that matches they announce the match and place the matched pair on the table.

If a player draws a card and does not have a match in their hand they do not lay any cards down and the next player continues.

The match does not have to be made from the card they pulled from the other player.

The loser is the person left with the “old maid” card. The winner is the person with the most matches.

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

1.A.1.a | 27

In Out 9 3

15 5 24 8

In Out 9 4

11 6 18 13

In Out 1 10 3 30 7 70

In Out 4 20 5 25 7 35

In Out 0 0 8 1

24 3

In Out 72 8 36 4 9 1

In Out 2 7 3 8 4 9

In Out 3 21 7 49 9 63

In Out 5 12

15 22 25 32

In Out 12 2 36 6 54 9

In Out 1 4 2 8 3 12

In Out 4 14 7 17 9 19

In Out 6 4 9 7

15 13

In Out 20 2 50 5 80 8

In Out 10 5 8 4 6 3

In Out 1 35 3 37

10 44

In Out 7 1

10 4 15 9

In Out 12 15 20 23 36 39

In Out 9 2

11 4 16 9

In Out 5 30 7 42 8 48

1.A.1.a | 28

n ÷ 3 n - 5 n x 10 n x 5

n ÷ 8 n ÷ 9 n + 5 n x 7

n + 7 n ÷ 6 n x 4 n + 10

n - 2 n ÷ 10 n ÷ 2 n + 34

n - 6 n + 3 n - 7 n x 6

1.A.1.a | 29

1.A.1.a | 30

1.A.1.a | 31

1.A.1.a | 32

1.A.1.a | 33

Technology Links

Math Playground Function Table Practice http://www.mathplayground.com/functionmachine.html On the opening screen be sure to press the BEGINNER button as it will give students practice with one-step functions. In this activity students can ask the computer for values or supply their own. Teachers can change the range of numbers that can be used in the function table.

http://www.mathplayground.com/functionmachine.html�

1.A.1.a | 34

Guess My Rule Game

The Function Machine Game

Materials (per partners): Guess My Rule card deck (copy decks onto card stock) Function Machine template in a plastic sheet protector dry-erase pen and eraser counters calculators (students may use calculators for algebra objectives), optional

Directions: • Partner A shuffles the card deck and turns over the first card without showing it to

Partner B. • Partner B uses the Function Machine template and records an “in” number. • Partner A uses this number and the rule from the card. Partner A announces the

“out” number. • Partner B writes the number in the “out” column on the Function Machine

template. • Partner B records a different “in” number on the Function Machine template. • Partner A again uses this number and the rule and announces the “out” number. • Player B may guess the rule at any time by writing the rule in the rule space on the

function machine and saying it aloud. • If Player B’s rule is correct, on the first time they guess, he/she receives 2 counters

to represent 2 points. • If Player B’s rule is incorrect, he/she writes down another “in” number and play

continues until Player B identifies the correct rule. When they state the correct rule they receive 1 counter.

• Players switch rolls, pull a roll card, and repeat the process. • When time is up, the player with the most counters wins.

Differentiation:

• Use different decks to best match ability levels (e.g. only addition and subtraction for a basic game).

1.A.1.a | 35

Guess My Rule Cards

Rule: add 20 Rule: subtract 5

Rule: add the number

Rule: subtract 3




Rule: add 7 Rule: subtract the

number

1.A.1.a | 36

Guess My Rule Cards

Rule: multiply by 2 Rule: add 2

Rule: multiply by 3 Rule: add 5

Rule: multiply by 5 Rule: subtract 6

Rule: multiply by 1 Rule: subtract 10

Rule: multiply by 0 Rule: multiply by 6

Rule: multiply by 4 Rule: multiply by 8

1.A.1.a | 37

1.A.1.a | 38

Exit Slip – 1.A.1.a

Name:

Ali and Brent are brother and sister. Ali’s age Brent’s age

8 10 9 11

11 13 14 16

1) What is the relationship between Ali’s age and Brent’s age?

add 2 subtract 2 multiply by 2 divide by 2

2) How old will Brent be when Ali is 19? ___________________


Name:

Ali and Brent are brother and sister. Ali’s age Brent’s age

8 10 9 11

11 13 14 16

1) What is the relationship between Ali’s age and Brent’s age?

add 2 subtract 2 multiply by 2 divide by 2

2) How old will Brent be when Ali is 19? ___________________

1.A.1.a | 39


Name: Mr. O’Reilly buys and sells used bikes. The table shows the prices he pays for the bikes and then what he sells them for.

BUY SELL 25 75 30 90 35 105 40 120

1) What is the rule Mr. O’Reilly uses to determine the selling price? ______________

2) If Mr. O’Reilly buys a bike for $80, how much will he sell it for? $______________


Name: Mr. O’Reilly buys and sells used bikes. The table shows the prices he pays for the bikes and then what he sells them for.

BUY SELL 25 75 30 90 35 105 40 120

1) What is the rule Mr. O’Reilly uses to determine the selling price? ______________

2) If Mr. O’Reilly buys a bike for $80, how much will he sell it for? $______________

1.A.1.a | 40


Name: Look at this function table.

In Out

18 6

21 7

12 4

What is the rule that describes the relationship between the “In” numbers and the “Out” numbers? ________________________________________________


Name: Look at this function table.

In Out

18 6

21 7

12 4

What is the rule that describes the relationship between the “In” numbers and the “Out” numbers? ________________________________________________

1.A.1.c | 1

1.A.1.c 1.A.1.c (5) Complete a one-operation function table AL: Use whole numbers with +, -, x, ÷ (with no remainders) or use decimals with no more than two decimal places with +, – (0-200)

Elementary and Middle School Mathematics, Seventh Edition, by John Van de Walle, Karen Karp, and Jennifer Bay-Williams, pages 269-272

Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and Lovin, pages 295-297, 316.

1.A.1.c | 2

Resource Alignment – 1.A.1.c


The Super Source

Snap Cubes 4-5 30, 70, 74,

82

Color Tiles 4-5 62, 66 Pattern Blocks 4-5 78, 82

20 Thinking Questions

Pattern Blocks 3-6 58 15

Base Ten Blocks 3-6 66 17 3-6 70 18

Hot Math Topics Algebraic

Reasoning 5 3

N.C.T.M. Navigations Algebra 3-5 27, 41, 58,

61


Speedy Starters 5 19 Mental Teasers 5 1, 3 Mind Benders 5 4, 20 Fast Figurers 5 1 Number Jugglers 5 4, 11


72-102,

104-126, 128-140

Math Focus Activities by Kim Sutton


22-25

1.A.1.c | 3

Instructional Notes – 1.A.1.c

This objective is most often taught in conjunction with 1.A.1.a. See the notes and activities in 1.A.1.a for activities which also fit 1.A.1.c.

Lesson Seeds

See the Lesson Seeds for 1.A.1.a – because these two objectives are similar, many of the activities in 1.A.1.a work well for 1.A.1.c.

Triangle Rule Machine

Post Patterns

1.A.1.c | 4

Triangle Rule Machine

Adapted from Navigating through Algebra 3-5 by NCTM.

Classroom Setup: small groups or pairs Materials pattern blocks triangles – 7 per group

Directions

1. Students will find the perimeter of triangles and record them in a function table. Students will then use the table to discover the rule for this function table.

2. Review finding perimeter using the square pattern blocks. What is the perimeter of 1 square pattern block? (4) What is the perimeter of 2 square pattern blocks (touching not separate)? (6).

3. Introduce the following question: What is the perimeter of a given number of triangles? What rule can you write that will help you determine the perimeter of a given number of triangles without using the pattern blocks, drawing a picture, or extending a function table?

4. Have students use the activity sheet to guide their exploration.

Instructional Notes Do not give students enough triangles to complete the entire table. If you give

students 7 triangles they will be forced to look for a pattern to complete the table. Be sure that students understand that the side of a triangle is 1 unit. Students will often notice that the pattern in the perimeter column increases by 1.

This is not a function. Students need to look at the relationship horizontally – between the number of triangles and the perimeter. If they do they should see that the rule is x + 2 or add 2.

Possible Questions

What is the relationship between the number of triangles and the perimeter? How can you use this rule to determine the perimeter of 30 triangles?

1.A.1.c | 5

1.A.1.c | 6

Post Patterns Number Number of posts of rails

1 0

2 3 4

How many rails will be required for 12 posts?

How many rails will be required for 50 posts?

1.A.1.c | 7

Exit Slip – 1.A.1.c

Name: Complete the function table.

In Out

9 27

11 33

14 42

16

20

Write the rule _______________________________________________


Name: Complete the function table.

In Out

9 27

11 33

14 42

16

20

Write the rule _______________________________________________

1.A.1.c | 8


Name:

A phone company charges $0.08 per minute for calls inside the state of Maryland. Complete the function table.

Phone Charges

Minutes Cost

5

8

10

60


Name:

A phone company charges $0.08 per minute for calls inside the state of Maryland. Complete the function table.

Phone Charges

Minutes Cost

5

8

10

60

1.A.1.c | 9


Name: Each fifth-grade student at Smithsburg Elementary School is expected to read 20 books a

year. Which numbers complete the function table that shows this rule?

Students’ Reading Number of Students Number of Books

2 5

10

A. 22, 25, 30 C. 20, 50, 100

B. 20, 40, 60 D. 40, 100, 200


Name: Each fifth-grade student at Smithsburg Elementary School is expected to read 20 books a

year. Which numbers complete the function table that shows this rule?

Students’ Reading Number of Students Number of Books

2 5

10

A. 22, 25, 30 C. 20, 50, 100

B. 20, 40, 60 D. 40, 100, 200

1.A.1.d | 1

1.A.1.d Apply a given two operation rule for a pattern AL: Use two operations (+, -, x) and whole numbers (0-100)


Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and Lovin, pages 295-297, 301-303.

1.A.1.d | 2

Resource Alignment – 1.A.1.d


20 Thinking Questions Rainbow Cubes 3-6 58 15


Reasoning 5

10, 15, 23, 29, 39, 42, 69, 86

Teaching Student Centered Mathematics-Van De Walle

3-5 295-297 301-303

N.C.T.M. Navigations Algebra 3-5 12, 15, 18,

61

Think Tank – Computation Speedy Starters 5 4 Brain Builders 5 13 Wise Workers 5 4

Think Tank – Problem Solving

The Think Tank cards below are 6th grade assessment limit level but can be simplified to use for grade 5. For example if the rule says y

=3(x+7) + 2 give the students this simplified rule: 3x + 23. Brain Booster 5 3


72-102,

104-126, 128-140

1.A.1.d | 3

Instructional Notes – 1.A.1.d

When teaching a two operation rule, the rule is applied to each term in the

pattern.

Example

Bobby created a pattern using the rule multiply by 2 , subtract 3. The first number in his pattern is 4. What are the next four numbers in Bobby’s pattern? a. 8, 5, 10, 7 b. 8, 5, 10, 6 c. 5, 7, 11, 19 correct answer d. 5, 7, 11, 18 C is the correct answer because each term is found by applying the 2 step rule: (4 × 2) – 3 = 5 (5 ×2) – 3 = 7 (7 × 2) – 3 = 11 (11 × 2) – 3 = 19

1.A.1.d | 4

I’m Thinking of a Number

A Problem Based Lesson Seed #1

Note: This problem forces students to add numbers to a sequence given a two-step rule and work backwards. The Problem: I’m thinking of a number. Multiply the number by 2. Then add 11. The answer is 39. What is the number? Including these first 2 numbers, what are the first 5 numbers in this pattern? _____, 39, _____, _____, _____

A Problem Based Lesson Seed #2

I’m thinking of a number. Three times the number plus 23 equals 53. What is the number? Including these first 2 numbers, what are the first 4 numbers in this pattern? _____, 53, _____, _____

1.A.1.d | 5

Exit Slip – 1.A.1.d

Name: Find the next two numbers in the following patterns. Use the rule given for each pattern. 1. Add 1, Multiply by 2: 6, 14, 30, ___, ___ 2. Multiply by 2, subtract 2: 4, 6, 10, ___, ___ 3. Add 7, Multiply by 1: 3, 10, 17, ___, ____


Name: Find the next two numbers in the following patterns. Use the rule given for each pattern. 1. Add 1, Multiply by 2: 6, 14, 30, ___, ___ 2. Multiply by 2, subtract 2: 4, 6, 10, ___, ___ 3. Add 7, Multiply by 1: 3, 10, 17, ___, ____

1.A.1.d | 6


Name:

Fill in your own number to the two-step rule below.

Add ______ (choose a number less than 10), Multiply by 2.

Starting with the number 5, use your two-step rule to find the first 5 numbers in your sequence.

5, _____, _____, _____, _____


Name:

Fill in your own number to the two-step rule below.

Add ______ (choose a number less than 10), Multiply by 2.

Starting with the number 5, use your two-step rule to find the first 5 numbers in your sequence.

5, _____, _____, _____, _____

1.B.1.a | 1

1.B.1.a Represent unknown quantities with one unknown and one operation (+, -, x, ÷ with no remainders) AL: Use whole numbers (0-100) or money ($0-100)

Elementary and Middle School Mathematics, Seventh Edition, by John Van de Walle, Karen Karp, and Jennifer Bay-Williams, pages 262-264. Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and Lovin, pages 306-308. Math at Hand by Great Source, page 235-241.

Instructional Notes – 6.C.1.a

Equations are mathematical sentences that include an equal sign. In an equation,

the following expressions on either side of the equals sign name the same quantity.

1.B.1.a | 2

MSDE Information – 1.B.1.a

MSDE Sample Problem

Alexander and Ruth both collect video games. Alexander has twice as many video games as Ruth. Let r represent the number of video games Ruth has.

Which expression represents the number of video games Alexander has?

2 – r

2 ÷ r

2 + r

2 x r

Resource Alignment – 1.B.1.a



Reasoning 5 8, 30

N.C.T.M. Navigations Algebra 3-6 44 Think Tank – Computation Mind Benders 5 16 MathStart Books Safari Park Level 3

1.B.1.a | 3

Literature Links – 1.B.1.a

Book Location Notes

Safari Park

by: Stuart Murphy

Location: SAS Resource Library

Grandpa's taking all the grandkids to the neatest amusement park ever: Safari Park. The Jungle King rides all cost 4 tickets. Rhino Rides are just two tickets. Monkey Games and Tiger Treats are a bargain at one ticket each. But a ride on the "spectacular, amazing, heart-pounding Terrible Tarantula" costs six tickets! Each of the kids has 20 tickets and has to figure out the best combination to have the most fun. What would you choose? An essential part of early algebraic thinking is understanding a "number sentence" with a missing element (8 + ? = 20), and the process for figuring out the unknown.

Lesson Seeds

Safari Park – This lesson is a problem based lesson seed. There are several

variations of the original problem that can be used with students of different ability levels.

Sample Word Problems - This is a sheet of problems that can be used in warm-ups, activities, lesson, etc… Students should first represent the problem with an equation (1.B.1.a) and then solve for the unknown quantity (1.B.2.B).

The Soda Problem

http://www.stuartjmurphy.com/books/level_3/detail.php?level_id=3&book_id=51�

1.B.1.a | 4

Safari Park Problem

This is a lesson seed for a problem based lesson.

Classroom Setup: Students in pairs or small groups Materials: Safari Park Book Chart Paper Markers Safari Park Ride Signs (included behind the problems) Manipulatives (an assortment of manipulatives for students to choose from) optional Safari Park Powerpoint (available with the unit guide electronic files)

The Problem (choose from the following problems based):

Variation 1

Abby decides she will at least ride 2 of the Jungle King Rides and 2 of the Rhino Rides. She knows that she will eat at least 2 items from Tiger Treats.

• Write an equation to show how she will spend her 20 tickets in the park today. Use the equation to figure out how many tickets remain to be spent.

• Come up with several different plans as to how Abby can spend her tickets at the park.

Be sure to explain how you know she will only spend 20 tickets on each possible plan.

Variation 2

Grandpa knows that he will ride the Terrible Tarantula along with other rides. He also knows he is going to want to try all the food at the park.

• Write an equation to show how he will spend his 20 tickets in the park today. Use the equation to figure out how many tickets remain to be spent.

• Come up with several different plans as to how Grandpa can spend his tickets at the park.

Be sure to explain how you know he will only spend 20 tickets on each possible plan.

1.B.1.a | 5

Variation 3

Chad knows that he will ride the Terrible Tarantula, at least 2 Monkey Games, and some food and other rides.


• Come up with several different plans as to how Chad can spend his tickets at the park.


Variation 4

Paul knows that he will ride all of the Rhino Rides, one of the Jungle Kings, as well as play some games and eat food.


• Come up with several different plans as to how Paul can spend his tickets at the park.


Variation 5

Alicia decides she will ride all of the Rhino Rides, play two of the games, and may eat and ride other rides as well.

• Write an equation to show how she will spend her 20 tickets in the park today. Use the equation to figure out how many tickets remain to be spent.

• Come up with several different plans as to how Alicia can spend her tickets at the park.

Be sure to explain how you know she will only spend 20 tickets on each possible plan.

Variation 6

Patrick has only decided (for sure) to ride one of the Jungle Kings rides. He may decide to do more at the park.


• Come up with several different plans as to how Grandpa can spend his tickets at the park.


1.B.1.a | 6

1.B.1.a | 7

1.B.1.a | 8

1.B.1.a | 9

1.B.1.a | 10

1.B.1.a | 11

Sample Problems

First write the equation using one or more variables, then solve the problem.

1. Rose had some marbles. Betty had 22 marbles. Together they had 50. How many marbles did Rose have?

2. Tommy made $12 mowing lawns which he added to his savings. He now has $38. How

much did Tommy have in his savings before? 3. There were 54 children at a party. Some more children came to the party and then

there were 99 children. How many more children came? 4. Dana bought a cd on sale for $8.50. She saved $4.75. How much was the cd at regular

price? 5. Alan bought a new helmet for $7.00 and also bought a pair of knee-pads. He had $20.00

to begin with and came home with $3.25. How much were the knee-pads? 6. Jennifer invited some friends to a party. Twice as many people showed up than what

she invited. Not including her, there was a total of 24 people at her party. How many friends did she invite?

7. For dinner, Matt bought some pizzas and cut each one into 8 slices. He ate three slices

while waiting for everyone else to come to the table and then there were 21 slices left. How many pizzas did he buy?

8. My secret number is 24 more than Mary’s. Her number is 31. What is my number? 9. Blake’s secret number is half of Michael’s. If Michael’s secret number is 128, what is

Blake’s? 10. Caitlin’s secret number is 9. Haley’s secret number is 7 more than 4 times Caitlin’s.

What is Haley’s number? 11. Rebecca has ten less than the sum of Tessa’s number and Emily’s number. If Emily’s

number is 42 and Tessa’s number is 28, what is Rebecca’s number? 12. If Ken’s secret number is twice John’s plus four more; and John’s secret number is 78,

what is Ken’s number?

1.B.1.a | 12

The Soda Problem

The Problem: There are cans and bottles of soda at the store. Two cans and one bottle of soda weigh the same as five cans of soda. If a can of soda weighs 12 ounces, then what does a bottle of soda weigh? Write an equation to help you solve this problem. Teachers may want to do a warm-up such as the following problem before giving

students this problem: There were 8 square tables in a restaurant that held a total of 48 people. How many people sit at each table if each table holds the same amount of people? Write an equation to help you solve this problem. (8 x s = 48)

It is helpful if students can first write an equation for what they know. For example: 2c + 1b = 5c.

Next students can substitute the information they know into their equation. For example: 2(12) + 1b = 5(12). So…24 + 1b = 60.

Finally students can figure out, 24 + what number = 60 (36)

1.B.1.a | 13

Exit Slip – 1.B.1.a

Name:

A store is having a $10 off sale on all sweatshirts. Which expression represents the cost of a sweatshirt on sale?

10 + s

10 - s

s - 10

10 ÷ s


Name:

A store is having a $10 off sale on all sweatshirts. Which expression represents the cost of a sweatshirt on sale?

10 + s

10 - s

s - 10

10 ÷ s

1.B.1.a | 14


Name: Ray has a part-time job that pays him $6.75 per hour. Which expression represents how much money Ray can earn?

6.75 x h

6.75 ÷ h

6.75 + h

h ÷ 6.75


Name: Ray has a part-time job that pays him $6.75 per hour. Which expression represents how much money Ray can earn?

6.75 x h

6.75 ÷ h

6.75 + h

h ÷ 6.75

1.B.1.b | 1

1.B.1.b 1.B.1.b(5) Determine the value of algebraic expressions with one unknown and one-operation AL: Use +, - with whole numbers (0-1000) or x, ÷ (with no remainders) whole numbers (0-100) and the number for the unknown is no more than 9


Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and Lovin, pages 306-313. Math at Hand by Great Source, page 239-241.

1.B.1.b | 2

Resource Alignment – 1.B.1.b

Resource Title Grade

Level Page Card


Reasoning 5

16, 26, 43

Literature Links – 1.B.1.b

Book Location Notes

Safari Park

by Stuart Murphy

SAS Resource Library

Grandpa's taking all the grandkids to the neatest amusement park ever: Safari Park. The Jungle King rides all cost 4 tickets. Rhino Rides are just two tickets. Monkey Games and Tiger Treats are a bargain at one ticket each. But a ride on the "spectacular, amazing, heart-pounding Terrible Tarantula" costs six tickets! Each of the kids has 20 tickets and has to figure out the best combination to have the most fun. What would you choose? An essential part of early algebraic thinking is understanding a "number sentence" with a missing element (8 + ? = 20), and the process for figuring out the unknown. Illustrated by Steve Björkman.

Ready, Set, Hop!

by Stuart Murphy


Who's the better hopper? Matty, the tall frog? Or Moe, who's just plain big? Only a hopping contest can settle the matter. It takes Moe only five hops to make it to the big rock. Matty needs two more hops. So how many hops did Matty take? (5 hops + 2 hops = ?). The happy hoppers keep going until—splash!—they're in the pond. Knowing how equations are built is central to children's learning how to interpret and write number sentences. Illustrated by Jon Buller.



1.B.1.b | 3

MSDE Information – 1.B.1.b

Clarification An expression is a relationship between quantities. Quantities may be numbers or variables. A variable is a letter or symbol which represents one or more numbers. An algebraic expression is a mathematical relationship that uses numbers, variables operation symbols. For example: Numerical Expressions:

3 + 6 21 ÷ 7 4 × (6+2) 8 - 5 Algebraic Expressions a + 5 b - 7 c × 2 d ÷ 4 5c To evaluate an algebraic expression:

• Replace the variable with a given number and • Simplify the expression by completing the computation

Classroom Example 1 Evaluate a + 3 for a = 7

Answer: Replace the variable a with 7 and complete the computation 7 + 3 = 10

1.B.1.b | 4


Classroom Example 2 Evaluate an expression that matches a problem situation.

Problem Solving Algebraic

Expression Evaluation

The after school club has 24 students. The teacher puts the students into teams. Let t equal the number of teams formed. How many students are on each team?

24 ÷ t

Evaluate the expression for t = 4 and t = 8. Answers: 24 ÷ 4 = 6 24 ÷ 8 = 3

A package of juice contains 6 juice boxes. Let p equal the number of packages of juice boxes. How many total juice boxes are there?

p × 6

Evaluate the expression for p = 3 Answer: 3 × 6 = 18

Jill has a bag of apples. Jill eats two apples. Let b equal the number of apples in the bag. How many apples are left?

b - 2

Evaluate the expression for b = 14 and b = 18 Answers: 14 - 2 = 12 18 - 2 = 16

1.B.1.b | 5

Lesson Seeds

Equation Old Maid

Land of the Unknown Game

1.B.1.b | 6

Land of the Unknown Game

Classroom Setup: Groups of 2-4 students Materials: Each group of 2-4 students needs: 1 Game board 4 pawns (piece to move on board) 1 Six-sided number cube 1 Alpha cube with sides: A, A, B, B, C, C Calculator (to check) Set of variable cards

Directions:

1. Shuffle the variable cards, and then place them on the table, face down. 2. Player 1 rolls the number cube and the alpha cube. 3. The letter showing on the alpha cube determines the variable the player will

insert into the equation (either choice a, b, or c). 4. Player 1 then answers the equation using the letter they chose. 5. Another player checks their answer using a calculator. 6. If the player solved the problem correctly, he or she moves forward on the

game board the number of spaces indicated by the roll of the die. If the problem is solved incorrectly, the player loses a turn.

7. The next player repeats steps 1-6. 8. Play continues until one player reaches the finish. 9. If the players use all the cards in the deck, they can reshuffle the deck and start

again. Example: Player 1 rolls b,6. He must substitute choice b (17) in the equation. If player 1 answers “22” (the correct answer to 5 + 17) the player moves ahead 6 spaces on the game board. If the player answers incorrectly, he loses a turn.

Variable card reads:

5 + x = _______ is

a. x is 3 b. x is 17 c. x is 7

1.B.1.b | 7

5 + x = ____ if

a. x is 3

b. x is 4

c. x is 9

x ÷ 6 = ____ if

a. x is 36

b. x is 54

c. x is 42

2x = ____ if

a. x is 5

b. x is 9

c. x is 7

4 + x = ____ if

a. x is 5

b. x is 3

c. x is 7

24 ÷ x = ____ if

a. x is 4

b. x is 12

c. x is 2

3x = ____ if

a. x is 5

b. x is 3

c. x is 1

6x = ____ if

a. x is 2

b. x is 5

c. x is 8

7x = ____ if

a. x is 9

b. x is 8

c. x is 6

9x = ____ if

a. x is 7

b. x is 10

c. x is 11

x + 9 = ____ if

a. x is 18

b. x is 14

c. x is 23

50 – x = ____ if

a. x is 9

b. x is 8

c. x is 7

8x = ____ if

a. x is 6

b. x is 5

c. x is 9

30 ÷ x = ____ if

a. x is 3

b. x is 10

c. x is 6

x + 12 = ____ if

a. x is 4

b. x is 5

c. x is 10

100 ÷ x = ____ if

a. x is 10

b. x is 5

c. x is 4

2x = ____ if

a. x is 10

b. x is 30

c. x is 20

10 – x = ____ if

a. x is 8

b. x is 6

c. x is 5

72÷x = ____ if

a. x is 9

b. x is 4

c. x is 8

60 ÷ x = ____ if

a. x is 10

b. x is 6

c. x is 2

40 ÷ x = ____ if

a. x is 10

b. x is 5

c. x is 8

24 ÷ x = ____ if

a. x is 6

b. x is 8

c. x is 3

(3 + 5) + x = ____ if

a. x is 0

b. x is 9

c. x is 2

18 ÷ x = ____ if

a. x is 3

b. x is 6

c. x is 9

x + 3 = ____ if

a. x is 15

b. x is 18

c. x is 20

12 ÷ x = ____ if

a. x is 4

b. x is 6

c. x is 2

15 + x = ____ if

a. x is 8

b. x is 7

c. x is 6

8 + x = ____ if

a. x is 7

b. x is 6

c. x is 10

x + 18 = ____ if

a. x is 8

b. x is 6

c. x is 5

32 ÷ x = ____ if

a. x is 4

b. x is 8

c. x is 2

12 + x = ____ if

a. x is 4

b. x is 8

c. x is 2

x – 2 = ____ if

a. x is 22

b. x is 12

c. x is 6

15 + x = ____ if

a. x is 10

b. x is 8

c. x is 4

1.B.1.b | 8

1.B.1.b | 9

Equation Old Maid

Classroom Setup: Put students into groups of 3 or 4.

Materials: Deck of equation cards copied and cut out of card stock

Directions:

1. Instruct students to deal out the cards. It is okay if some players have 1 more card than the others.

2. The players put all of the cards into their hand.

3. The dealer begins. The dealer draws one card from the person on the right. If they

have a pair of cards in their hand that match they announce the match and place the matched pair on the table.

4. The next player draws a card from the person on his/her right. If they have a pair

of cards in their hand that matches they announce the match and place the matched pair on the table.

5. If a player draws a card and does not have a match in their hand they do not lay

any cards down and the next player continues.

6. The match does not have to be made from the card they pulled from the other player.

7. The loser is the person left with the “old maid” card. The winner is the person with

the most matches.

1.B.1.b | 10

Equation Old Maid

a + 6 = 12

a = ?

a = 6

a – 120 = 100

a = ?

a = 220

5 x a = 45

a = ?

a = 9

72 ÷ a = 9

a = ?

a = 8

5 + a = 28

a = ?

1.B.1.b | 11

Equation Old Maid

a = 23

36 ÷ a = 6

a = ?

a = 6

6 x a = 60

a = ?

a = 10

42 – a = 30

a = ?

a = 12

a + 18 = 28

a = ?

a = 10

1.B.1.b | 12

Equation Old Maid – One of these cards needed for each game.

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

The Old Maid

1.B.1.b | 13

Exit Slip – 1.B.1.b

Name:

1. What is the value of the following expression n – 199, if n = 312? ______________

2. What is the value of the following expression 96 ÷ x, if x = 3? ______________


Name:

1. What is the value of the following expression n – 199, if n = 312? ______________

2. What is the value of the following expression 96 ÷ x, if x = 3? ______________

1.B.1.b | 14


Name: There are 365 days in a year. The expression below names the number of days remaining in the year if d days have passed.

365 – d

What is the value of the expression if d = 42? ______________________


Name: There are 365 days in a year. The expression below names the number of days remaining in the year if d days have passed.

365 – d

What is the value of the expression if d = 42? ______________________

1.B.2.a | 1

1.B.2.a Represent relationships using relational symbols (<, >, =) and one operational symbols (+, -, x, ÷ with no remainders) on either side AL: Use whole numbers (0-400)


Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and Lovin, pages 310-312.

1.B.2.a | 2



The Super Source Cuisenaire Rods 3-4 58, 86 Base Ten Blocks 3-4 86

20 Thinking Questions Rainbow Cubes 3-6 10 3


Reasoning 5

6, 11, 22, 60

Nimble with Numbers 5-6 15-19 N.C.T.M. Navigations Algebra 3-6 44, 48


Speedy Starters 5 9, 16 Brain Builders 5 14 Mind Teasers 5 2 Mind Benders 5 16 Head Sharpeners 5 4, 8 Pace Setters 5 3 Fast Figurers 5 19 Wise Workers 5 10

Think Tank – Problem Solving

Head Polishers 5 15 Cracker Jacks 5 9 Cool Heads 5 11 Super Sleuths 5 7

1.B.2.a | 3


Book Location Notes

More or Less

By: Stuart Murphy


Mr. Shaw, the principal of Bayside School is retiring, so all the students and teachers, and family and friends are having a picnic in his honor. There are lots of game booths, and the most popular is "Let Eddie Guess Your Age!" Eddie, blind-folded and sitting on a chair over a large tub of water, can figure out how old someone is by asking a few key questions: "Is you age less than 10?" "Yes." "More than 7?" "Yes." "It is an even number?" "No." "Then you're 9 years old," says Eddie triumphantly. If Eddie has to ask more then 6 questions, he gets dunked. Find out whether Eddie can swim! Comparing numbers is an important part of the understanding the mathematical concepts of "greater than" and "less than," and for developing skills for making logical guesses. Illustrated by David T. Wenzel.


1.B.2.a | 4

Instructional Notes – 1.B.2.a

MSDE Clarification

There are three relationships that can exist between two quantities: the first is greater than the second, the first is less than the second, or the first and the second are the same or equal. The symbols that show these relationships between quantities are, as examples:

1. 3 > 1 Three is greater than 1 2. 1 < 3 One is less than 3 3. 3 = 3 Three is equal to three.

3 is greater than 1 (3>1) because 3 of something: 3 cats, 3 bananas, 3 toys, etc. is a greater quantity than 1 which represents only a single item, such as a cat, a banana, a toy. 1 is less than 3 (1<3) because 1 represents an individual object while 3 represents multiple objects. 3>1 and 1<3 are two ways of describing the relationship between two numbers and are equivalent statements. When comparing any pair of numbers, the questions of:

• Which has more? • Which has less? • Are they equal?

are used to determine their relationship. If necessary, students can use manipulatives to explore the one–to–one correspondence of the two numbers. This will physically show which has more or less, or if they are equal. Students can also use the number line to determine one of the three relationships between two numbers. As students represent numbers on a number line, they should discover and be able to model that, as you move to the right on a number line, the value increases. They should also discover and be able to model that, if you move to the left, the value decreases. The statement of an equation or an inequality is called a number sentence. An inequality compares expressions using a > (greater than) or < (less than) symbol. The expressions on opposite sides of the relational symbol do not have the same value.

1.B.2.a | 5

4 < 5 is read "Four is less than five." 10 > 2 is read "Ten is greater than two." 72 + 30 > 45 + 45 is read "Seventy–two plus thirty is greater than forty–five plus forty–five." An equation shows expressions on both sides of an = sign that have the same numerical value. Both inequalities and equations are made up of only numbers and symbols. They do not contain words. They have only one >, <, or = sign. At this level students are expected to write equations and inequalities using whole numbers through 200. Expressions indicate an operation between numbers and represent a single numeric quantity. For example, 5+3 represents the quantity 8. There are many expressions that also represent the quantity 8. Students should be encouraged to explore the many expressions that can represent a numeric quantity. At this level students should increasingly throughout the year be able to write expressions with all four operational symbols that represent whole numbers through 200. Students often confuse expressions with equations and use the symbol = along with the expression. Expression: 3 + 8 Equation: 3 + 8 = 11

Inequality: 3 + 8 > 9 Inequalities: 988 > 878 3 × 4 < 20 - 5 12 < 15 Equations: 14 + 1 = 15 15 = 15 25 × 4 = 200 - 100 (Both sides of the equation are equivalent to 100.) 100 = 100 195 + 5 = 50 × 4 (Both sides of the equation are equivalent to 200.) 200 = 200

1.B.2.a | 6

MSDE Information – 1.B.2.a

Brief Constructed Response (BCR) Item

On Monday, 32 people went to the park before noon. In the afternoon, 24 more people came. On Tuesday, 26 people came to the park before noon. In the afternoon, 29 more people came.

Step A

Write a number sentence showing the relationship between the number of people at the park on Monday and the number of people at the park on Tuesday.

Step B

Explain why your answer is correct. Use what you know about number relationships in your explanation. Use words and/or numbers in your explanation.

Correct Answer: Step A 32 + 24 > 26 + 29 or 56 > 55

View Scoring Information

Lesson Seeds

Cube Calculations

Open-Ended Problems

http://mdk12.org/instruction/sampitems/mathematics/grade5/msa_math_5_023.html�

1.B.2.a | 7

Cube Calculations

Classroom Setup: whole class Materials: (each student needs) 20 cubes Dry erase boards

Directions:

1. Tell students that you have 20 cubes that are arranged in four different piles. Tell them that you are going to give them clues to see if they can figure out your piles.

2. Reveal the first clue: The first pie has 4 more cubes than the second pile. Ask students to write down something on their dry erase board that they know before moving their cubes. (They may write the first pile is > than the second pile, 1st pile has 4 more than the 2nd pile, etc…)

3. Reveal the rest of the clues. Ask students to write down something they know about each clue on their boards as they work.

4. When students are finished has them to compare their answer to neighbor.

5. As a whole class ask students to justify their thinking.

1.B.2.a | 8

Cube calculations

Use 20 cubes to make 4 piles so that:

• The first pile has 4 more cubes than the second pile.

• The second pile has one cube less

that the third pile.

• The fourth pile has twice as many cubes as the second pile.

You should not have any cubes left over.

1.B.2.a | 9

Open- Ended Problems

If the temperature during the day was less than 15° and it dropped 5° during the

night, what might the temperature be? How can we use an inequality to express this situation?

Possible responses: If it were 14° during the day, it would be 9° at night. If it were 0° during the day, it would be -5° at night. If it were -5° during the day, it would be -10° at night.

1.B.2.a | 10


Name:

Insert the correct symbol (<, >, =) to compare the expressions.

1. 3 + 21 ____ 23 – 5

2. 122 + 42 ____ 387 – 213

3. 232 + 48 ____ 123 + 232

4. 23 + 384 ____ 11 + 400


Name:

Insert the correct symbol (<, >, =) to compare the expressions.

1. 3 + 21 ____ 23 – 5

2. 122 + 42 ____ 387 – 213

3. 232 + 48 ____ 123 + 232

4. 23 + 384 ____ 11 + 400

1.B.2.a | 11


Name: Insert the correct symbol (<, >, =) to compare the expressions.

1. 89 – 37 ____ 80 – 30 -2

2. $20 - $12.49 ____ $20 - $12 + 49¢

3. 10 x 325 ____ 5 x 650


Name: Insert the correct symbol (<, >, =) to compare the expressions.

1. 89 – 37 ____ 80 – 30 -2

2. $20 - $12.49 ____ $20 - $12 + 49¢

3. 10 x 325 ____ 5 x 650

1.B.2.a | 12


Name:


Name:

1.B.2.b | 1

1.B.2.b Find the unknown in an equation use one operation (+, -, x,

÷ with no remainders) AL: Use whole numbers (0-2000)



1.B.2.b | 2



Hot Math Topics

Algebraic Reasoning 5 7, 8 Estimation and

Computation with Large Numbers

5 10, 57


Brain Builders 5 10 Mind Benders 5 16 Head Sharpeners 5 4 Pace Setters 5 3 Fast Figurers 5 19

MathStart Books Ready, Set Hop! Safari Park

Level 3

Nimble with Numbers 5-6 137-141, 145-146

Weight Ways by: Marcy Cook

YOUR SAS HAS A COPY OF THIS BOOK!

ENTIRE BOOK

1.B.2.b | 3

Instructional Notes – 1.B.2.b

The number line balance is a good manipulative to

have students see the concrete representation of equations. Your SAS has sets of these balances.


Look at the equation below. 125 x N = 375

What value of N makes this equation correct?

A. 2 B. 3 C. 4 D. 5

1.B.2.b | 4

Lesson Seeds

Weight Ways by Marcy Cook – Your SAS has a copy of this book. It is full of

problems that can be used for this objective.

Finding Unknowns – Adapted from Nimble with Numbers 6-7.

Equation Puzzlers - Students determine the values of the symbols so that each equation is true. For example, if students find that a ♥= 3 in the first equation, then it must work in each equation.

1.B.2.b | 5

Finding Unknowns

Classroom Setup: Students arranged in pairs Materials: Finding Unknowns game board 2 transparent chips different kinds of markers for each player

Directions:

1. The first player places on e transparent chip in each of the two rows below the gameboard, indicating two sides of an equation. The same player finds the value of x and places a marker on the corresponding square in the grid.

2. The other player moves only one of the transparent chips to a new amount. This player then fins the value of x and places a marker on that corresponding square in the grid.

3. Players alternate turns, moving one transparent chip each time, solving for x, and covering the corresponding square in the grid.

4. The winner is the first player to have four markers in a row horizontally, vertically, or diagonally.

Variations: If a student has a solution which is already covered by an opponent’s piece, then they may remove their opponent’s piece and replace it with their own. Possible questions for reflection after the game: What are some good beginning plays? Explain. What strategies helped you get your markers in a row? How did you solve the equation? What did you think in your head?

1.B.2.b | 6

1.B.2.b | 7

Equation Puzzlers

If:

+ ♦ = 13 2() + ♥= 20 + ♦ + ♥ = 17

3(♥) = 12 2(♦) + 3() = 19

Then:

= _____ ♦ = _____ ♥ = _____ = _____

If:

+ + = 18 + = 10

Then:

♦ = _____ = _____

If:

+ + = 12 + + = 9 + = 6

Then:

♦ = _____ = _____ = _____

If:

+ ♥= 13 ♦ + + ♦ = 22 + ♥ + ♦ = 20

Then:

♦ = _____ ♥= _____ = _____

1.B.2.b | 8


Name:

A board game costs $12. The board game and a game cartridge together cost $28(n).

How much did the game cartridge cost?

Use the equation to help you find the cost of the cartridge.

$12 + n = $28

n = ______


Name:

A board game costs $12. The board game and a game cartridge together cost $28(n).

How much did the game cartridge cost?

Use the equation to help you find the cost of the cartridge.

$12 + n = $28

n = ______

1.B.2.b | 9

Technology Links

Illuminations Shape Balance - Build up to algebraic thinking by exploring this balance tool using shapes of unknown weight. Challenge yourself to find the weight of each shape in one of six built-in sets or a random set. Detailed instructions and a lesson plan are included with the site sponsored by NCTM. http://illuminations.nctm.org/ActivityDetail.aspx?ID=33 Illuminations Number Balance - Use this tool to strengthen understanding and computation of numerical expressions and equality. In understanding equality, one of the first things students must realize is that equality is a relationship, not an operation. Many students view "=" as "find the answer." For these students, it is difficult to understand equations such as 11 = 4 + 7 or 3 × 5 = 17 – 2. http://illuminations.nctm.org/ActivityDetail.aspx?id=26

http://illuminations.nctm.org/ActivityDetail.aspx?ID=33�

http://illuminations.nctm.org/ActivityDetail.aspx?ID=33�

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1.B.2.b | 10


Name: Write a number that completes each number sentence.

A. 425 - _____ = 175 B. 25 x 6 = _____

Which is greater, A or B? _____________

How do you know?


Name: Write a number that completes each number sentence.

A. 425 - _____ = 175 B. 25 x 6 = _____

Which is greater, A or B? _____________

How do you know?

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Name: The letter w stands for a whole number. What value for w makes this statement true?

17 < 2w + 5 < 48

W = _________ Explain your thinking:


Name: The letter w stands for a whole number. What value for w makes this statement true?

17 < 2w + 5 < 48

W = _________ Explain your thinking:

1.C.1.b Create a graph in a coordinate plane AL: Use the first quadrant and ordered pairs of whole numbers (0-50)

Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and

Lovin, pages 239-242. Math at Hand by Great Source, page 265-266.

Resource Alignment – 1.C.1.b

Resource Title Grade Level Page Card The Super Source Color Tiles 4-5 62 Think Tank – Computation 5

Think Tank – Problem Solving Super Sleuths 5 8 Mega Minds 5 3, 7

MathStart Books Treasure Map Level 3 Dynamic Dice by Kim Sutton

112-115

Instructional Notes – 1.C.1.b

Students learn to graph on a coordinate plane in grades 4 and 5 so that they can

graph functions, transformations, etc… in future grade levels. You can connect this objective to 1.A.1.a, 1.A.1.b, and 1.A.1.c by having students graph the points in a function table. Students should see a pattern in graph of a function table.

For example, the following function table is from the “Building Chicks” activity in 1.A.1.a. The graph is a representation of this function table. Teachers should ask students what they notice about the graph and how it might help them to find the total number of blocks for stage 6. Typically students do not need a lot of instruction with this particular objective as the

fourth grade objective is basically the same. The only difference between the grade 4 and 5 limit is the limit in grade 4 are grids 0-20 and grade 5 are grids 0-50. Use pre-assessment data to determine the amount of instruction students need with the objective.

Building Chicks Function Table Stage

(x) Total Blocks

(y) 1 6 2 7 3 8 4 9 5 10


Book Location Notes A Fly On the Ceiling

by Julie Glass

Marilyn Burns Library

All grade 4 and 5

teachers have this book in the Marilyn Burns 4-

6 library.

Recognized as the father of analytic geometry, René Descartes was a French mathematician and philosopher. Kids will love this funny and very accessible tale - based on one of math's greatest myths - about the man who popularized the Cartesion system of coordinates.

Lesson Seeds Coordinate Practice I – This activity can be cut apart and completed as mini practices.

You may cut out one of the Roman Numeral picture directions for each student (so that there are several of each picture in the room). Once students have plotted their picture, have them find others in the room with the same directions and compare their pictures. Students should check each point to make sure each person in their group has the correct solution. This activity can also be cut apart and 1 or 2 might be sent home for homework. It is not suggested that students complete the entire sheet of pictures as this objective is not typically one that students struggle with.

Coordinate Practice II – This activity connects algebra and geometry. In this activity students plot points. All shapes can be drawn on the same coordinate grid.

Coordinate Grid 4 in a Row – Students may be familiar with this game from grade 4.

This also makes a good take home game.

Coordinate Grid Hangman – Students may be familiar with this game from grade 4.

Constellation Coordinates – This is an AIMS activity that connects astronomy and constellations with coordinate planes. The challenge in this activity is that several points have the decimal 0.5. Students can manage this with a little instruction about finding ½ of a square.

Tic Tac Toe Coordinate Grid – This is a game students can play in pairs in class or at

home for homework.

Tic Tac Toe Coordinate Grid

Game Object: To be the first player to get 4 x’s or o’s in a row on the coordinate grid. Directions: On your turn, choose an ordered pair and write it in the chart in your column. Please an X/O on the coordinate grid to match the ordered pair you wrote in the chart. If a player puts their mark in an incorrect location, the mark is erased and the player loses their turn. Players continue writing down a ordered pair, placing the X/O until one player has 4 in a row. This player is the winner.

X Ordered Pairs

O Ordered Pairs

Match My Masterpiece

Classroom Setup: pairs Materials: Graph paper sectioned into (3) 6x6 grids (can also use blackline master included with

this plan) Colored pencil or marker

Directions:

1. Give each student (3) 6x6 grids and have them use plot points to create a three letter word on their paper.

2. Once the three letters are plotted, list the ordered pairs table used for each individual

letter.

3. Display the original grids in the classroom. Have students switch their sheets of ordered pairs.

4. Have students plot out the points which correspond with the ordered pairs they are

given and connect them to form words.

5. Them have students match up their work with the original.

Coordinate Grid 4 in a Row

Classroom Setup: pairs Materials: 4 in a Row Game Board Chips (one color for each player to mark points on the grid) Spinners

Directions:

1. The first player spins both spinners to form an ordered pair. They then use their marker to put their color dot on that coordinate on the board. If the player spins a “wild” they may choose any number to use.

2. Players continue taking turns spinning and marking ordered pairs until a player gets 4 in a row anywhere on the board.

3. If a player spins an ordered pair that is already on the board, they lose their turn. Variations: If a player spins an ordered pair that their opponent already has covered then they may either remove their opponents chip from that ordered pair or they may spin.

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Coordinate Plane Hangman

VSC Objective: 1.C.1.b Identify positions in a coordinate plane. A.L. Use the first quadrant and ordered pairs of whole numbers (0-50).

Audience: Whole class or small groups Materials: Each student needs a copy of the Coordinate Plane Hangman Handout Directions: This game is played just like regular “Hangman” except instead of calling out

letters, students call out the coordinates for that letter.

1) The teacher puts blanks on the board to indicate a word/phrase she is thinking of. There should be one blank for each letter.

2) Call on students to give an ordered pair for a letter. If the letter is in the phrase the

teacher places the letters accordingly. If the letter is not there, the students receive part of the “hangman”.

3) Students continue guessing ordered pairs until they either guess the correct phrase

or they complete the “hangman”.

4) Once this is introduced to the whole group students can play in pairs or in groups.

5) Additionally teachers can have students create their own Coordinate Plane Hangman using the attached blank. Students should put a dot on for each letter of the alphabet.

Variations: Size of the group can be varied: whole group, small group, or pairs. Use vocabulary words as the “guessing word”. Students with difficulty could use a smaller grid (0-10) instead of (0-20).

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Function Table - Find Your Partner

Classroom Setup: Whole Class Materials: One set of Coordinate Plane Cards Note: Print the Coordinate Grid cards on one color of card stock and the Ordered Pair cards on a different color of card stock. This will make it easier for students to make matches. Directions:

1. Hand out one card to each student. 2. Have all students stand up. 3. Play some music and instruct students to walk around and trade their cards until

the music stops. 4. When you stop the music tell students to “Find the Partner” – find the person who

has the coordinate that matches the ordered pair. 5. When students have found their partners then they should rule and the missing

numbers to make sure the match. 6. Have several pairs put their matches on the document camera and have the class

check them. 7. Play music and have students switch cards until the music stops. 8. Repeat steps 4-6.

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Coordinate Plane Find Your Partner

(3, 2) (7, 4)

(3, 7) (9, 5)

(1, 9) (0, 0)

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(9, 0) (5, 5)

(10, 10) (2, 1)

(4, 1) (7, 2)

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(8, 4) (7, 8)

(8, 9) (1, 9)

(8, 2) (2, 5)

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Exit Slip – 1.C.1.b

Name:

A map of an amusement park is pictured below.

1. Identify the coordinates of the Ice Cream Stall. _____________

2. Which ride is located at (5, 10)? _________________________

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Name:

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3.C.2.a Determine start, elapsed, and end time AL: Use the nearest minute



Math at Hand by Great Source, page 324.

3.C.2.a | 2

Resource Alignment – 3.C.2.a


Hot Math Topics Geometry &

Measurement 5 28

Estimation & Computation

5 24

Special Note

It is recommended that converting units of time be taught at the same time as elapsed time. Teachers can ask students to turn the elapsed time they found into another unit of time. For example, if the students found the amount of time they spent in school as 6 ½ hours, ask them how many minutes or seconds this is equivalent to.

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ELAPSED TIME information from Elementary and Middle School Mathematics by John Van de Walle, Karen S. Karp, and Jennifer M. Bay-Williams, pages, 384-385, 2010.

Determining elapsed time is a skill required by most state curricula starting in about grade 3. It is also a skill that can be challenging for students, especially when the period of time includes noon or midnight. Students must know how many minutes are in an hour. If given the digital time or the time after the hour, students must be able to tell how many minutes to the next hour. This should certainly be a mental process of counting on for multiples of 5 minutes. Avoid having students use pencil and paper to subtract 25 from 60. Figuring the time from, say, 8:15 a.m. to 11:45 a.m. is a multistep task regardless of how it is done. Keeping track of the intermediate steps is difficult, as is deciding what to do first. In this case you could count hours from 8:15 to 11:15 and add on 30 minutes. But then what do you do if the endpoints are 8:45 and 11:15? To propose a singular method or algorithm is not helpful. Next is the issue of a.m. and p.m. The problem is due less to the fact that students don’t understand what happens on the clock at noon and midnight as it is that they now have trouble counting the intervals. In the discussion so far, we have only addressed one form of the problem. There is also the task of finding end time given the start time and elapsed time, or finding the start time given the end time and the elapsed time. In keeping with the spirit of problem solving and the use of models, consider the following. As a general model for all of these elapsed time problems, suggest that students sketch an empty time line. Examples are shown below. It is important not to be overly presciprtive in telling students how to use the time line since there are various alternatives. For example, in the figure below, a students might count by full hours from 10:45 (11:45, 12:45, 1:45, 2:45, 3:45) and then subtract 15 minutes.

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MSDE Information – 3.C.2.a

MSDE Lesson Seeds

• Counting to the Next Hour: If the start time is not at a whole number hour, counting to the next hour and then counting on can help students keep track of the time. At the last whole number hour, students can then count on to get to the end time.

How much time has elapsed between 12:20 and 4:15?

Then combine minutes and hours to find the elapsed time: 3 hours and 55 minutes

• Counting by Hours: A variation on that strategy is to count by hours and then count on at the last time to the end time.

How much time has elapsed between 12:20 and 4:15?

Then combine minutes and hours to find the elapsed time: 3 hours and 55 minutes

Try another example from 3:40 to 6:15

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Or

• How Many In a Minute? The teacher will time and count how many jumping jacks students can do in one minute. Based on the data from the jumping jack activity, students will calculate how many seconds it took to do one jumping jack and how many jumping jacks they can do in one hour. The purpose of this activity is for students to begin to understand just how long a minute is.

Note: Adjustments to the activity could be tapping finger, drawing circles or other short activities.

• How Long is 30 Seconds? A Minute? To help students understand the length of 30 seconds as opposed to a minute, play the following game. Tell students they are going to estimate how long 30 seconds is. Students need to close their eyes. Tell them that when you say "Go", they will count and when they think 30 seconds is up, they should raise their hands. Say "Go" and time 30 seconds. After 30 seconds is up, say "Stop" and students can open their eyes. Discuss what happened. Some students raised their hands very quickly, while others may not have raised their hands at all, thinking there was still time to go.

Repeat the activity. After several trials, students will become better at estimating the 30 seconds' length of time.

After playing a few times, tell students you are now going to time for one minute. Discuss that 1 minute is twice the length of 30 seconds. Students should consider this when deciding when to raise their hands.

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Note: This is a game that can be played while students are standing in line or waiting to use the water fountain. Time increments could be 30 seconds, 1 minute, 2 minutes or any reasonable time interval.

• Following a Schedule Use a schedule such as a movie, bus, train, or plane schedule or make up one. Have students work in partners to make up questions involving start, end, or elapsed time based on the given schedule. Each pair of students can then trade with another pair and answer each others questions.

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MSDE Thinking Skills

Traveling by Plane

Question

Level 1: Knowledge/Comprehension

Bill's flight left Washington DC at 7:45 a.m. and landed in Orlando, Florida at 10:05 a.m. How long was his flight?

A direct flight from Miami, Florida to New York, New York takes 2 hours and 45 minutes. If Sue lands in New York at 2:20, what time did she leave Miami?

Level 2: Application/Analysis

Andrea needs to be at a meeting in Miami, Florida at 5:00 PM. A flight, with no layovers, from Washington DC to Miami, Florida takes 2 and one half hours. Andrea checks the schedule and finds the following flights to Miami. Which one should Andrea take? Explain Why.

Level 3: Synthesis/Evaluation

Peter is creating a schedule for the fifth grade field day. The opening activity will take place from 8:30 A.M. until 9:15 A.M. Each of the field day events takes one hour. 15 minutes time should be allowed between each event, including the opening activity. Lunch will be served from 11:30 A.M. until 12:15. Awards will be presented at 3:00 P.M. The following are field day events from which Peter may choose.

• mile hurdles • mile sprint • Potato sack race • Egg balancing run • Metric measurement course • High jump • Long jump

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• Limbo contest

Create a schedule for Peter by selecting several events in the field day. Include a start time and stop time for: The opening activity, each event before lunch, lunch, each event after lunch, and the awards ceremony. Don't forget to schedule 15 minutes between each event.

Traveling by Train

Question

Use the information from the sign to answer the following questions.


What time will it be when the second train stops?


You want to catch a train as close to 1:00 p.m. as possible. Does a train stop at 1:00 p.m.? Which train should you catch if you want to arrive before 1:00 p.m., but as close to 1:00 p.m. as possible?

You have a dentist appointment at 3:00. It takes 15 minutes from the Green Line Express Station to get to your dentist. What is the latest train you could take and not be late for your dentist appointment?


You and your family are traveling from Baltimore to Australia. The flight is 27 hours long. You leave at 9:00 A.M. on Monday. You have two layovers—one in San Francisco of 4 hours and one in Hawaii of 3 hours. On what day and at what hour do you arrive, Baltimore time?

What Time Will It Be?

Question


Look at the time shown on the clock. What time will it be in 2 hours and 25 minutes?

Irene goes to sleep at 9:10 p.m. Her alarm is set to go off at 6:30 a.m. How much time does

3.C.2.a | 9

Irene have to sleep?


Mike's alarm clock goes off at 5:40 a.m., but he hits the snooze button and goes back to sleep. The snooze button goes off every 10 minutes. Mike finally got up at 6:10 a.m. How many times did Mike hit the snooze button? Explain your answer.


Dan's alarm clock goes off at 5:40 a.m., but he hits the snooze button and goes back to sleep. If the snooze button goes off every 9 minutes, how many times can Dan hit it and not get up later than 6:30 a.m.? Explain your answer.

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Technology Links

Clock Clipart – If you need clipart of any time be sure to go to http://etc.usf.edu/clipart/sitemap/clocks.php . Each clock is available in three sizes (small, medium, and large). Each time is available.

http://etc.usf.edu/clipart/sitemap/clocks.php�

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Lesson Seeds

Elapsed Time Graphic Organizer – This graphic organizer can be reproduced, placed inside clear plastic sheet protectors and written on with dry erase markers. This organizer helps students first identify they type of time problem they are solving, identify important information from the problem, and then use the empty/open time line to solve the problem.

Tracking Time – NCTM Article from Teaching Children Mathematics, August 2008, which explains how students can use open/empty timelines to solve elapsed time problems.

Elapsed Time Sort

Elapsed Time Strings

Hot Topics Time Problem Modified – These problems are modified from Hot Math Topics. Each problem can be used to differentiate for different student abilities.

Elapsed Time Open Ended Problems

Elapsed Time Problems – These problems are sorted by time interval to allow the teachers to quickly select problems that are appropriate for their student’s ability level.

Additional Elapsed Time Graphic Organizers - This is another format of an empty time line that might be helpful to some students.

3.C.2.a | 12

Time Problem – Work it Out!

What is the problem asking for? Start time – the time something starts

Elapsed time – the time between

End time – the time something ends

What are the facts?

Use the empty time line below to solve the problem.

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Elapsed Time Sort

Classroom Setup: Whole class arranged in small groups Materials: Category Cards (Start, End, Between Time) copied on different colors of card stock.

Each group needs 1 set of category cards (3 cards total). Copy the sample elapsed time problems on card stock, cut apart, and shuffle (one

set for each group) Directions:

1. Give each group the category cards and the elapsed time problems. 2. Ask students to read each problem and sort them into the given categories. These

problems are only meant for sorting, at this point, not solving. 3. When students have finished, ask students to talk about what the problems in each

category have in common. 4. Introduce the Elapsed Time Graphic Organizer and other strategies to help

students begin to solve problems.

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Elapsed (Between)

Time Problems

Problems which ask you to find the amount of time between two times.

Elapsed (Between)

Time Problems


Elapsed (Between)

Time Problems


Elapsed (Between)

Time Problems


Elapsed (Between)

Time Problems


Elapsed (Between)

Time Problems


Elapsed (Between)

Time Problems


Elapsed (Between)

Time Problems


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End

Time Problems

Problems which ask you to find the time something ends.

End

Time Problems


End

Time Problems


End

Time Problems


End

Time Problems


End

Time Problems


End

Time Problems


End

Time Problems


3.C.2.a | 23

Start (Beginning)

Time Problems

Problems which ask you to find the time something starts or begins.

Start (Beginning)

Time Problems


Start (Beginning)

Time Problems


Start (Beginning)

Time Problems


Start (Beginning)

Time Problems


Start (Beginning)

Time Problems


Start (Beginning)

Time Problems


Start (Beginning)

Time Problems


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The late movie started at 11:15 p.m. and lasted 2 hours and 15 minutes. When did the movie end? Sam went golfing at 8:30 a.m. and golfed for 5 hours and 30 minutes. At what time did he complete his round of golf? Carol started on a trip at 7:15 a.m. and arrived at her destination 8 hours and 30 minutes later. At what time did she arrive? A train leaves Chicago at midnight and arrives in Kansas City 6 hours and 15 minutes later. What time did she arrive? A TV show started at 10:00 p.m. and lasted 2 hours and 30 minutes. What time did the show end?

Carol arrived at work at 6:30 a.m. and left work at 11:45 a.m. How long was she there? A plane takes off at 8:15 p.m. and arrives at 10:00 p.m. How long is the flight? Joe went to sleep at 10:30 p.m. and woke up at 7:15 a.m. How long did he sleep?

3.C.2.a | 25

A bus left Atlanta at 4:30 p.m. If it arrives in New York at 8:45 a.m., how long was the trip? Mary started taking a test at 9:30 a.m. and finished it at 10:00 a.m. How long did she work on the test?

It took Ken 2 hours and 45 minutes to mow the lawn. If he finished at 10:45 a.m., when did he start? Martin wants to eat dinner at 6:15 p.m. If it takes 1 hours and 30 minutes to prepare the meal, what time should he start? A football game, which lasted 3 hours and 15 minutes, ended at 4:30 p.m. When did it begin? A restaurant plans to serve a banquet at 7:30 p.m. If it takes 7 hours to prepare the meal, what time should the preparation begin? A baseball game lasted 2 hours and 45 minutes. If it ended at 11:15 p.m., when did it begin?

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“After” Time Examples

String Brainstorm: What are some real world reasons to find the “end time” of something? Have students brainstorm a list of ideas. For example: You need to know “end time” to be able to tell your

mom to pick you up after soccer practice.

What is the end time? 3 hours after 10 am

3 hours 15 minutes after 10 am 3 hours 18 minutes after 10 am

3 hours 18 minutes after 10:20 am

What is the end time? 2 hours after 1 pm

2 hours 10 minutes after 1 pm 2 hours 14 minutes after 1 pm

2 hours after 1:21 pm 2 hours 10 minutes after 1:21 pm 2 hours 12 minutes after 1:21 pm

What is the end time?

8 hours after 11 am 8 hours after 11:40 am 8 hours after 11:47 am

8 hours 10 minutes after 11:47 8 hour 18 minutes after 11:47


12 hours after 2 pm 12 hours after 3 pm 12 hours after 4 pm 12 hours after 5 pm

12 hours 10 minutes after 2 pm 12 hours 15 minutes after 3 pm 12 hours 40 minutes after 4 pm

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“Before/Start” Time Examples

String Brainstorm: What are some real world reasons to find the “beginning time” of something? Have students brainstorm a list of ideas. For example: You need to know “beginning/start” time to decide

what time to get up in the morning to be at the bus stop by 7:15.

What is the start/beginning time? 2 hours before 4:00 pm 2 hours before 4:30 pm

2 hours 10 minutes before 4:30 pm 2 hours 10 minutes before 4:32 pm 2 hours 12 minutes before 4:32 pm

What is the start/beginning time?

1 hour before 8:00 am 1 hour 10 minutes before 8:00 am 1 hour 10 minutes before 8:45 am 1 hour 12 minutes before 8:45 am

What is the start/beginning time?

4 hours before 3:00 am 4 hours before 3:40 am

4 hours 30 minutes before 3:40 am 4 hours 30 minutes before 3:42 am 4 hours 35 minutes before 3:42 am


12 hours before 5:00 am 12 hours before 7:00 am 12 hours before 8:00 am

12 hours before 11:00 am 12 hours before 2:00 pm

12 hours 15 minutes before 5:00 pm 12 hours 20 minutes before 7:00 pm 12 hours 50 minutes before 9:00 pm

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“Elapsed” or “Between” Time Examples

What is the elapsed time? 1:00 pm – 2:00 pm 1:10 pm – 2:10 pm 1:10 pm – 2:17 pm 1:10 pm – 2:35 pm 1:30 pm – 2:46 pm

What is the elapsed time?

4:00 pm – 9:00 pm 4:35 pm – 9:35 pm 4:35 pm – 9:52 pm 4:36 pm – 9:46 pm


12:00 pm – 8:00 pm 12:00 pm – 8:25 pm 12:27 pm – 8:27 pm 12:27 pm – 8:30 pm 12:27 pm – 8:42 pm


8:00 am – 4:00 pm 8:00 am – 4:38 pm 8:22 am – 4:38 pm 8:22 am – 4:50 pm 8:22 am – 4:00 am


7:00 am – 7:00 pm 10:00 am – 10:00 pm

2:00 am – 2:00 pm 6:00 am – 6:00 pm 7:00 am – 7:30 pm 7:00 am – 7:42 pm 7:12 am – 7:32 pm

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Hot Topics Problem Modified

This problem is the original problem from Hot Math Topics. The problem is a nice connection between elapsed time and addition/multiplication of decimals.

The problems on the following pages, are different variations/modifications of the original problem.

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I parked from 9:15 in the morning until 1:00 in the afternoon.

How much did I pay for parking?

I parked from 8:25 in the morning until 9:15 in the evening.


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I parked from 8:05 in the morning until 9:35 in the evening.


I parked from 7:05 in the morning until 4:45 in the afternoon.


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Elapsed Time Open Ended Problems

Jamie has 2 hours and 30 to do both his homework and play outside. If he does his homework for _____ minutes, then he can play outside for _____ minutes. Rachel ate her breakfast in _____ minutes. Larry took half as much time to eat his lunch. How would you determine how long it took Larry to eat his breakfast? There are 60 seconds in 1 minute. Write a short story from this sentence. Miguel played for 2 hours and 15 minutes. He played soccer with his friends for ______ minutes and rode his bike for ______ minutes. He only played soccer and rode his bike during that time. Good Questions For Math Teaching, pg. 62 What is something we could do that takes exactly one minutes? What are some things you do in the morning and some things you do in the afternoon? What things could you do in about one hour? My mom said that I went to bed later than my usual bedtime of 8 o’clock. What time might I have gone to bed? What are something you do each school day between 12 o’clock and 4 o’clock?

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The problems that follow are NOT meant to be reproduced and handed out to students as worksheets. These problems are intended for teachers to select problems that are appropriate for their students.

Activities that these problems might be used for:

Time Problem Sorts – print one problem on each index card. Ask students to read each problem and to decide what the problem is looking for; Start, Elapsed, or End time. Then have students choose one of each type of problem to solve.

Warm-ups Exit Slips Differentiation – These problems are organized so that teachers can quickly find

problems that are fit their student’s instructional needs.

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Ending Time Problems

Hour and Half Hour Intervals

Ending Time Problems Fifteen-Minute Intervals

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Ending Time Problems Five-Minute Intervals

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Hour and Half Hour Intervals (next hour)

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Fifteen-Minute Intervals (next hour)

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Five-Minute Intervals (next hour)

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Start/Beginning Time Problems Hour and Half Hour Intervals

Start/Beginning Time Problems Fifteen-Minute Intervals

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Start/Beginning Time Problems

Hour and Half Hour Intervals (next hour)

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Start/Beginning Time Problems

Fifteen-Minute Intervals (next hour)

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Start/Beginning Time Problems Five-Minute Intervals (next hour)

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Elapsed/Between Time Problems Hour and Half Hour Intervals

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Elapsed/Between Time Problems Fifteen-Minute Intervals

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Elapsed/Between Time Problems Five-Minute Intervals

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WARMUP – Elapsed Time (End Time)

1) Marissa puts a turkey in the oven at 10:00 a.m. The turkey cooks for 4 hours. What time will the turkey be ready to take out of the oven?

2) You call a friend at 4:30 and talk for 1 hour and 15 minutes. What time does your conversation end?

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Find Elapsed Time

Nancy’s train left at 8:30 a.m. and traveled for 5 hours and 45 minutes. What time did it arrive at its destination? a) 1:15 p.m.

b) 1:30 p.m. c) 2:00 p.m.

d) 2:15 p.m.

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Elapsed Time – End Time 1) The late movie started at 11:15 p.m. and lasted 2 hours and 15 minutes. When did the movie end?

2) Sam went golfing at 8:30 a.m. and golfed for 5 hours and 30 minutes. At what time did he complete his round of golf?

3) Carol started on a trip at 7:15 a.m. and arrived at her destination 8 hours and 30 minutes later. At what time did she arrive?

4) A train leaves Chicago at midnight and arrives in Kansas City 6 hours and 15 minutes later. What time did she arrive?

5) A TV show started at 10:00 p.m. and lasted 2 hours and 30 minutes. What time did the show end?

6) Jan went shopping at 9:30 am and shopped for 3 hours and 45 minutes. At what time did she finish shopping?

7) It takes 1 hour and 45 minutes to drive to the beach. If you leave at 7:30 a.m., what time will you arrive?

8) If you enter an amusement park at 10:15 a.m. and stay for 10 hours and 45 minutes, when do you leave the park?

9) It takes Mark 30 minutes to drive to his job. If he leaves home at 6:40 a.m., when does he arrive?

10) Lana and Al went to a concert. They arrived at 10:30 p.m. and stayed for 1 hour and 30 minutes. What time did they leave?

11) Pam put a roast in the oven at 11:00 a.m. It took 3 hours and 30 minutes to cook. What time did she remove it from the oven?

12) Jane’s teacher said her math assignment should take 45 minutes to complete. If Jane begins the assignment at 6:45, what time should she finish?

13) A train that normally arrives at 11:45 a.m. was 30 minutes late. What time did it arrive?

14) Mary’s dance class begins at 4:45 p.m. If she dances for 2 hours and 45 minutes, what time is it when she is finished dancing?

15) It is not 2:45 a.m. What time is it in 12 hours and 15 minutes?

3.C.2.a | 49

WARMUP – Elapsed Time

1) A bus leaves Baltimore at 9:00 a.m. and arrives in Virginia Beach at 2 p.m. How long was the trip?

2) You leave your house at 11:55 a.m. and arrive at the mall at 12:20 p.m. How long did it take you to get to the mall?

3.C.2.a | 50

Find Elapsed Time

Fred went to sleep at 10:45 p.m. and woke up at 6:15 a.m. How long did he sleep? a) 16 hours

b) 17 hours c) 7 hours and 30 min.

d) 8 hours and 30 min.

3.C.2.a | 51

Elapsed Time

1) Carol arrived at work at 6:30 a.m. and left work at 11:45 a.m. How long was she there?

2) A plane takes off at 8:15 p.m. and arrives at 10:00 p.m. How long is the flight?

3) Joe went to sleep at 10:30 p.m. and woke up at 7:15 a.m. How long did he sleep?

4) A bus left Atlanta at 4:30 p.m. If it arrives in New York at 8:45 a.m., how long was the trip?

5) Mary started taking a test at 9:30 a.m. and finished it at 10:00 a.m. How long did she work on the test?

6) David babysat on Saturday from 3:00 p.m. until 8:30 p.m. How long did he babysit?

7) The school day starts at 8:00 a.m. and ends at 3:15 p.m. How long is school in session?

8) Frank worked on Thursday from 1:15 p.m. until 9:00 p.m. How long did he work?

9) An amusement park opened at 9:30 a.m. and closed at 11:00 p.m. How long was the park open?

10) Joan went to sleep at 9:00 p.m. and woke up at 6:15 a.m. How long did she sleep?

11) Linda starts to do her homework at 6:45 p.m. and finished it at 9:15 p.m. How long did she spend on the homework?

12) A shopping mall opens at 9:30 a.m. and closes at 10:00 p.m. How long is it open?

13) Mrs. Nelson started grading papers at 3:00 p.m. and finished at 7:15 p.m. How long did she grade papers?

14) The plane from Pittsburgh was scheduled to arrive in Hagerstown at 11:45 a.m. but did not arrive until 1:15 p.m. How late was it?

15) Helen left the store at 9:15 a.m. She returned after shopping, lunch and a movie at 5:00 p.m. How long was she gone?

3.C.2.a | 52

WARMUP – Elapsed Time (Start Time)

1) You and your family arrive at your vacation destination at 1:00 p.m. If you traveled for 3 hours, what time did you leave?

2) You take a cake out of the oven at 4:15 p.m. After it has baked for 45 minutes. What time did you put the cake in the oven?

3.C.2.a | 53

Find Elapsed Time

A science class took a field trip that lasted 5 hours and 45 minutes. If they returned at 2:30 p.m., what time did they leave? a) 8:45 a.m.

b) 9:45 a.m. c) 7:15 p.m.

d) 8:15 p.m.

3.C.2.a | 54

Elapsed Time (Start Time)

1) It took Ken 2 hours and 45 minutes to mow the lawn. If he finished at 10:45 a.m., when did he start?

2) Martin wants to eat dinner at 6:15 p.m. If it takes 1 hours and 30 minutes to prepare the meal, what time should he start?

3) A football game, which lasted 3 hours and 15 minutes, ended at 4:30 p.m. When did it begin?

4) It took Mike 3 hours and 30 minutes to wax his truck. If he finished at 11:15 a.m., when did he start?

5) A teacher’s workshop lasted for 6 hours and 15 minutes. If the workshop was over at 3 p.m., what time did it start?

6) A restaurant plans to serve a banquet at 7:30 p.m. If it takes 7 hours to prepare the meal, what time should the preparation begin?

7) A baseball game lasted 2 hours and 45 minutes. If it ended at 11:15 p.m., when did it begin?

8) A bus traveled for 9 hours and 15 minutes. If it arrived at its destination at 9:15 a.m., when did it begin its journey?

9) The school day usually ends at 3:30 p.m. If it closed 1 hour and 30 minutes early because of snow, what time did it close?

10) Judy wants to serve Sunday dinner at 12:30 p.m. If her ham takes 2 hours and 15 minutes to cook, what time should she put it in the oven?

11) Peter arrived at his destination at 12:00 p.m. If he traveled for 6 hours and 15 minutes, what time did he begin the trip?

12) Joe spent 5 hours and 30 minutes working on his car. If he finished at 4:15 p.m. what time did he begin?

13) Nora woke up at 6:30 a.m. after sleeping for 8 hours and 50 minutes. What time did she go to bed?

14) School ends at 2:15 p.m. If the school day is 6 hours and 30 minutes long, what time does school begin?

3.C.2.a | 55

15) Eric’s swim practice lasted for 2 hours and 45 minutes. If practice ended at 7:15 p.m., what time did practice begin?

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Note: This ruler can be used with students but students gradually begin to use an open/empty time line to solve elapsed time problems as they cannot use this tool for county/state/national assessment.

3.C.2.a | 60

3.C.2.a | 61

Exit Slip – 3.C.2.a

Name: Rachel came to work at 8:30 am. She left work at 4:15. How long did she work? What kind of time are we finding here? the time something starts (Start Time) the time something ends (End Time) the time between (Elapsed Time) How long was Rachel at work? _____________________ Show your work below.


Name: Rachel came to work at 8:30 am. She left work at 4:15. How long did she work? What kind of time are we finding here? the time something starts (Start Time) the time something ends (End Time) the time between (Elapsed Time) How long was Rachel at work? _____________________ Show your work below.

3.C.2.a | 62


Name:

At 1:28 p.m., Celina and Mike finished a hike that lasted 4 hours 35 minutes. At what time did they start hiking?

What kind of time are we finding here? the time something starts (Start Time) the time something ends (End Time) the time between (Elapsed Time) At what time did they start hiking? _____________________ Show your work below.


Name:

At 1:28 p.m., Celina and Mike finished a hike that lasted 4 hours 35 minutes. At what time did they start hiking?

What kind of time are we finding here? the time something starts (Start Time) the time something ends (End Time) the time between (Elapsed Time) At what time did they start hiking? _____________________ Show your work below.

3.C.2.a | 63


Name:

Joe left for football practice at 2:47 p.m. He returned home 2 hours and 45 minutes later. At what time did Joe return home? What kind of time are we finding here? the time something starts (Start Time) the time something ends (End Time) the time between (Elapsed Time) At what time did Joe return home? _____________________ Show your work below.


Name:

Joe left for football practice at 2:47 p.m. He returned home 2 hours and 45 minutes later. At what time did Joe return home? What kind of time are we finding here? the time something starts (Start Time) the time something ends (End Time) the time between (Elapsed Time) At what time did Joe return home? _____________________ Show your work below.

3.C.2.b | 1



3.C.2.b | 2



Hot Math Topics Geometry &

Measurement 5 33, 44

Fractions & Decimals 5 11, 50

Number Sense 4-6 124-129


Sample Assessment Questions

Donna is mixing different colors of paint together to match the color of her house. The amounts of paint are shown below.

2 gallons of white paint 2 quarts of yellow paint 1 quart of blue paint

3 quarts of red paint 1 quart of brown paint 2 pints of orange paint

How many gallons of paint will Donna have after she has mixed all of the paint colors together?

A. 3 gallons B. 4 gallons C. 6 gallons D. 11 gallons

3.C.2.b | 3


Sample Assessment Questions

Terry is making drinks from a mix for the fifth grade class party. The ingredients for making the drinks are listed in the chart below.

Terry wants to make 12 quarts of drinks. How many gallons of water will she need?

A. 2 gallons B. 4 gallons C. 6 gallons D. 12 gallons

Tonya's dad is making a concrete patio in their backyard. Concrete is made from cement, sand, gravel and water. It takes twice as much sand as cement to make the concrete mix.

Tonya's dad used 3 gallons of sand in the mix.

Step A

How many quarts of cement did he use?

Step B

Explain how you found your answer. Use what you know about measurement in your explanation. Use words, numbers and/or symbols in your explanation.

Scoring information found at: http://mdk12.org/instruction/sampitems/mathematics/grade5/msa_math_5_018.html

3.C.2.b | 4


This objective asks students to convert between units. Fifth grade students are assessed on converting units of time (hours, minutes, seconds) and units of capacity (pints, quarts, and gallons). Grade three students are assessed on converting units of length (inches, feet, yards). Anything assessed in a prior grade can also be assessed in this grade level. It is recommended that teachers also review the conversions involving inches, feet, and yards.

It is recommended that converting units of time be taught at the same time as elapsed time. Teachers can ask students to turn the elapsed time they found into another unit of time. For example, if the students found the amount of time they spent in school as 6 ½ hours, ask them how many minutes or seconds this is equivalent to.

Review with your children that capacity describes how much a container can hold. Some children may be familiar with volume, or the amount of space something takes up, which is usually measured in cubic units. Your children should also be familiar with standard units of capacity, including cups, pints, quarts, and gallons. We recommend doing plenty of hands-on activities together, such as cooking, baking, or just measuring a variety of classroom materials to help your children understand how the units are related. Show your children a glass and a pitcher. Which has the greater capacity? Which can hold more? Guide them to understand that the bigger container holds more and therefore has a greater capacity. Then show two different shaped glasses and ask the question again. You may want to pour water, uncooked rice, beans, small cubes, or other classroom materials from one glass into the other to demonstrate how one has a greater, smaller, or equal capacity to the other. Remind your children that just because two glasses are different sizes, it does not necessarily mean they have different capacities. Tall and skinny glasses may hold the same amount of water as short and wide glasses. Have your children experiment with different containers and compare shapes and capacities using a variety of pourable materials. Ask them to estimate and predict which container has the greater capacity before they begin their experiments.

3.C.2.b | 5

Show a measuring cup and explain that a cup is a unit of measurement. Show a mug or a plastic cup and remind your children that while they are both cups, they are not the standard size used in measurement. Ask your students to discuss why they think we use a universal measurement called a “cup”. Some cups may hold more than a cup! Fill a measuring cup and model how to write the measurement 1 c. Remind your children that we use the abbreviation "c" to stand for cups. Challenge your students to think of items that come in cup-sized containers such as single servings of yogurt or small school milk cartons. Show a pint measure and explain that a pint is a unit of measurement that is larger than a cup. Ask a student to pour 2 cups into the pint measure to demonstrate that 2 cups are equal to 1 pint. Explain that we use the abbreviation "pt" to stand for pints. Brainstorm different items that come in pint sizes, such as ice cream, milk, and blueberries. Show a quart measure and explain that a quart is a unit of measurement that is larger than both a pint and a cup. Have students pour 2 pints into the quart measure to demonstrate that 2 pints are equal to 1 quart. Help your students recognize that since there are 2 cups in a pint, there are 4 cups in a quart. They can pour 4 full measuring cups into a quart measure to demonstrate. Remind children that we use the abbreviation "qt" to stand for quarts. Brainstorm different items that come in quart sizes, such as juice, milk, strawberries (large package), and paint. A gallon is a unit of measurement that is larger than a quart, pint, and cup. You may want to present to your children with an empty gallon carton of milk or a gallon soup pot. With some assistance they can pour 4 quarts into the gallon container to understand that 4 quarts are equal to 1 gallon. Since there are 2 pints in a quart, there are 8 pints in a gallon. Since there are 2 cups to a pint, there are 16 cups in a gallon. You can demonstrate how the units are related by measuring different materials and pouring them into the carton or pot. We use abbreviation "gal" to stand for gallons. Brainstorm different items that come in gallons, such as juice, milk, and gasoline. Working with cups, pints, quarts, and gallons can be confusing for some children and we suggest using plenty of hand-on activities to help them understand how the units are related. It is helpful to create a class chart of equivalent amounts, including pictures of the different measurements, to help students visualize and retain the relationships between units. Graphic organizers, mnemonics, and silly songs may also help drive the concepts home.

3.C.2.b | 6

Lesson Seeds

Gentle Giant PowerPoint – This is available with the electronic copies of the unit guide. See you SAS if you cannot locate it. Use the included activity sheet with the PowerPoint.

Gallon Man – Like Gentle Giant, this is another device that can be used to help students remember the conversions between pints, quarts, and gallons.

Create a Song - Together as a class, write a silly song about cups, pints, quarts, and

gallons. You may want to use a tune from a classic song or have partners make up a rap of their own. Distribute cup, pint, quart, and gallon containers and have students use them as props as they sing or rap.

Contain Yourself - Have your students each bring in different containers from home.

Encourage them to be creative and bring in large and small containers, such as juice boxes, pots, casserole pans, baby bottles, etc. Then have students use cup, pint, or quart measures to find out how much their containers can hold. Students may want to use more than one unit to measure, such as cups and pints. Make a chart together listing the measurements.

Lemonade Stand Song – You can listen to this song at:

http://www.totally3rdgrade.com/lemonade_stand.html . It can also be found on iTunes. This song goes beyond the conversions of grade 5 but it does include conversions that students need to make.

Hot Math Topics: Fractions and Decimals #11- This problem involves both fractions

and conversions of time (depending on how it is solved). Students will probably first subtraction 8 ½ from 14 and get 5 ½. Then they have to divide 5 ½ equally between 5 days. They will easily divide the whole number (1 hour) but may struggle with dividing ½ into 5 equal parts. Many students will discover that one way to solve it is to think of the ½ as 30 minutes (equivalent unit) and then divide 30 minutes by 5 and get 6 minutes. Students may also change ½ to an equivalent fraction which they can take 5 equal parts of easier – such as 5/10. Once they find 1 hour and 6 minutes they must convert the answer to minutes (as the problem asks) – 66 minutes.

Hot Math Topics: Fractions and Decimals #50 – This problem involves both

fractions and converting from yards to inches.

http://www.totally3rdgrade.com/lemonade_stand.html�

3.C.2.b | 7

Hot Math Topics: Fractions and Decimals #76 – This problem requires students to

convert to ounces to pound. The tricky part of this problem is the decimal. This problem might be reserved to be used after or during unit 2 since it involves a decimal.

3.C.2.b | 8

Gallon Man

3.C.2.b | 9

Mr. Gallon’s Parts

3.C.2.b | 10


Mr. Gallon

3.C.2.b | 11


Quart

Quart

Quart

Quart

3.C.2.b | 12


Pint

Pint

Pint

Pint

Pint

Pint

Pint

Pint

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Cups Cups

Cups Cups

Cups Cups

Cups Cups

Cups Cups

Cups Cups

Cups Cups

Cups Cups

3.C.2.b | 14

The Gallon Man Song Tune: Ants Go Marching

Two pints go marching two by tow, Hurrah! Hurrah! Two pints go marching two by two, Hurrah! Hurrah!

As doubles they plunge into a quart, standing so quiet,

as if they’re in court…. As they all go marching into the chest to get out of the rain.

Four quarts go marching four by four, Hurrah! Hurrah! Four quarts go marching four by four, Hurrah! Hurrah!

All four follow and slip inside, standing so close as if they were tied…

As they all go marching into the chest to get out of the rain.

A gallon goes marching one by one, Hurrah! Hurrah! A gallon goes marching one by one, Hurrah! Hurrah!

Add together eight points or four quarts, the total is always one

gallon of course! As they all go marching equivalent and dry out of the rain.

-Lauria Kagan

Kaganonline.com/newsletter/blacklines/gallon_man.html

3.C.2.b | 15

Name ______________________________ Date ________________

“The Gentle Giant”

Equivalent Measurements

Use this activity sheet with the Gentle Giant PowerPoint. Recreate the story of the Gentle Giant below as you listen again.

There was a very gentle giant who lived in a large castle all by himself

One cold, stormy night 4 queens knocked on the door of his castle. They asked if they could come in to warm up by the fire.

He agreed and welcomed them into his home. When the 4 queens sat down around the fire, 2 little puppies scurried out from under each queen’s dress.

Each puppy had 2 big beautiful brown eyes with which to “c”. The giant understood why the puppies were so special to the queens.

3.C.2.b | 16

Questions to think about…

1. How many cups are in a gallon? ______________ 2. How many pints are in a quart? ______________ 3. How many quarts are in a gallon? _____________ 4. How many cups are in 3 pints? _____________ 5. How many pints are in 2 gallons? ______________ 6. How many cups are in 2 quarts? ______________

Write 2 statements about gallons, quarts, pints, and cups.

Example: I know that there are 4 pints in 2 quarts.

1. ____________________________________________________________________

2. ____________________________________________________________________

Now get those thinking caps on…

You’re standing in the dairy aisle of the grocery store. Your grocery list states that you need 6 cups of milk to make your favorite cheesy potato soup. The cartons of milk are packaged in pints, quarts, half gallons, and gallons.

Which container(s) would give you the amount of milk you need with the least amount of milk left over? Explain how you know your answer is correct.

3.C.2.b | 17

"Lemonade Stand" lyrics How much lemonade can the animals drink? At the lemonade stand in the crazy jungle Pint, cup, tablespoon, teaspoon You will learn the difference soon Cuz a monkey drinks more than a mouse In the jungle.

The Sun came up and the jungle was getting hot A mouse knew a teaspoon of lemonade would hit the spot Then a toad hopped by and croaked a tune "I'm bigger than a mouse; I can drink a tablespoon" Three teaspoons to make a tablespoon... in the jungle

The mouse and the toad were sitting on a piece of wood And the little bit of lemonade was tasting very good Then a toucan flew by and said, "What's up?" "I need a lot more may I please have a cup" 16 tablespoons to make one cup 3 teaspoons to make a tablespoon... in the jungle

But the day was young and there was more to drink Wasting lemonade would really, really stink Then a monkey dropped in from out of sight "I'm twice as big and I need a pint." It takes 2 cups to make one pint 16 tablespoons to make one cup 3 teaspoons to make a tablespoon... in the jungle

How much lemonade can the animals drink? At the lemonade stand in the crazy jungle Barrel, gallon, quart and pint They all want a different size Cause a hippo drinks more than a mouse ...In the jungle.

Well after the monkey had ordered himself one pint A growl from the bushes gave him quite a fright A tiger jumped through and said with a snort "I'm twice as big and I can drink a quart" Cuz it takes 2 pints to make one quart, Takes 2 cups to make one pint, 16 tablespoons to make one cup, 3 teaspoons to make a tablespoon... in the jungle

While the monkey hanged in a tree with his pint (which had spilled) And the tiger enjoyed his quart, which didn't seem right A hippo came by whose name was Allan "I'm 4 times as big and can drink a gallon" Cuz it takes 4 quarts to make one gallon, Takes 2 pints to make one quart, Takes 2 cups to make one pint, 16 tablespoons to make one cup, 3 teaspoons to make a tablespoon... in the jungle

A monkey with a pint and a tiger with a quart, what a sight! And hippo with a gallon and a sound coming from the right Here comes the elephant, his name is Darrel "I'm really thirsty, please give me a barrel" That's 42 gallons to make one barrel, Takes 4 quarts to make one gallon, Takes 2 pints to make one quart, Takes 2 cups to make one pint, 16 tablespoons to make one cup, 3 teaspoons to make a tablespoon... in the jungle, or the city, or the desert or the moon.

Hey, Mr. Elephant, how many teaspoons are there in a barrel?

© 2005 Power Arts Company, Inc.

3.C.2.b | 18

Hot Math Topics: Fractions and Decimals #11

3.C.2.b | 19

A Weighty Money Problem

Regardless of the value, each bill weighs about 0.033 ounce. A car costs $9,000. Could you buy this car with a pound of $20 bills? Explain your thinking.

3.C.2.b | 20

Technology Links

Measurement Clipart – For measurement clipart go to the ETC Clipart site at: http://etc.usf.edu/clipart/mysearch.php?searchWords=quart&mySubmit=Search

BrainPop Jr. Cups, Pints, Quarts, Gallons – Each school and teacher has access to BrainPop Jr. through WCPS. See your SAS if you are not sure how to access BrainPop Jr. Once you have logged in, go to Math and click on Measurement. It is under the Measurement topic that you will find the converstions information.

http://etc.usf.edu/clipart/mysearch.php?searchWords=quart&mySubmit=Search�

3.C.2.b | 21

Equivalent Units of Time Concentration – This application allows students to match equivalent units of time. Students progress to more difficult levels as they complete easier levels.

http://www.sheppardsoftware.com/mathgames/time/TimeConversions.htm

http://www.sheppardsoftware.com/mathgames/time/TimeConversions.htm�

3.C.2.b | 22


Name:

Michael made 72 pints of lemonade for his friends.

Step A How many gallons of lemonade did Michael make? __________gallons

Step B Explain how you found the number of gallons. Use what you know about equivalent units of measurement in your explanation. Use words, numbers, and/or symbols in your explanation.


Name:

Michael made 72 pints of lemonade for his friends.

Step A How many gallons of lemonade did Michael make? __________gallons

Step B Explain how you found the number of gallons. Use what you know about equivalent units of measurement in your explanation. Use words, numbers, and/or symbols in your explanation.

6.B.1.a | 1


Math at Hand by Great Source, page 053-055.



Think Tank – Problem Solving Prickly Problems 5 4, 12 Quick Quizzes 5 20 Cool Heads 5 15

6.B.1.a | 2

Instructional Notes – 6.B.1.a

Prime and composite numbers are useful to make computation with fractions easier

(i.e. LCM and GCF). One and Zero are not considered prime or composite. List of prime numbers less than 1,000 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 One and Zero are not considered prime or composite

6.B.1.a | 3

Lesson Seeds

11x17 Number Line by Kim Sutton - Each teacher in WCPS will receive a 0-144

number line. See the teaching notes under the lesson seed titled: Kim Sutton Number Line Development. Each student should create a 11x17 number line to keep in their math tools box. This will be helpful for identifying factors, multiples, GCF, LCM, primes, composite numbers, etc…

Eliminate It! Revise It!

Sum Square Puzzles

Prime or Composite Bingo – There are 3 variations of this game included for different levels of student understanding.

Factor Finding Game

6.B.1.a | 4

Kim Sutton Number Line Development

Information on Kim Sutton’s Number Line Development can be found in the following book titled, The Number Line Workbook by Kim Sutton (Each SAS has a copy of this book). Kim’s number line is a number line showing the numbers 0-144 in a continuous line from left to right. The numbers are coded with colored dots to show the factors of 2-12 on the number line. This single took is the most important visual for all elementary classrooms. The colored dots should be consistent from grade level to grade level so students see the same visual patterns each year. The Color-Coding System is found on the page that follows these instructions. Older students (grade 4 and 5) should each have an 11x17 number line in which to identify the multiples. Students will use markers to identify the multiples early in the year. This 11x17 number line should be a part of the students Math Tool Kit for use throughout the entire year.

For older students, this visual assists them with factoring and reducing fractions. Students look for the same colored dot as a shared attribute of two numbers. For example, if students are trying to decide if they can simplify 12/32 they can look at those two numbers on the number line and determine that they both have several multiples in common and use this information to simplify the fraction. Numbers without colored dots are prime, numbers with colored dots are composite. To introduce the idea of multiples the teacher will use objects that come in a constant of count to create a picture in the mind’s eye. To introduce multiples of two, I recommend playing the game called “The Stand Up Game.” One student stands up. The teacher directs the activity by asking, “How many students are standing? How many eyes do these people have?” Have students read the “groups of sign” filling in the groups that are

6.B.1.a | 5

represented by the standing students. After the solution is found, have all students identify the multiple on the class number line and individual student 11x17 number lines. Build the completed number line by completing whole class activities that develop each multiple (see below). After each multiple, the “groups of” statement should be read (groups of sign on the pages that follows). The dots should attached the class number line with Velcro and drawn on each student 11x17 number line.

6.B.1.a | 6

6.B.1.a | 7

Number Line Velcro The list below shows the number of pieces of Velcro needed to identify the

multiples of numbers 2-12. Velcro coins = round Velcro dots. Cheapest place to purchase Velcro coins is feinersupply.com (as of June 2011). If purchasing from feinersupply.com be sure to purchase a roll of “hook” and a roll

of “loop” Velcro coins.

6.B.1.a | 8

Number Line Color-Coded System

2s Red

3s Green

4s Orange

5s Yellow

6s Light Blue

7s Neon Orange

8s Neon Green

9s Black

10s Navy Blue

11s Purple

12s Gold Star

6.B.1.a | 9

Ideas to build the Multiples

2s

number of eyes number of ears number of hands number of feet

3s

sides on a triangle wheels on a tricycle legs on a tripod meals in a day

4s sides on a quadrilateral legs on a dog legs on a table legs on a cat

5s

sides on a pentagon number of dimes number of points on a star fingers on a hand toes on a foot

6s sides on a hexagon legs on an insect wheels on a train

7s days in a week sides on a septagon/heptagon

8s sides on an octagon legs on a spider legs on an octopus

9s

sides on an nonagon

6.B.1.a | 10

10s

sides on a decagon number of dimes total fingers total toes

11s sides on a undecagon

12s sides on a dodecagon months in a year eggs in a dozen

Using an Idea to build the Multiples

For example, if you are building the 12s with your class (to identify them on your class and individual number lines) the teacher may choose to use the number of eggs in cartons of eggs. The conversation with the class might look as follows: Teacher: I have one egg carton, and I need someone to come up and hold it. How many eggs are in 1 carton of eggs? Students: 12 Teacher: Let’s read this situation using our “group of” statement. (Teacher hold up groups of statement.) Students: 1 group of 12 equals 12 Teacher: I need someone to come up and velcro the gold star above 12. Teacher: I now have two egg cartons, and I need another person to come up and hold my second egg carton. How many eggs do I have all together now? Students: 24. Teacher: Let’s count what we see…

6.B.1.a | 11

Students: 12, 24… Teacher: Let’s read this situation using our “group of” statement. (Teacher holds up groups of statement.) Students: 2 groups of 12 equals 24. Teacher: I need someone to come up and velcro the gold star above 24. Teacher: I am going to add a third egg carton. I will need another person to come up and hold my third carton. How many eggs do I have all together? Students: 36. Teacher: Let’s count what we see… Students: 12, 24, 36… Teacher: Let’s read this situation using our “group of” statement. (Teacher holds up groups of statement.) Students: 3 groups of 12 equals 36. Teacher: I need someone to come up and velcro the gold star above 36. Teacher continues adding egg cartons until all the multiples of 12 are covered up to 144 (12 groups of 12). The teacher should then give students time to put a gold star above the multiples on their own personal number line (11x17 version).

6.B.1.a | 12

Eliminate It! Revise It!

Materials: consensus mat for each group (chart paper with sections for each student to write

and a center section for the group to “come to consensus”)

4 index cards – with 4 words, expressions, number sentences, etc… (these are the 4 items which students will choose 3 to keep and 1 to eliminate)

markers (for each student) Revise it! sheets

Eliminate It! Directions (cooperative):

• Put students into groups of 4.

• Give each group 4 index cards.

• Set a timer for 2-3 minutes and ask students to, on their own and without talking, decide which 3 cards they will keep and which one they will eliminate. They should write their thinking in their own section of the mat.

• After the time is up, give each group time to share out individual student’s thinking and have the group “come to consensus” on which card to eliminate and why. Groups must also give the 3 cards they are keeping a title. The group then writes their justification in the center of their consensus mat.

• Have each group share out (to the whole group) which card they eliminated and why.

Revise It! Directions (independent):

• Each student will need a Revise It! activity sheet.

• Students independently write down the three cards they will keep and then create a fourth card that fits their group.

• Students then title their group and justify their choice.

6.B.1.a | 13

Name ____________________________________________________________________________________

Eliminate It!

39 54

61 46

Cross out the number that does not belong with the others. Justify your answer.

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

Revise It!

______________________________________

Record the 3 numbers that go together. Decide on a title for your group of numbers. Add 1 more number that belongs with the others. Justify why your new number belongs in this group.

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

6.B.1.a | 14

Name ____________________________________________________________________________________

Eliminate It!

41 61

71 81


___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

Revise It!

______________________________________


___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

6.B.1.a | 15

Eliminate It! Revise It! Teacher Notes

39 54

61 46

The intent behind this set of numbers is to eliminate 61 because all of the other numbers are composite and 61 is a prime number.

41 61

71 81

The intent behind this set of numbers is to eliminate 81 because it is composite and all of the other numbers are prime numbers.

6.B.1.a | 16

Prime or Composite Bingo

Classroom Setup: Groups of 3 students (2 players and 1 checker) Materials: Prime or Composite Game Board 2 kinds of markers (one color for each player) paper clip and pencil for spinner Dry Erase Board

Directions:

1. Player A spins both spinners. The player adds the two numbers on the spinner to come up with a two digit number. The player then states whether the number formed is prime or composite. The checker in the group uses the answer key to check their answer. If it is correct, the player can cover a C or P (C if it was a composite number or P if it was a prime number) on the board. If it is incorrect, they lose their turn.

2. Players repeat step 1 until 1 player has 3 markers in a row on the game board.

6.B.1.a | 17

P C P C

C P C P

P C P C

C P C P

6.B.1.a | 18

PRIME or COMPOSITE Answer Key NUMBER P or C?

1 Neither 2 P 3 P 5 P 7 P 9 C

11 P 12 C 13 P 15 C 17 P 19 P 21 C 22 C 23 P 25 C 27 C 29 P 31 P 32 C 33 C 35 C 37 P 39 C 41 P 42 C 43 P 45 C 47 P 49 C 51 C 52 C 53 P 55 C 57 C 59 P

6.B.1.a | 19

P C P C

C P C P

P C P C

C P C P

6.B.1.a | 20

PRIME or COMPOSITE Answer Key NUMBER P or C?

11 P 13 P 14 C 15 C 17 P 19 P 21 C 23 P 24 C 25 C 27 C 29 P 31 P 33 C 34 C 35 C 37 P 39 C 41 P 43 P 44 C 45 C 47 P 49 C 51 C 53 P 54 C 55 C 57 C 59 P 61 P 63 C 64 C 65 C 67 P 69 C

6.B.1.a | 21

P C P C

C P C P

P C P C

C P C P

6.B.1.a | 22

PRIME or COMPOSITE Answer Key

NUMBER P or C? 41 P 43 P 47 P 49 C 51 C 53 P 57 C 59 P 61 P 63 C 67 P 69 C 71 P 73 P 77 C 79 P 81 C 83 P 87 C 89 P 91 C 93 C 97 P 99 C

6.B.1.a | 23

Sum Square Puzzles

These are puzzles that are similar to

those that are produced by Origo Math (Zuplez). These are original and do not duplicate the Zuplez cards (These were not purchased by the county. Some schools purchased them on their own).

These cards were created to fit the grade 4 and 5 objectives from the State Curriculum. These cards develop computation skills as well as logical thinking and reasoning.

When using, the students fill in the digits so that each row and column has the sum

that is indicated (beside each row and column). Students should first fill in the digits that have clues that they can solve.

These puzzles make a good review throughout the year.

These puzzles could be used for a warm-up, center, homework, etc…

A blank Sum Square template is included in case you would like to create your own

puzzles. To create you own puzzle: 1. Fill in each number one time into a one square in the puzzle (using all 9 digits). 2. Find the sums of each row and column. 3. Fill in at least 1 clue into each row and column. Fill in a second clue to one of the

rows or columns. Possible Clue Topics: factors, multiples, primes, composites, facts, LCM, GCF, measurement topics, elapsed time, fractions, etc…

4. Erase the digits and check to be sure your puzzle can be solved. 5. Give students a blank with the sums and clues filled in.

6.B.1.a | 24

not prime or composite

x + 6 = 10 x = ?

smallest prime

72 ÷ 9

1

2

3

4

5

6

7

8

9

product of 2 and 3

smallest odd #

56 ÷ 8

largest factor of 2

odd number

1

2

3

4

5

6

7

8

9

6.B.1.a | 25

odd prime factor of 10, not 1

89 – x = 87 x = ?

42 ÷ 7

factor of 7

odd prime

largest composite digit

1

2

3

4

5

6

7

8

9

# of feet in 1 yard

360 ÷ 40

# of hours between 3:15 pm & 5:15 pm

odd prime factor of 28

2 x 2 x 1

1

2

3

4

5

6

7

8

9

6.B.1.a | 26

inches in ½ a foot

2 x 2 x 2

49 ÷ 7


1

2

3

4

5

6

7

8

9

even factor of 16 less than 8

odd factor of 20, not 1

smallest prime

odd composite

1

2

3

4

5

6

7

8

9

6.B.1.a | 27

½ of 18

odd factor of 9, not 1

largest prime

500 ÷ 100

1

2

3

4

5

6

7

8

9

hours between 11 pm and 5 am

# of inches in 1/3 of a foot

(12 ÷ 2) - 1

composite factor of 27

1

2

3

4

5

6

7

8

9

6.B.1.a | 28

77 ÷ 11


factor of 10

odd composite

(24 ÷ 4) + 2

1

2

3

4

5

6

7

8

9

72 ÷ 12

factor of 12 and 16

factor of 25, not 1

smallest prime #

1

2

3

4

5

6

7

8

9

6.B.1.a | 29

1

2

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

9

6.B.1.a | 30

Factor Finding Game

Materials Needed: 10 colored disks or markers each Pair of dice Factor Finding game board

Directions: The starting player rolls the dice and forms a two digit number with the numbers rolled. The largest number is in the tens and the smallest is in the ones every time. For example, if he rolls a 2 and a 3, the number formed would be 32 not 23. The player places only one disk during each turn. He places it on the playing board over any number that is a factor of the number he created in his roll. For example, he could place his marker over 2,4,8,16 or 32 (if he rolled a 32).

• If a player rolls doubles, his turn is lost. • If a player rolls a prime number, he places a marker on any PRIME square. • If a square is already covered, a player cannot use it. • The first player to get four disks in a row wins. • If the grid gets locked and no one can win, players start a new game.

6.B.1.a | 31

5 3 7 Prime

2 6 8 17

Prime 21 4 16

13 9 Prime 26

6.B.1.a | 32

Technology Links

King Kong’s Prime Numbers – In this game students whack King Kong if he is holding a prime number. If they hit a composite number, they lose points. http://www.xpmath.com/forums/arcade.php?do=play&gameid=60

Prime or Composite Fruit Shoot – In this game students shoot the numbers that match the word (prime or composite) on their target. http://www.sheppardsoftware.com/mathgames/numbers/fruit_shoot_prime.htm

http://www.xpmath.com/forums/arcade.php?do=play&gameid=60�

http://www.sheppardsoftware.com/mathgames/numbers/fruit_shoot_prime.htm�

6.B.1.a | 33


Name:

1. Jack picked up his new jersey for spring lacrosse. The number on her jersey is a prime number that is greater than 31 but less than 40. What is his jersey number? ________

2. Write down 2 composite numbers that are between 50 and 60.

___________ and ___________ are composite numbers.


Name:

1. Jack picked up his new jersey for spring lacrosse. The number on her jersey is a prime number that is greater than 31 but less than 40. What is his jersey number? ________

2. Write down 2 composite numbers that are between 50 and 60.

___________ and ___________ are composite numbers.

6.B.1.a | 34


Name:

Fill in the solution beside each question. Check off whether each of your answer is prime or composite.

Prime Composite

What is your age right now?

How old will you be 13 years from now?



Name:

Fill in the solution beside each question. Check off whether each of your answer is prime or composite.

Prime Composite

What is your age right now?



6.B.1.a | 35


Name:

Look at the numbers below. 20 21 22 23 24 25 26 27 28 29 30

Sort the numbers into the correct circles

Prime Composite


Name:

Look at the numbers below. 20 21 22 23 24 25 26 27 28 29 30

Sort the numbers into the correct circles

Prime Composite

6.B.1.a | 36


Name:

Mike’s grandfather said, “My age is the only prime number between 55 and 60.” What is the age of Mike’s grandfather? ________________


Name:

Mike’s grandfather said, “My age is the only prime number between 55 and 60.” What is the age of Mike’s grandfather? ________________

6.B.1.b | 1

6.B.1.b Identify and use divisibility rules AL: Use the rules for 2, 3, 5, 9, or 10 with whole numbers (0-10,000)




Nimble with Numbers 4-5 86

98-101

Think Tank – Problem Solving Prickly Problems 5 14 Good Questions for Math Teaching

45 9 38 5

Fundamentals 5-6 24-27

6.B.1.b | 2

Literature Links – 6.B.1.b

Book Location Notes

Divide and Ride

by: Stuart Murphy


In order to ride the Dare-Devil roller coaster at the Carnival, there must be two kids in each seat. But what if you're part of a group of 11 best friends? Ten kids will fit in five seats, but what do you do about the one who's "left over"? Meanwhile, chairs on the Satellite Wheel seat three, which means two best friends will be left over. Every ride presents a problem. Can the kids figure out how to fill all the seats so that everybody gets to ride? Understanding the meaning of remainders in simple division problems is a precursor to solving more difficult division problems. Illustrated by George Ulrich.

Instructional Notes – 6.B.1.b

The rules of divisibility are simple formulas for understanding how fair shares can

be created from large numbers without practicing long or short division. Students usually come to fifth grade with an implicit understanding about why numbers are divisible by 2, 5, and 10, but it is important in fifth grade to make that understanding explicit.


6.B.1.b | 3

Divisibility Rules

A number

is divisible

by:

If: Example:

2 The last digit is even (0,2,4,6,8) 128 is 129 is not

3 The sum of the digits is divisible by 3 381 (3+8+1=12, and 12÷3 = 4) Yes 217 (2+1+7=10, and 10÷3 = 3 1/3) No

4 The last 2 digits are divisible by 4 1312 is (12÷4=3) 7019 is not

5 The last digit is 0 or 5 175 is 809 is not

6 The number is divisible by both 2 and 3

114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes 308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No

7

If you double the last digit and subtract it from the rest of the number and the answer is divisible by 7 or 0. (Note: you can apply this rule to that answer again if you want)

672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes 905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No

8 The last three digits are divisible by 8 109816 (816÷8=102) Yes 216302 (302÷8=37 3/4) No

9

The sum of the digits are divisible by 9 (Note: you can apply this rule to that answer again if you want)

1629 (1+6+2+9=18, and again, 1+8=9) Yes 2013 (2+0+1+3=6) No

10 The number ends in 0 220 is 221 is not

11 If you sum every second digit and then subtract the other digits and the answer is divisible by 11 or 0

7392 ((7+9) - (3+2) = 11) Yes 25176 ((5+7) - (2+1+6) = 3) No

12 The number is divisible by both 3 and 4 648 (6+4+8=18 and 18÷3=6, also 48÷4=12) Yes 916 (9+1+6=16, 16÷3= 5 1/3) No

6.B.1.b | 4

Alternate Set of Divisibility Rules

Digital Root = sum of the digits (keep adding digits until a single digit, the digital root, is found). For example the digital root of 54 = 5 + 4 or 9. The digital Root of 87 = 8 + 7 =

15 = 1 + 5 = 6, so the digital root of 87 is 6.

6.B.1.b | 5

Lesson Seeds

Eliminate It! Revise It! – See the directions for this is section 6.B.1.a.

Divisibility Lesson – This is a lesson that could be used to introduce the divisibility rules.

Divisibility Rocks Game

Three Digit Divisibility Problem Based Lesson Seed

Open Ended Problems

Kim Sutton Number Properties Checklist

Kim Sutton Number Lines – All grade 5 teachers were provided with this tool in the fall of 2011. Students can use this tool to look at patterns of divisibility. See section 6.B.1.a for detailed information about this number line as well as the 11x17 student version.

6.B.1.b | 6

Name ____________________________________________________________________________________

Eliminate It!

250 6,960

985 8,940


___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

Revise It!

______________________________________


___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

6.B.1.b | 7

Name ____________________________________________________________________________________

Eliminate It!

3,312 5,215

6,483 9,993


___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

Revise It!

______________________________________


___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

6.B.1.b | 8

Eliminate It! Revise It! Teacher Notes

250 6,960

985 8,940

The number 985 should be eliminated because all of the other numbers are divisible by 2, 5, and 10. 985 is only divisible by 5.

3,312 5,215

6,483 9,993

The number 5,215 should be eliminated because it is not divisible by 3 as all the other numbers are.

6.B.1.b | 9

Divisibility Lesson

Before:

1. Divide the class into teams of three members each. One member is the director, one the recorder, and one the materials coordinator.

2. Each team takes four index cards and writes a different digit from 0-9 on each card.

Then, from the four choices of digits, the team makes a list of all the possible four-digit number combinations using each digit once. There will 24 possible number combinations.

3. Next, have the students each take a graphic organizer, Divisibility Test, with

columns for the numbers they created, plus the columns for 2, 3, 5, 6, 9, and 10 listed across the top. Using calculators if you wish, have the students divide each of their 24 numbers by 2, 3, 5, 6, 9, and 10 to decide if their numbers divide evenly without leaving remainders. If the number divides evenly, have the students write “yes” in the column on the graphic organizer. If the number does not divide evenly, have the students write “no” in the column on the graphic organizer.

4. After the graphic organizer is complete, have each team record their “yes”

examples on chart paper hanging around the room, one piece for each of the numbers 2, 3, 5, 6, 9, and 10.

5. Once this is done, have each team make a hypothesis about a “rule” for divisibility for each of the numbers 2, 3, 5, 9, and 10. Have them record their hypotheses on the graphic organizer labeled Divisibility Rules. It is important that each child have his or her own copy of the two graphic organizers because the next part of the lesson is done as a whole class.

During:

1. After teams have completed their Divisibility Test graphic organizer, recorded their numbers on the chart paper, and made hypotheses about divisibility on their Divisibility Rules graphic organizer, have them return to their individual seats for a whole-class lesson.

2. Using the chart paper lists as summaries of numbers generated by the class teams, discuss each chart and have the students share their hypotheses of divisibility rules. Guide their discussions to the correct rules for each number, and have them

6.B.1.b | 10

write them on the graphic organizer. Then have them trim the edges of their graphic organizers and glue them into their math journals for later referencing.

3. Ask the students if it is possible to divide their rules into two main categories, using a Venn Diagram to compare and contrast the categories. Lead them to separate the numbers where the ones digit determines the divisibility (2, 5, 10) from the numbers that require adding all the digits (3, 9). Have them complete a Venn Diagram in their math journals while you model one on the board.

4. Play Divisibility Rocks using students’ journals as reminders o the divisibility rules. Note: if this game is used as one station in a variety of center activities, fewer sets of the game will need to be produced.

After: Formative assessment: Check for accuracy as students write correct rules on their

graphic organizers, complete their Venn diagrams, and verbalize their responses during the Divisibility Rocks game.

Final assessment: Using the Divisibility Test graphic organizer as a master, list ten

numbers with a variety of divisibilities and have the students complete the chart with “yes” or “no” answers.

6.B.1.b | 11

Divisibility Test 1. Write the 24 numbers you created in the first column. 2. Decide if your numbers are divisible by 2, 3, 5, 6, 9, or 10. Write yes or no in the

correct columns.

Number 2 3 5 6 9 10

6.B.1.b | 12

Divisibility Rules Graphic Organizer

6.B.1.b | 13

Divisibility Rocks

1. Take a deck of cards, a Divisibility Key, and a bag of rocks/counters/chips. 2. Divide the cards face down evenly among players. Discard any extras. 3. Place the pile of rocks in the center of the playing circle. 4. Decide who is first. The person to his right is in charge of the Divisibility Key. 5. The first player turns over his top card and decides if the number on the card is

divisible by 2, 3, 5, 9, and 10. He takes one rock from the center pile for each “yes” answer.

6. If the player to the left disagrees, he or she may “challenge” by saying “Challenge!”

Then both players appeal to the person holding the key to see who is right. If the challenger is correct, that person gets the rocks. If the challenger is incorrect, the original player gets to keep the rocks and the challenger loses his or her turn.

7. Play continues clockwise with each person taking a turn, rotating the person who

holds the key and the person who is the challenger. 8. When every player has had a turn, the rocks are counted. Whoever has the most

rocks gets to keep all the cards from that turn. The rocks are returned to the center pile.

9. If there is a tie, both players involved in the tie turn over their next card and collect

the rocks for that card. Whoever holds the card that earns the most rocks wins the round.

10. A player is out when he or she is out of cards; the player with all the cards at the

end of the game is the winner.

11. To shorten the game, the teacher may set a time limit; the person with the most cards at the end of the allocated time is the winner.

6.B.1.b | 14

Divisibility Rocks Cards

24 34

35 36

44 46

48 55

6.B.1.b | 15


56 57

60 62

65 72

74 75

6.B.1.b | 16


80 84

98 115

117 128

130 140

6.B.1.b | 17


150 160

171 175

190 196

200 216

6.B.1.b | 18


240 256

260 285

308 309

335 338

6.B.1.b | 19


385 408

429 438

447 495

524 567

6.B.1.b | 20


625 657

666 669

700 711

715 728

6.B.1.b | 21


735 741

770 771

849 888

915 960

6.B.1.b | 22


1115 1135

1280 1324

2204 2220

2225 2318

6.B.1.b | 23

6.B.1.b | 24

Three-Digit Divisibility

A Problem Based Lesson Seed

Note: Students should be allowed to use calculators for this so that they can discover the pattern of divisibility by 3.

The problem:

• Who am I? • Each of my digits is different. • I am divisible by 3.

The above riddle has many different solutions. This poses a dilemma. How many answers are there to this riddle? What patterns do you see in all of the solutions? Can you discover a rule for dividing by 3? Your challenge is to see how many solutions you can find. With some mathematical thinking and organizational skills, you may be able to find all the solutions.

6.B.1.b | 25

Open Ended Problems

I’m thinking of a number. It is divisible by 5, it is odd, and it has 2 digits. What do

you know about the number?

Possible responses: It ends in 5. The tens’ digit can be any digit 1 through 9. If you count by 5s, every other number beginning with 15 and ending with 95 will work.

I’m thinking of a 3-digit number greater than 900. It’s divisible by 2, and the sum of

its digits is divisible by 6.

Possible responses: The hundreds digit must be 9. The units digit must be 0, 2, 4, 6, or 8. If the units digit is 0, the number could be 930 or 990 because 9 + 3 + 0 is divisible by 6, as is 9 + 9 + 0. If the units digit is 2, the number could be 912 or 972, because the sum of the digits must be either 12, 18, or 24. There are only 5 other possibilities: 954, 936, 996, 918, and 978. The tens digit must be odd.

6.B.1.b | 26

6.B.1.b | 27

Technology Links

Divisibility Rules Practice – This activity gives the students the rules and asks them which rules applies to the number that they are given. This activity would be good to send home to parents who often like a reminder of how the rules of divisibility work. http://www.vectorkids.com/vkdivisible.htm

Divisibility Dash – This is an APP for the itouch/iphone. Some schools have access to this technology. http://itunes.apple.com/us/app/everyday-mathematics divisibility/id428594346?mt=8itouch/iphone app

http://www.vectorkids.com/vkdivisible.htm�

6.B.1.b | 28


Name:

Which numbers on this sign are divisible by 3?

____________________________________


Name:

Which numbers on this sign are divisible by 3?

____________________________________

Welcome to Laketown! Established: 1793 Elevation: 1,347 feet Population: 8,634

Welcome to Laketown! Established: 1793 Elevation: 1,347 feet Population: 8,634

6.B.1.b | 29


Name:

1. An arena has 8,658 seats. The arena’s seats are

divided into equal sections.

2. Use the divisibility rules to determine if the number of

seats in the arena is divisible by 2, 3, 5, 9, or 10.

3. The seats are divisible by _______________.


Name:

1. An arena has 8,658 seats. The arena’s seats are

divided into equal sections.

2. Use the divisibility rules to determine if the number of

seats in the arena is divisible by 2, 3, 5, 9, or 10.

3. The seats are divisible by _______________.

6.B.1.c | 1

6.B.1.c Identify the greatest common factor AL: Use 2 numbers whose GCF is no more than 10 and whole numbers (0-100)


Resource Alignment – 6.B.1.c


Nimble with Numbers 4-5

86 98-101

5-6 135-136 142-143

Think Tank – Problem Solving Prickly Problems 5 14 Good Questions for Math Teaching

45 9 38 5

Fundamentals

These games involve finding factors and are a good prerequisite activity to finding GCF.

4-5 28-31 36-39

5-6 24-27

6.B.1.c | 2

Instructional Notes – 6.B.1.c

Greatest Common Factor (GCF) may also be referred to as Greatest Common Divisor

(GCD).

METHODS TO FIND GCF

Option A: Traditional Elementary Model

Steps Example: Find the GCF of 24 and 12 1. Have students list all of the factors of

each number. 12: 1, 2, 3, 4, 6, 12

24: 1, 2, 3, 4, 6, 8, 12, 24 2. Circle the highest number that they

both have in common. 12: 1, 2, 3, 4, 6, 12

24: 1, 2, 3, 4, 6, 8, 12, 24

6.B.1.c | 3

Option B: Venn Diagrams

Steps Example: Find the GCF of 24 and 36

1. Draw a Venn diagram.

2. Put all the factors in the Venn – the ones that are in common are placed in the intersection of the Venn.

3. Circle the largest factor they have in common in the intersection of the Venn. This is the GCF.

GCF = 12

6.B.1.c | 4

Option C: Prime Factorization To use this method, students must be able to identify prime numbers and find the prime factorization of a number (commonly found using a factor tree). The Virtual Manipulatives website has a program to practice prime factorization. This site is found at: http://www.matti.usu.edu/ma/nav/activity.jsp?sid=nlvm&cid=3_2&lid=202.


1. Find the prime factorization of both numbers.

Prime Factorization 24=2 x 2 x 3 36 = 2 x 2 x 3 x 3

2. Write down all the prime numbers that they have in common.

24=2 x 2 x 3 36 = 2 x 2 x 3 x 3

In common: 2 x 2 x 3

3. Multiply the numbers they have in common.

In common: 2 x 2 x 3 = 12

The GCF = 12

http://www.matti.usu.edu/ma/nav/activity.jsp?sid=nlvm&cid=3_2&lid=202�

6.B.1.c | 5

2 24 2 12 2 6 3 3 1

2 24 12

2 24 2 12 6

2 24 2 12 2 6 3 3 1

Option D: Alternate Prime Factorization Model – This model is the same as option C but written in a little different way. Sometimes this method is easier for students to understand because it looks like division.



Prime Factorization 24=2 x 2 x 3 36 = 2 x 2 x 3 x 3

2. Write down all the prime numbers that they have in common.

24=2 x 2 x 3 36 = 2 x 2 x 3 x 3

In common: 2 x 2 x 3

3. Multiply the numbers they have in common.

In common: 2 x 2 x 3 = 12

The GCF = 12

This format is just another way to find the prime factorization (like a factor tree). Here is how this method works:

1. Write down the number to be factored: 24

2. Draw a line beside and under the number (like an upside down division sign).

3. Think, “What prime number can I divide this number by? Write that prime number outside and complete the division.

4. Think again,” What prime number can I divide this number by? Write that prime number outside and complete the division.

5. Keep dividing the prime numbers out of the new number until you are left with “1”. Then stop.

2 24 2 12 2 6 3 3 1

3 36 3 12 2 4 2 2 1

24

6.B.1.c | 6

Lesson Seeds

Common Factor Riddles

GCF Problem Samples

GCF Song

GCF Bingo – This activity was adapted from Nimble with Numbers 6 & 7.

6.B.1.c | 7

Greatest Common Factor Bingo

Materials:

Greatest Common Factor Game Board 2 kinds of markers (one color for each player) paper clip and pencil for spinner Dry Erase Board

Classroom Setup: Groups of 3 students (2 players and 1 checker)

Directions:

1. Player A spins both spinners. The player uses their dry erase board to find the Greatest Common Factor (GCF). The checker in the group uses the answer key to check the solution. If it is correct, the player can cover that GCF on the board. If it is incorrect, they lose their turn.


6.B.1.c | 8

8 2 20 6

4 8 12 4

12 8 4 16

4 10 6 4

6.B.1.c | 9

1st Spinner

2nd Spinner GCF

12 28 4 12 30 6 12 32 4 12 40 4 12 56 4 12 60 12 16 28 4 16 30 2 16 32 16 16 40 8 16 56 8 16 60 4 20 28 4 20 30 10 20 32 4 20 40 20 20 56 4 20 60 20 24 28 4 24 30 6 24 32 8 24 40 8 24 56 8 24 60 12 36 28 4 36 30 6 36 32 4 36 40 4 36 56 4 36 60 12 48 28 4 48 30 6 48 32 16 48 40 8 48 56 8 48 60 12

6.B.1.c | 10

Greatest Common Factor Song Use the tune for Three Blind Mice

Greatest Common Factor

Greatest Common Factor

We will only use

We will only use

The factors which both the numbers share

Use only those twin common factors there

A common factor must have a pair,

In the Greatest Common Factor.

6.B.1.c | 11

Common Factor Riddles

I am a common factor of 27 and 45. I am an odd number. When you multiply me by 3, you get a number greater than 10. What number am I? I am a common factor of 36 and 48. I am also a factor of 30. I am an even number. I am divisible by 3. What number am I? I am a common factor of 60 and 100. I am an even number greater than 4. I am divisible by 4. What number am I? I am an odd number. I am a common factor of 135 and 210. I am greater than 7. What number am I?

I am a common factor of 24 and 60. I am an even number. I am divisible by 3 and 4. What number am I? I am an odd number. I am a common factor of 54 and 63. When you multiply me by 2, you get a number greater than 10. What number am I? I am a common factor of 80 and 120. I am greater than 5. I am less than 40. I am divisible by 4 and 10. What number am I?

I am an odd number. I am a common factor of 120 and 150. I am not prime. What number am I?

6.B.1.c | 12

GCF Sample Problems

1. You are making 75 mint chocolate bars and 45 caramel pecan bars for some gift

boxes. If each box will contain exactly the same bars, what is the greatest number of gift boxes you can put together? How many of each bar will be in a gift box?

2. A party store is making balloon bouquets for a Halloween party. Every bouquet will be identical. The store will use 24 orange, 36 black and 12 purple balloons altogether. What is the greatest number of balloon bouquets the store will put together? How many of each color balloon will be in a bouquet?

3. Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips?

4. I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?

5. Mrs. Evans has 120 crayons and 30 pieces of paper to give to her students. What is the largest # of students she can have in her class so that each student gets equal # of crayons and equal # of paper.

6. Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest size tile she can use?

6.B.1.c | 13

Technology Links

GCF Fruit Shoot – In this game students shoot the numbers that are the GCF of the given numbers. http://www.sheppardsoftware.com/mathgames/fractions/GreatestCommonFactor.htm

http://www.sheppardsoftware.com/mathgames/fractions/GreatestCommonFactor.htm�

6.B.1.c | 14

Exit Slip – 6.B.1.c

Name: Fill in the blanks.

1. The greatest common factor (GCF) is the _______________ factor shared by two numbers. (largest or smallest)

2. The GCF of 36 and 45 is __________.

3. Look at these numbers: 20 48

What is the greatest common factor (GCF)? __________


Name: Fill in the blanks.

1. The greatest common factor (GCF) is the _______________ factor shared by two numbers. (largest or smallest)

2. The GCF of 36 and 45 is __________.

3. Look at these numbers: 20 48

What is the greatest common factor (GCF)? __________

6.B.1.c | 15


Name:

Find the GCF:

1. 12, 8 __________

2. 12, 18 __________

3. 27, 18 __________


Name:

Find the GCF:

1. 12, 8 __________

2. 12, 18 __________

3. 27, 18 __________

6.B.1.d | 1

6.B.1.d Identify a common multiple and the least common multiple AL: Use no more than 4 single digit whole numbers

Math at Hand by Great Source, page 061. Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and Lovin, pages 166.

Resource Alignment – 6.B.1.d


Hot Math Topics

Algebraic Reasoning 5 17, 82 Estimation &


5 1

Think Tank – Problem Solving Head Polishers 5 4 Thorough Thinkers 5 11 Cool Heads 5 20

The following Grade 4 Think Tank (Problem Solving) cards practice finding multiples. Think Tank – Problem Solving

Brain Boosters 4 12 Cracker Jacks 4 4 Thorough Thinkers 4 9 Cool Heads 4 4

Math Drills to Thrill by Kim Sutton

164-166

6.B.1.d | 2

Instructional Notes – 6.B.1.d

METHODS TO FIND LCM

Option A: Traditional Elementary Model

Steps Example: Find the LCM of 3 and 8 1. Have students list all of the multiples

of each number. 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 8: 8, 16, 24, 32, 40, 48, 56, 64, 72

2. Circle the least number that they both have in common.

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 8: 8, 16, 24, 32, 40, 48, 56, 64, 72

The LCM = 24

Option B: Venn Diagrams


1. Draw a Venn diagram.

2. Put all the factors in the Venn – the ones that are in common are placed in the intersection of the Venn.

3. Circle the smallest multiple they have in common in the intersection of the Venn. This is the LCM.

The LCM is 24.

6.B.1.d | 3

Option C: Prime Factorization To use this method, students must be able to identify prime numbers and find the prime factorization of a number (commonly found using a factor tree). The Virtual Manipulatives website has a program to practice prime factorization. This site is found at: http://www.matti.usu.edu/ma/nav/activity.jsp?sid=nlvm&cid=3_2&lid=202.

Steps Example: Find the LCM of 6 and 8


Prime Factorization 6 = 2 x 3 8 = 2 x 2 x 2

2. Count the number of times each prime

number appears in each of the factorizations...

The number of primes in 6 is one 2 & one 3.

The number of primes in 8 are three 2’s.

3. For each prime number, take the largest of these counts.

The largest number of 2’s is three. The largest number of 3’s is one.

So…the LCM is 2 x 2 x 2 x 3 which is 24.

http://www.matti.usu.edu/ma/nav/activity.jsp?sid=nlvm&cid=3_2&lid=202�

6.B.1.d | 4

MSDE Information – 6.B.1.d

MSDE PUBLIC RELEASE QUESTION #1

Bengy is working at a restaurant. Bread is delivered to the restaurant every third day. Meat is delivered to the restaurant every fifth day. Both were delivered today. In how many days will both items again be delivered on the same day?

A. 3 B. 5 C. 8 D. 15

Correct Answer: D

MSDE PUBLIC RELEASE QUESTION #2

Christina takes out the trash every 3 days. She cleans her room every 4 days. She feeds her pet turtle every 6 days. Christina took out the trash, cleaned her room, and fed her turtle today.

In exactly how many days will she do all three of these tasks again on the same day?

A. 6 B. 8 C. 12 D. 18

Correct Answer: C

6.B.1.d | 5

Lesson Seeds

Math Drills to Thrill by Kim Sutton pages 164-166 – This book

gives students an opportunity to practice finding multiples of a number. Once students know the multiples of a number they can use this information to find the LCM.

Least Common Multiple Bingo - Adapted from Nimble with Numbers 6 & 7.

LCM Sample Problems

Sum Squares Puzzles – These are puzzles that are similar to those that are

produced by Origo Math (Zuplez). These are original and do not duplicate these cards (These were not purchased by the county. Some schools purchased them on their own). These cards were created to fit the grade 4 and 5 objectives from the State Curriculum. When using, the students fill in the digits so that each row and column has the sum that is indicated (beside each row and column). Students should first fill in the digits that have clues that they can solve.

Hot Math Topics: Fractions and Decimals #29 – One way students could solve this problem would be to find a common multiple.

6.B.1.d | 6

Least Common Multiple Bingo

Materials:

Least Common Multiple Game Board 2 kinds of markers (one color for each player) paper clip and pencil for spinner Dry Erase Board

Classroom Setup: Groups of 3 students (2 players and 1 checker)

Directions:

1. Player A spins both spinners. The player uses their dry erase board to find the Least Common Multiple (LCM). The checker in the group uses the answer key to check the solution. If it is correct, the player can cover that LCM on the board. If it is incorrect, they lose their turn.


6.B.1.d | 7

12 15 4 35 10

24 8 30 42 6

6 40 21 12 20

12 3 14 7 28

8 12 5 6 4

6.B.1.d | 8

1st Spinner

2nd Spinner LCM

1 3 3 1 4 4 1 5 5 1 6 6 1 7 7 1 8 8 2 3 6 2 4 4 2 5 10 2 6 6 2 7 14 2 8 8 3 3 3 3 4 12 3 5 15 3 6 6 3 7 21 3 8 24 4 3 12 4 4 4 4 5 20 4 6 12 4 7 28 4 8 8 5 3 15 5 4 20 5 5 5 5 6 30 5 7 35 5 8 40 6 3 6 6 4 12 6 5 30 6 6 6 6 7 42 6 8 24

6.B.1.d | 9

LCM Sample Problems

1. A package of hotdogs contains 10 hot dogs. A package of bun contains 8 buns.

What is the least number packages of buns and hot dogs you must purchase, so you won’t have left over hot dogs?

2. You are making cookies for a party. You are not sure whether you will have 12

friends or 20 friends show up at the party, and you want each person to have the same number of cookies. What is the least number of cookies you must make in order to share equally with either 12 friends, or with 20 friends?

3. Ben exercises every 12 days and Isabel every 8 days. Ben and Isabel both exercised today. How many days will it be until they exercise together again?

4. The radio station Z100 gave away a $100 bill for every 100th caller. Every 30th caller received free concert tickets. How many callers must get through before one of them receives both a coupon and a concert ticket?

5. Two bikers are riding a circular path. The first rider completes a round in 12 minutes. The second rider completes a round in 18 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?

6. Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How many of each piece would each child need to build tracks that are equal in length?

6.B.1.d | 10

Hot Math Topics: Fractions and Decimals

6.B.1.d | 11

Exit Slip – 6.B.1.d

Name:

1. The least common multiple (LCM) is the ______________ (smallest or largest) multiple shared by two numbers.

2. Look at these three numbers: 3, 4, 5 What is the LCM of these numbers? ________________


Name:

3. The least common multiple (LCM) is the ______________ (smallest or largest) multiple shared by two numbers.

4. Look at these three numbers: 3, 4, 5 What is the LCM of these numbers? ________________

6.B.1.d | 12


Name: On Monday Joe had both soccer and baseball practice. If he has soccer every three days

and baseball every 5 days, on what day will he have both soccer and baseball again?

_____________________


Name: On Monday Joe had both soccer and baseball practice. If he has soccer every three days

and baseball every 5 days, on what day will he have both soccer and baseball again?

_____________________

6.B.1.d | 13


Name: Find the LCM:

1. 8, 4, 6 ________

2. 5, 4, 2 ________

3. 4, 9 ________


Name: Find the LCM:

1. 8, 4, 6 ________

2. 5, 4, 2 ________

3. 4, 9 ________

6.C.1.a | 1

6.C.1.a Multiply whole numbers AL: Use a 3-digit factor by another factor with no more than 2-digits and whole numbers (0 - 10,000)

Elementary and Middle School Mathematics, Seventh Edition, by John Van de Walle, Karen Karp, and Jennifer Bay-Williams, pages 226-231. Teaching Student-Centered Mathematics Grades 3-5 by Van de Walle and Lovin, pages 8, 15, 116-118, 120, 129-130. Math at Hand by Great Source, page 137-141.

6.C.1.a | 2

Resource Alignment – 6.C.1.a


Hot Math Topics Estimation and


5

4, 5, 10, 12, 14, 23, 36, 54, 55, 73, 75


55, 56-59, 60-61, 62-63, 64-70

Think Tank - Computation

Speedy Starters 5 2, 10 Brain Builders 3, 4 Mental Teasers 8, 14 Mind Benders 8, 15 Super Solvers 10, 20 Grand Masters 6, 9


30 2, 8

32 8

Fundamentals

4-5 20-23, 36-39

5-6 12-15 16-19 20-23

Mathementals 5 55-76 Math Focus Activities by Kim Sutton


50-53

6.C.1.a | 3


This website gives teachers examples of alternative algorithms for division. Each

method includes a video demonstration of the alternative algorithm. http://mb.msdpt.k12.in.us/Math/Algorithms.html

Below are examples (array, partial products, lattice, algorithm, etc…) of different ways to solve multiplication problems. Students should be allowed to choose the method they prefer as long as the method is “efficient” and “accurate”.

Multiplication Models: Below are two models of multiplication that can assist

students in looking at different ways to break apart numbers to multiply.

http://mb.msdpt.k12.in.us/Math/Algorithms.html�

6.C.1.a | 4

6.C.1.a | 5

6.C.1.a | 6

Lesson Seeds

Fundamentals 4-5 and 5-6 – Both of these books include games to practice mental

math strategies with computation concepts. In unit 5 it is still very important to continue to help students develop mental computation concepts. Developing mental math concepts will also help students with estimating. Students who lack number sense and mental math strategies are often unable to estimate efficiently.

Math Strings – Adapted from Minilessons for Extending Multiplication and Division by Fosnot and Uittenborgaard. What are math strings? Math strings are designed as a whole group, on the carpet, guided and explicit mini-lesson to help students develop efficient computation skills. These lessons can also be used with small groups of students as you need to differentiate instruction. These mini-lesson strings are “tightly structured computation problems” designed to help students be able to look at number first, make connections, and then decide on the computation strategy to be used. These strings are designed to support the development of a variety of mental math strategies as well as traditional algorithms.

Cluster Problems – These problems give students a “cluster” of expressions that could be used to solve the given problem. Students may use one, or more, or none of the suggested problems. This scaffolding will help some students get started and for other students it will give them some other ways to think of the problem.

NCTM Sample Problems

The Candy Bar Problem – This is a lesson seed for a problem based lesson.

The Penny Problem – This is a lesson seed for a problem based lesson.

Product Problem – This is a lesson seed for a problem based lesson.

6.C.1.a | 7

Math Strings

What are math strings? Math strings are designed as a whole group, on the carpet, guided and explicit mini-lesson to help students develop efficient computation skills. These lessons can also be used with small groups of students as you need to differentiate instruction. These mini-lesson strings are “tightly structured computation problems” designed to help students be able to look at number first, make connections, and then decide on the computation strategy to be used. These strings are designed to support the development of a variety of mental math strategies as well as traditional algorithms. What materials does the teacher need?

• Large chart paper (Teachers are encouraged to use paper so that they can be referred to later on in lessons and when doing future strings as opposed to writing on the board and erasing.)

• 2 markers (different colors)

How do I use these math strings in my classroom? Math string mini-lessons are usually done with the whole class together in a meeting area (carpet/rug). This allows students to interact with you and each other (think/pair/share) as appropriate. The problems are written one at a time (use one color ink for the problem and another color for the student’s thinking) and the learners are asked to determine an answer. Students are encouraged to use mental math, but they do not have to always compute mentally. Encourage students to examine the numbers in the problem and think about creating, efficient ways to find the solution. As students share their thinking, the teacher will write their thinking using a different color marker (so that the students can clearly see the thinking they brought to the problem). It is also important to see if students can discover the relationships between each of the problems in the string. Keep in mind that we need to honor students’ strategies when using strings. Teachers should accept alternative solutions and explore why they work. Use models and

6.C.1.a | 8

manipulatives as needed to facilitate thinking. The intent is not to box students into one particular strategy but to help students developed number sense, computation, problem solving, and critical thinking. Second, do not use the string as a recipe that cannot be varied. You will need to be flexible. The strings are designed to encourage discussion and reflection on various strategies important for numeracy. The math strings below are samples of strings that can be used in your classroom. Teachers are encouraged to develop their own strings based on the knowledge and level of their own students.

These strings are designed so that students can see how breaking apart a number can help in finding the product. For example, if a student is given the problem 2 x 32, the goal is for them to see the ways they can break it apart. In this case 2 x 10 (this is easy if kids understand the pattern of multiplication by 10), added 3 times (20 + 20 + 20), plus the product of 2 x 2 (4). Thus they would find the answer to be 60 + 4 or 64. Student could short cut this process by multiplying 2 x 30 (60) and then adding the product of 2 x 2 (4).

6.C.1.a | 9

Multiplication String Samples The questions typed small between problems are questions that teachers can ask

students to help guide them in their thinking.

String 1 String 2 String 3 String 4 3 x 10 3 x 40

How does the 1st problem relate to the 2nd problem?

3 x 42 How could our answers to

the first 2 problems help us with this problem?

How can what we learned in the first three problems help

you with these problems? 6 x 10 6 x 50 6 x 53

4 x 100 4 x 2

4 x 98 How are the first 2 problems similar to the 3rd problem? Could you use the products of the first two problems to

help you solve the last problem?

6 x 200 6 x 14

6 x 186 How are the first 2 problems similar to the 3rd problem? Could you use the products of the first two problems to

help you solve the last problem?

What strategies helped us

solve these problems?

2 x 500 2 x 530 2 x 532

4 x 500 4 x 530 4 x 532

What do you notice about the product of 2 x 532 and 4 x 532? How could this help you in solving problems that are multiplied by 4?

2 x 500 2 x 580 2 x 581

10 x 581 20 x 581 22 x 581


5 x 350 5 x 353

How could multiplying by 10 help you with these problems?

10 x 9 9 x 10

What do you notice about the first two problems? Is

this always true? 3 x 9

13 x 9 100 x 9 9 x 136

43 x 1,000 43 x 100 43 x 10 43 x 1

43 x 0.1 43 x 0.01

3 x 7 6 x 7

How does 3 x 7 relate to 6 x 7? Do the products have a

similar relationship?

36 x 7 18 x 14

How do these two problems relate? Could this

relationship help you find 18 x 14 without using the traditional algorithm?

28 x 18 56 x 36

How do these two problems relate? Could this

relationship help you find 18 x 14 without using the traditional algorithm?

6.C.1.a | 10


How do the first two problems relate to each

other? How can we use the first product to help us solve

the second problem?

99 x 15 Which other problem most

closely relates to this problem?

110 x 15 200 x 15 201 x 15

1001 x 15 999 x 15

4 x 25 Can you relate this to

money? How could quarters help you solve this problem?

16 x 25 400 x 25

Could the first problem help you solve this problem?

1600 x 25 How does this relate to 16 x

25?

30 x 100 30 x 50 32 x 50 33 x 50 84 x 50

10 x 127 127 x 2

12 x 127 10 x 44 9 x 44 9 x 43 8 x 43

10 x 126 126 x 2

12 x 126 10 x 49 9 x 49 9x 48 8 x 48

6.C.1.a | 11

Sample Cluster Problems

Solve the problem 67 x 6.

You may want to consider using on the following expressions to help you:

7 x 6 6 x 6 10 x 7 60 x 6 10 x 6

Be prepared to explain how you solved the problem. Can you solve this problem a different way?

Solve the problem 96 x 52


96 x 100 96 x 50 96 x 2 100 x 52 4 x 52




60 x 50 2 x 50 62 x 100 60 x 100


6.C.1.a | 12

Solve the problem 235 ÷ 5


100 ÷ 5 200 ÷ 5 35 ÷ 5 5 x 20 5 x 7




3 x 82 10 x 82 5 x 82 30 x 82 300 x 82 310 x 82




400 x 9 500 x 9 90 x 9 8 x 9 2 x 9




7 x 40 300 x 40 250 x 40 280 x 40 282 x 10 282 x 20

2 x 40 80 x 40


6.C.1.a | 13



25 x 10 25 x 100 25 x 50 10 x 160 20 x 160 5 x 160




103 x 100 100 x 100 3 x 100 100 x 75 100 x 70 3 x 5 100 x 50


Solve the problem 1,640 ÷ 40


1,000 ÷ 40 1,600 ÷ 40 600 ÷ 40 2,000 ÷ 40 80 ÷ 40 320 ÷ 40


6.C.1.a | 14

NCTM Sample Problems

NCTM Problems - These problems can be made into problem based lessons

and/or challenge problems or projects to extend and connect students’ thinking about math concepts.

After studying the length of a dinosaur's stride the distance between its footprints—scientists have determined from tracks made by medium-sized dinosaurs that the fastest speed they could travel was about 27 miles per hour. At this speed, how long would it take a medium-sized dinosaur to travel 60 miles? How long would it take this dinosaur to travel 167 miles? How long would it take this dinosaur to travel from your home to your school? From your school to the nearest park or grocery store? Try counting the blades of grass in the patch of lawn that you are sitting on. It is not as hard as it sounds. Cut a one-inch square from the middle of a piece of paper. Lay the paper with its one-inch hole on the grass. Count only the blades of grass that peek through the hole. Figure out how many square inches of grass are in the patch of lawn. How could this information help you find the solution? National parks are among America's treasures. A Congressional act set aside nearly 400 sites because of their unique physical or cultural value to the nation. The U.S. Department of the Interior oversees the parks for public use, including Yellowstone National Park in Wyoming, Yosemite National Park in California, and Bryce Canyon and Zion National Parks in Utah. Imagine you have decided to take a journey around the country to see all these parks. How many months would it take if you decided to visit 2 parks per month? 4 parks per month? 6 parks per month? 8? 10? How many years would it take at those rates? Organize your data by making a chart. Look for patterns and share what you notice with a friend. To learn more about the national parks, visit www.seeamerica.org.

The 112 fourth-grade students at Edgemont Elementary School are planning to donate pennies to a local charity. About how many pennies will each student need to bring to school if they are to meet their goal of collecting $75? If your grade level was to donate the same amount, how many pennies would each student need to bring?

http://www.seeamerica.org/�

6.C.1.a | 15

The Candy Bar Problem


This problem has a nice connection to objective 3.C.2.b. This problem requires

students to convert miles to inches. Let students use the internet to find the number of feet in a mile, if they don’t know it already know this information (they probably won’t know this).

Materials: 1 candy bar for each group (it is suggested that each group have a different

length of candy bar) chart paper internet access rulers

The Problem: How many candy bars would be in a mile if they were laid end to end? Round your candy bar to the nearest inch. Be prepared to explain and justify your solution. Classroom Set-up: There are several ways to set up this problem. Variation 1: Each group has the same length of candy bar.

Variation 2: Each group has a different length of candy bar. In the end this

allows the teacher to ask questions such as: “Why did the groups with shorter candy bars have larger answers?”, etc…

Variation 3: Put the class into 6 groups and have three different length candy

bars – each candy bar would be in two groups. This allows groups to check their solution against another group with the same length bar and discuss the question in Variation 2.

6.C.1.a | 16

The Penny Problem


This problem has a nice connection to objective 3.C.2.b. This problem requires

students to convert miles to inches. Let students use the internet to find the number of feet in a mile, if they don’t know it already know this information (they probably won’t know this).

Materials: coins chart paper internet access rulers

The Problem: How many pennies (or dimes, nickels, quarters, etc…) would it take to cover a distance of two miles? Classroom Set-up: There are several ways to set up this problem. Variation 1: Each group uses the penny.

Variation 2: Each group has a different coin in the problem. In the end this

allows the teacher to ask questions such as: “Why did the groups with coins with shorter diameters have larger answers?”, etc…

Variation 3: Put the class into 6 groups and have three different coins – each

coin would be in two groups. This allows groups to check their solution against another group with the same length bar and discuss the question in Variation 2.

6.C.1.a | 17

The Product Problem


This problem will probably lead students to “guess and check”. This is an

appropriate strategy if students can organize the numbers they tried that didn’t work and use this information to make reasonable guesses! For example if they start with the number 5 and the solution is too small that they would have to try a larger start number. If they try the number 3 next ask them questions such as “When you used the number 5 what was your solution? What does this answer tell you?”

The Problem: I’m thinking of a number. Multiply the number by itself and then by itself again and you will get 216. What is the number? How do you know?

6.C.1.a | 18


Name: Mrs. Jacob’s has 25 students in her class. Each student brought in 20 pencils to use this school year. How many total pencils does Mrs. Jacob’s class have? You may want to consider using one of the following expressions to help you solve this problem. If you do, circle the one(s) you use and show your work. If you choose not to use one of the expressions, be sure to show the work that you use to solve the problem.

25 x 100 25 x 10 5 x 20 20 x 20


Name: Mrs. Jacob’s has 25 students in her class. Each student brought in 20 pencils to use this school year. How many total pencils does Mrs. Jacob’s class have? You may want to consider using one of the following expressions to help you solve this problem. If you do, circle the one(s) you use and show your work. If you choose not to use one of the expressions, be sure to show the work that you use to solve the problem.

25 x 100 25 x 10 5 x 20 20 x 20

6.C.1.a | 19


Name: A dishwasher sells for $399 at one store. The store sold 42 of these dishwashers this month. What were the total sales on this model of dishwasher? Be sure to show your work.


Name: A dishwasher sells for $399 at one store. The store sold 42 of these dishwashers this month. What were the total sales on this model of dishwasher? Be sure to show your work.

6.C.1.b | 1

6.C.1.b Divide whole numbers AL: Use a dividend with no more than a 4-digits by a 2-digit divisor and whole numbers (0 – 9999)



6.C.1.b | 2



The Super Source Base Ten Blocks 5-6 42 20 Thinking Questions Base Ten Blocks 3-6 70

Hot Math Topics Estimation and


5 4, 36, 41,

51, 63, 73, 75


54, 56-59, 62-63, 64-70

Think Tank - Computation

Speedy Starters 5 6, 11 Mental Teasers 5 11, 15 Mind Benders 5 9 Pace Setters 5 10 Super Solvers 5 15

Think Tank – Problem Solving Super Sleuths 5 14 Mega Minds 5 16


43 2 44 4, 5

Mathementals 5 81-96 Fundamentals 5-6 8-11 Math Focus Activities by Kim Sutton


54-57

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It is highly suggested that teachers take time to have students explore what happens

when students divide numbers by 10, 100, 1000. Students can use calculators to explore what happens when numbers of different size are divided by 10, 100, and 1000. Once they try problems, students should be able to make a generalization about division by 10, 100, 1000. Once students understand the pattern of division of 10, 100, and 1000 they will be able to employ flexible strategies to the division of larger numbers.

Be sure to read Teaching Student-Centered Mathematics Grades 3-5 by Van de

Walle and Lovin, Pages 121-123. Van de Walle suggests several methods of division such as using partial products, repeated subtraction, explicit trades, etc…

Elementary and Middle School Mathematics by Van de Walle, John, Karp, Karen, Bay-

Williams, Jennifer. 2010. Pages 232-237. Begin with Models. Traditionally, if we were to do a problem such as 583 divided by

4, we might say “4 goes into 5 one time.” This is quite mysterious to children. How can you just ignore the “83” and keep changing the problem? Preferably, you want students to think of 583 as 5 hundreds, 8 tens, and 3 ones, not as the independent digits 5, 8, and 3. One idea is to use a real-world context to understand the problem.

Language plays an enormous role in thinking about the algorithm conceptually.

Most adults are so accustomed to the “goes into” language that it is hard to let it go. For the problem 583 ÷ 4, here is some suggested language:

o I want to share 5 hundreds, 8 tens, and 3 ones amoung these four sets. There are enough hundreds for each set to get 1 hundred. That leaves 1 hundred that I can’t share.

o I’ll trade the hundred for 10 tens. That gives me a total of 18 tens. I can give each 4 tens and have 2 tens left over. Two tens is not enough to go around the four sets.

o I can trade the 2 tens for 20 ones and put those with the 3 ones I already had. That makes a total of 23 ones. I can give 5 ones in each of the four sets. That

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leaves me with 3 ones as a remainder. In all I gave out to each group 1 hundred, 4 tens, and 5 ones with 3 left over for 145 r 3.

Based on the information about invented strategies a

WCPS resource that can be used to explore these strategies are Origo Fundamentals and Mathementals resource books.

Additional Invented Strategies for multiplication might include:

o Halve – multiples of 10 o Halve – dividing by 4 o Place Value o Divide the parts o Break up the dividend

This website gives teachers examples of alternative algorithms for division. Each

method includes a video demonstration of the alternative algorithm. http://mb.msdpt.k12.in.us/Math/Algorithms.html

http://mb.msdpt.k12.in.us/Math/Algorithms.html�

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Division Models: Below are four different models of division that students can use. Ruby has a 224 photos. Each page of her photo album hold 17 pictures. How many pages will she fill up completely with her pictures? Repeated Subtraction Chimney Division Alternate Method Traditional Algorithm

In this model students find the number of pages by subtracting 17, repeatedly, until no more groups of 17 can be subtracted. This model is effective if students do not know their multiplication facts but, they must be able to subtract accurately and it takes up lots of paper.

This method asks students to look at the dividend as a whole number instead of as digits as in the traditional algorithm. Students think, how many groups of 17 can I take out of 224? They may choose any number as long as the product is less than or equal to 224. Many students will start with 10. Each time they multiply and subtract they write the partial quotients above the problem. In the end they add all of the partial quotients to get the solution (in this case 13 R 3).

This alternate method uses partial solutions to solve the problem. Like the chimney method, students look at the dividend as a whole number instead of digits and think, “How many groups of 17 are in 224?”

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6.C.1.b | 7

Partial Quotient Sample

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Lesson Seeds

Open-Ended Problems

More Open-Ended Problems

Division Poem

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Open-Ended Problems

There are many great open-ended problems in the purple book titled, Good Questions for Math Teaching. Here are some additional open-ended division problems:

o Nine hundred people were divided into teams. If there were always the same number of people on all teams, what do you know about the number of possible teams and the number of members on each team?

o A group of students shared 120 cookies. What can you say about the number of students and the number of cookies they each got?

o Richardsville School has 600 students in K-5. There are as close to 18 students per class as possible. What can you say about the number of classes?

o Lincoln Elementary has nearly 1,000 children from K-5, with about the same number of students in each grade. Most classes have close to 25 students. No class has more than 25 students. What can you figure out from this information?

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More Open Ended Problems

A number of cookies may be divided onto two plates so that each plate contains

the same number of cookies. How many cookies might there be and how could they be split?

Possible responses: If there were two-dozen cookies, there would be one dozen, or 12 cookies on each plate. If there were 13 cookies, there would be 6 ½ on each plate. If there is an even number of cookies there are only whole cookies on the plates, but if there is an odd number of cookies, one cookie can be broken in half and there will still be an equal number on both plates.

Martha collects pennies. She likes to put them in more than one stack, keeping the stacks equal in size, with more than one penny in each stack. With the pennies she has now, she can put them into equal stacks in more than one way without any leftover pennies. What do you know about the number of pennies she has?

Possible responses: If she has 50 pennies, she can put them in stacks of 2, 5, 10, and 25. She can’t have 5 pennies. She can’t have 25 pennies (there is only one way to put these in stacks of 5). The smallest number she could have is 6.

Nine hundred people were divided into teams. If there were always the same number of people on all teams, what do you know about the number of possible teams and the number of members on each team?**

Possible responses: If a team must contain more than 1 person, then the smallest team could have 2 members, and there would be 450 two-member teams. There could be teams of 3, 4, 5, 6, 10, 15, 18 and other numbers. There could be 30 teams with 30 team members. There could also be 45 teams of 20. 900 can be divided evenly many ways. **This problem would also work well for divisibility.

A group of students shared 120 cookies. What can you say about the number of students and the number of cookies they each got?

Possible response: If the group is a multiple of 2 then they each got the same number of cookies.

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The Opposite of Multiplication is the Rule

by Wendy M. Smith

The components of division, Shared a little house.

Dividend on the inside, Divisor on the out.

The quotient always somehow,

Ends up on the roof. Listen to this story,

You’ll enjoy my little spoof.

Divisor, Divisor, Was knocking at the door.

Dividend said, “You can’t enter anymore!”

“Every time you do,

You make me scream and shout. You split me into equal parts,

With a remainder lying about.”

“I understand the opposite, Of multiplication is the rule.

But I don’t care, I wonder how You could be so cruel!”

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Name: On Tuesday, the library received a shipment of 234 books. Twelve librarians were available to shelve the books. Each librarian shelved an equal number of books. The rest are waiting to be put away on Wednesday. How many books did each librarian shelve on Tuesday?


Name: On Tuesday, the library received a shipment of 234 books. Twelve librarians were available to shelve the books. Each librarian shelved an equal number of books. The rest are waiting to be put away on Wednesday. How many books did each librarian shelve on Tuesday?

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Name: Renaldo has 644 marbles. He wants to put them in bags that hold 23 marbles each. How many full bags of marbles will he have?


Name: Renaldo has 644 marbles. He wants to put them in bags that hold 23 marbles each. How many full bags of marbles will he have?

6.C.1.c | 1

6.C.1.c Interpret quotients and remainders mathematically and in the context of a problem AL: Use dividend with no more than a 3-digits by a 1 or 2 digit divisor and whole numbers (0 – 999)

Math at Hand by Great Source, page 148-149.

Resource Alignment – 6.C.1.c


The Super Source Base Ten Blocks 5-6 42 20 Thinking Questions Base Ten Blocks 3-6 18, 50 Hot Math Topics

Estimation and Computation with Large Numbers

5 20, 41, 63

Nimble with Numbers 5-6 54,

62-63 64-70


23 5, 7, 8 43 2 44 8

Fundamentals 5-6 28-31 4-5 24-27

Number Sense 4-6 209-211

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Literature Links – 6.C.1.c

Book Location Notes

Divide and Ride by Stuart Murphy

MathStart Literature

Book Location: SAS Resource

Library

In order to ride the Dare-Devil roller coaster at the Carnival, there must be two kids in each seat. But what if you're part of a group of 11 best friends? Ten kids will fit in five seats, but what do you do about the one who's "left over"? Meanwhile, chairs on the Satellite Wheel seat three, which means two best friends will be left over. Every ride presents a problem. Can the

kids figure out how to fill all the seats so that everybody gets to ride?

Understanding the meaning of remainders in simple division problems is a precursor

to solving more difficult division problems. Illustrated by George Ulrich.

Instructional Notes – 6.C.1.c

This objective is best when taught with a real-world context. Without a context

it is impossible for children to interpret the solution. In real life, most division problems have remainders that need to be dealt with in context. Children need to encounter lots of problems in which the context affects the remainder differently. Young Mathematicians at Work by Catherine Twomey Fosnot and Maarten Dolk.


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Lesson Seeds

Three Remainder Plays – These are three plays to explore the concept of remainders

(“Round-Up”, “You Just Drop It”, “Sharing is Very Important”). Each one deals with real-world situations and how to interpret remainders. All three plays are important to considering the different ways to interpret remainders. It is recommended that all three plays be used and afterward have a whole class discussion (where process charts are created) where the situations and solutions are discussed

Remainder Plays Questions for Discussion – It is very important that students can

discuss these plays so that they can form generalizations about each type of interpretation of remainders. It is highly recommended that these questions be discussed as a whole group and that they class creates a process chart about each type of remainder interpretation. The answers to the listed questions could be used to create the process chart.

Remainder Stories – These are intended to be used after students have read the 3

Remainder Plays and have a whole group class discussion of the play questions. These problems could be used a sort as well as having students solve them.

Remainder Game

Remainder Sample Problems

Remainder of One Lesson by Marilyn Burns – This lesson sample can give discussion

ideas to help teachers guide students in making meaning from remainders.

20 Thinking Questions Base Ten Blocks – Question 11

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6.C.1.c | 5

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Round-Up!

Characters: Narrator Wrangler John Mom Tyler Nikki Brittany Tyler’s Dad Voice

Scene 1 Narrator: Our play begins in the family room of a modern home where two 11-year-old children are gathered around the TV. Mom: (entering from the kitchen) Tyler! Nikki! I want to talk to you! (The children stay glued to the TV.) Nikki! Tyler! You’ll want to hear what I have to say! Tyler and Nikki together: Okay, Mom, what’s up? Mom: We have our plans for the family reunion. We’re going to a dude ranch with all the cousins. You’ll spend a week away from the TV—riding horses, rafting a river. You might even get to take part in a cattle round up! Tyler: Cool! When are we going? Mom: Next Friday. Nikki: Can I ride with my cousin Brittany?” Mom: Everyone’s coming to our house to meet. I don’t think we’ll need to take everyone’s cars. Gas is so expensive, we might as well take as few cars as possible.

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Scene 2

Narrator: Now the setting changes to the front yard outside Nikki and Tyler’s house. All the relatives are gathered to go to the reunion together. Nikki is standing by her mom, not really listening. Tyler is standing next to his dad. Tyler’s dad: All right, everyone! Stand together! How many people do we have? Let’s see…I think we have 23 people, counting all the children. Each car we are taking has 5 seat belts, so how many cars do we need? Tyler: That’s easy, Dad. 23 divided by 5 = 4R3. We need 4R3 cars! Narrator: A strange voice is heard above the crowd. Everyone freezes as it calls in a low, slow, Western drawl… Voice: Round-up! Narrator: Slowly the action returns, but Tyler acts as if he has been struck by lightning. Tyler: Dad, no. We don’t need 4R3 cars. I have to round up that remainder. We need 5 cars.

Scene 3 Narrator: We join our cast outside the main lodge at the No-Remainder Ranch. Nikki and her mom are standing in front of Wrangler John. Wrangler John: Welcome, everyone! Gather round so I can assign you a bunk. Let’s see, there are 23 of you, and I can put 4 in a cabin. How many cabins do I need? Nikki: I can do that problem in my head! 23 divided by 4 = 5R3. We need 5R3 cabins! Narrator: Again, a strange voice is heard above the crowd. Everyone freezes as it calls in a low, slow, Western drawl… Voice: Round-up! Narrator: Slowly the action returns, but now Nikki acts as if she has been struck by lightning.

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Nikki: Wait! 5R3 cabins doesn’t make any sense. I need to round up the remainder! We need 6 cabins for 23 people. One bunk will just have to be empty.

Scene 4 Narrator: Join Nikki and Tyler’s family in a clearing next to the bank of a fast-moving river. Family members are putting on life jackets and waiting for instructions from Wrangler John. Nikki and her cousin Brittany are standing together. Wrangler John: Be sure your life jacket is on properly. The river is fast and you will encounter some class 4 rapids. We haven’t lost anyone yet this year, and we don’t expect to. Each raft holds 6 guests, plus a guide who knows the river well. Let’s see…we have 23 guests. How many rafts do we need to take? Brittany: That’s easy! 23 divided by 6 = 3R5. We need 3R5 rafts! Narrator: Everyone suddenly becomes silent. Tyler and Nikki look around, as if expecting the voice. And, sure enough, seemingly out of nowhere, it calls… Voice: Round-up! Narrator: Brittany rubs her forehead as if she has been hit by lightning. Then she excitedly calls… Brittany: Wait! 3R5 rafts doesn’t make any sense! I have to round up! We need 4 rafts.

Scene 5 Narrator: It’s night time, and the guests of the No-Remainder Ranch are seated around a campfire. They are listening to Wrangler John tell stories about the mountains around them. Wrangler John: Do you want to hear another story? Tyler, Nikki, Brittany: Yes! Wrangler John: Well, okay. This story has been around for a long time, and folks around here believe it to be true. Have you wondered, since you have been here, how the ranch got its name?” (The assembled guests nod their heads, and Wrangler John continues.) “A

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long time ago, people around here couldn’t stay safely through the winter. Gathering enough provisions took too much work, and it made sense to go down to town where it was warmer. So, early every November, after all the harvestin’ was done, the animals were driven down to lower ground. There wasn’t much of a ranch here, and it wasn’t named at all. Those who worked here came back after the animals were secure and gathered the last of their things and then went back to town in their wagons. This happened year after year without incident. That is until 1906. In 1906 snow came earlier than usual, and the cattle drive had to be put together quickly. Five men came back to the ranch after that, just to tidy things up and get the last of their provisions. They had to hurry, because a fierce storm was just a few hours away, and getting stuck at the ranch over the winter would be no picnic. Narrator: Wrangler John looked carefully over his audience to see that they were paying attention. No one spoke. Wrangler John: The men had one wagon, drawn by two work horses. They divided into teams of two for the last of their chores and then got into the wagon and drove away. What they didn’t realize was that in dividing 5 men by 2, they had left one man out. ‘Scorch’, as they called him, because he usually burned dinner, had no partner, no job, and had been left to winter alone at the ranch. By the time they realized they’d forgotten ‘Scorch’, the high country was buried in three feet of snow and it was too late to go back and search for him. Tyler: Was he ever seen again? What happened to him? Wrangler John: No. The next spring, when the wranglers returned to the ranch, a careful search was conducted. But no remains were ever discovered. However, a strange legend surrounding ‘Scorch’s disappearance is told today. It is said that he protects people all over these parts from being left behind. Whenever a group is dividing into sets, and an important remainder might be forgotten, he calls in a low, slow drawl, ‘Round-up!’ and the group remembers to include the remainder. In fact, it’s after one such experience that the name of the ranch was changed to the No-remainder Ranch. But it’s just a legend. I don’t know anyone personally who has heard the voice… Narrator: The crowd grows silent as Brittany, Nikki, and Tyler look at each other in amazement. They know THEY’VE heard the voice. Each time they were about to leave an important remainder behind, the voice instructed them to round up. And, as if to remind them forever, once more they heard the low, slow, Western drawl… Voice: Round-up!

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“You Just Drop It!”

Characters: Narrator Marisol Shailee David Sean

Scene 1

Narrator: Marisol and Shailee have lived next door to each other for nine of their eleven years, and except for a few fights every now and then have been best friends the entire time. Marisol puts up with Shailee’s moodiness, and Shailee puts up with Marisol’s clumsiness. Best friends have to forgive each other—that’s why they are best friends. They do have a lot in common: both love sports and good music, and right now both of them want to be veterinarians when they grow up. In fact, they are discussing their future right now. Marisol: Shailee, how do you think we are going to be able to afford all the school it takes to be veterinarians? Shailee: I think we should start saving our money now! Marisol: What money? I don’t even get an allowance. Shailee: Well, let’s start a business! If we can start earning money, we’ll be able to start saving money. Marisol: What could we do? We’re a little old to sell lemonade. Shailee: Actually, I’ve been thinking about this for a while. We could set up a roadside stand and sell baked goods, lemonade, and flowers. If we are smart about it, I think we could earn a lot of money.

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Scene 2

Narrator: Marisol’s mom had a connection with a flower wholesaler, and Shailee’s grandma made the best cookies and brownies in town. It didn’t take long for Marisol and Shailee to have a whole kitchen full of flowers and goodies to sell. Shailee: Hold these flowers, Marisol, while I tie ribbons around them. I want to put them in bunches of 7. Hmm…we have 37 flowers. How many bunches of 7 can we make with 37 flowers? Marisol: That’s easy! We can make 5R2 bunches. Oops, Shailee, I’m sorry! I dropped those two flowers! I’m so clumsy! I accidentally dropped the remainder! Shailee: Don’t worry. We couldn’t make a bunch with just two flowers; we couldn’t use them anyway. It was okay to drop the remainder. We really only could make 5 bunches. Now, hand me those brownies… Narrator: Marisol gave Shailee a tray of brownies. Shailee: Okay, we can fit 6 brownies on each plate. How many brownies do we have? Marisol: We have 34 brownies. With 6 on a plate, we can fill 5R4 plates of brownies…Oh, no! I accidentally dropped 4 brownies! They’re just crumbs on the floor now! I’m sorry I’m so clumsy. Shailee: Marisol, you are clumsy, but you dropped just the remainder, and we couldn’t use it anyway. No one would want to pay for a plate that was only 2/3 full. We still have 5 plates of brownies. But will you carefully hand me the chocolate chip cookies? I need to count them. Marisol: I’ll count them. There are 50 cookies, and they look really yummy! Let’s put them in sets of 8. That way we’ll have 6R2 plates. Narrator: Marisol started handing the tray of cookies to Shailee. But just before Shailee grasped them, Marisol slipped on the brownie crumbs on the floor and two cookies slid off. Marisol: Shailee, I just dropped two of the cookies! What will we do now? Shailee: Marisol, don’t worry about that! You just dropped the remainder! They were extra anyway. We still have 6 plates of cookies to sell.

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Scene 3

Narrator: Every weekend Shailee and Marisol sold flowers and baked goods at their roadside stand. Soon their business grew so large that they had to hire more employees. David and Sean: Marisol and Shailee, thanks for letting us work for you. What do you want us to do? Shailee: David, will you put the flowers in bunches of 7 and tie ribbons around them? Try to choose colors that look good together. Marisol: Sean, will you put the brownies and cookies on plates and wrap them? We sell brownies in sets of 6 and cookies in sets of 8. David: There are 58 flowers. That means I can make 8 bunches of flowers with a remainder of two. What do I do with the remainder? Sean: There are 40 brownies. That means I can make 6 plates with a remainder of two. And there are 46 cookies. I have enough cookies for 5 plates with a remainder of 6. What do I do with the remainder? Narrator: Shailee and Marisol just looked at each other and laughed. Then they said to David and Sean… Marisol and Shailee: YOU JUST DROP IT!

Scene 4 Narrator: The money kept piling up in the bank, and in a little over fourteen years Marisol and Shailee had their very own veterinary clinic. They were still best friends—Shailee was still moody and Marisol was still clumsy. On a June morning as Shailee was standing behind the front desk, she was surprised to see David and Sean show up at their shop. It had been years since the childhood friends had seen one another. Shailee: Hi, David and Sean. It’s wonderful to see you! Marisol, (she calls into a room behind her), will you bring drinks for everyone? (She turns back to David and Sean.) David: Hi! I’d like you to meet my wife, Brianna, and our Golden Retriever, Lucky. We brought him to you so he could get his shots. You remember Sean, don’t you?

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Sean: Hi! This is my Chihuahua, Bentley. He needs shots too. Marisol: (entering with 6 cups of water) Hi! Here, have some water. Oh, I brought 6 cups when I only needed five… (she slips, spilling one of the cups onto the floor.) Uh, oh—I dropped it! Oh, well—it was an unimportant remainder anyway. There’s nothing wrong with dropping an unimportant remainder!

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“Sharing is Very Important”

Characters:

Narrator 1 Narrator 2 Scott Travis Samantha Mom Hector

Scene 1

Narrator 1: Have you ever had a little brother or sister turn into a nosy tattle-tale? Scott and Travis did. Their little sister Samantha turned five and thought she was the boss of everything! But one day, they decided they were glad to have her around. That day, Little Samantha saved Travis’ life. Narrator 2: Our story begins in the Hunter family’s back yard. Scott is 13, Travis is 10, and Samantha is 5. As usual, Scott and Travis are trying to accomplish something, and Samantha is in their way. Scott: Travis, hand me that rope. I want to tie knots in it. We can climb it to get into our tree fort. (Travis hands Scott the rope.) If we cut it in two pieces, we can use ½ for the front door and ½ for the back door. Hmm…we have 11 feet of rope. How long does each piece need to be? Travis: That’s easy! 11 divided by 2 = 5R1. Each piece needs to be 5R1 feet long. Samantha: I’m telling Mom! You’re not sharing! Travis: Not sharing what? What are you talking about? Scott: Just ignore her. You said what about the rope? Travis: Each piece needs to be 5R1 feet long.

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Narrator 1: Samantha didn’t want to be ignored, so she went to their mother for help. Soon Mom came into the back yard. Mom: Boys, Samantha says you aren’t sharing. Don’t you know that you need to share whenever you can? Sharing is very important. Narrator 2: With that bit of advice, Mom went back into the house. And Travis and Scott went back to work. Travis: (with a long look at Samantha) Scott, something Mom just said made sense. We can share this remainder. Each piece of rope can be 5 ½ feet long. Thanks, Samantha. You actually helped us with this tree house.

Scene 2

Narrator 1: Within a few days the tree house was finished, and it was time to have a sleepover in it. Scott and Travis decided there was room for 4 sleeping bags, so each of them invited his best friend. As soon as it was dark, they climbed the ropes and settled in. Narrator 2: Of course, no one really sleeps at a sleepover, right? Within minutes, on each boy’s sleeping bag was heaped a pile of treasure—whole bags of candy, stacks of baseball cards for trading, and Game Boy’s and Ipods for later, when the talking wore thin. Scott: Justin, are you ready to share your Airheads? I want a blue one. Justin: There are 17 in the bag and we have 4 kids. How many does that give each of us? Travis: I’m good at division. 17 divided by 4 = 4R1. Each kid gets 4R1 Airheads. Narrator 1: At just that moment, Samantha’s head popped up in the entrance to the tree fort. Samantha: Hey, you guys forgot to invite me. And you’re not sharing! Don’t you know sharing is very important? Scott: (with a long look at Samantha) Travis, you’re right about Samantha. Sometimes she says just the right thing. We can share that remainder. Each kid gets 4 Airheads, and we can divide the last one into 4 pieces. We’ll each get 4 ¼ Airheads.

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Travis: I’m okay about Airheads, but what I’m really eyeing is Hector’s Reese’s Peanut Butter Cups. Hector, how many Reese’s do you have? Hector: There are 10 in the bag. And I know that 10 divided by 4 = 2 R2, so we each get… Samantha: If you don’t start sharing, I’m telling Mom again! Travis: (looking at Samantha) Okay, we’ll share the remainder. 10 divided by 4= 2R2. But if we share the remainder, we’ll each get 2 1/2 Reese’s. Scott: Now, Samantha, get lost. This is a BOY tree house!

Scene 3

Narrator 2: The tree house was a big hit. For most of the summer Scott and Travis had a sleepover in it at least once a week. But in mid-August, Scott’s friend, Justin, had another big idea. Justin: Hey guys, let’s do a survival camp-out on Slickrock Mountain! Hector: What’s a survival camp-out? Justin: It’s when we each go our own way and we have to stay alone all night, without a tent or anything! Travis: Is it safe? Scott: Sure! We don’t go very far from each other—just far enough to not see each other. We’ll stay at the old mine camp. Narrator 1: The boys got permission from their parents, and decided to meet in exactly one week with all their camping gear. They would get ready in Scott and Travis’ back yard.

Scene 4

Narrator 2: It was still hot at 7 p.m. when the boys gathered for their campout. The mine camp was just a couple of miles from Scott and Travis’ house, so they decided to hike in

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and then separate at bedtime. They piled their stuff on the concrete patio, just to be sure they had thought of everything. Justin: Does everyone have a flashlight? Boys: Yeah! Hector: What about mosquito repellent? Boys: Yeah! Scott: What about matches? Justin: Oh, I don’t. Travis: Neither do I. Hector: I don’t either. Scott, do you? Scott: Yeah, I have a few books of them. Do you guys want to use some? Boys: Yeah! Scott: Okay, I have 5 books. With 4 boys, we each get… Travis: I know! 5 divided by 4 = 1R1. We each get 1R1 books of matches. Narrator 1: All of a sudden Samantha appeared around the corner of the house. Samantha: Hey, guys, are you sharing yet? If you don’t share, I’m telling Mom. Sharing is very important! Travis: (looking at Samantha) Hmm…can we share this remainder? I guess so. We’ll split open the book and each take 5 matches. How’s that for sharing?

Scene 5

Narrator 1: Travis, Scott, Justin and Hector took off for the old mine camp. There they cooked a fine dinner over a large campfire and then sat late into the evening, roasting

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marshmallows and counting the constellations. Travis absent-mindedly threw his book of matches into the fire and watched it flare up and then disappear. Narrator 2: Then it was time to find a solitary place to camp. The boys decided to each take 100 steps in a different direction, so they wouldn’t be too far away. Travis chose to walk 100 steps up the side of Slickrock Mountain, hoping to find a sheltered niche against a fir tree. Travis: This is a good spot. I think I’ll sleep here. Narrator 1: And so he fell asleep with a sweatshirt for a pillow and fir branches for a blanket. He slept soundly all night. Narrator 2: But when he woke up, he wasn’t sure at all where he was. Everything looked different by daylight. He tried calling his brother and friends, but no one answered. Knowing the rules of survival, he didn’t hike away—instead he waited in the same spot for someone to find him. Travis: I’ll stay right here. I know my family will come looking soon. Narrator 1: The day passed without anyone finding Travis. And as night came, it looked like it would snow. Suddenly, Travis was afraid he was in real trouble! Travis: I wish I hadn’t thrown all my matches in the fire. I could really use a signal fire about now. I bet if I built a fire, my family would find me soon, and I would stay warm too. Narrator 2: Travis reached his hand deep into his left front pocket, wishing he had that book of matches. Almost unbelievingly, his hand found the five remainder matches that Samantha had insisted be shared. Travis: Hey! I have 5 matches! It is important to share a remainder! I can build a fire with these and my family will rescue me! Narrator 1: It didn’t take long for Travis to build a roaring fire, with smoke and flames reaching high into the sky. It didn’t take much longer for Travis’ family to find him, high on Slickrock Mountain, and to bring him home. They had been searching all day, but they had been on the opposite side of the mine camp. Narrator 2: Travis was very happy to be home. He’d survived all right, because of Samantha’s insistence that they share a remainder.

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Travis: Thanks, Samantha. Samantha: Sharing is very important!

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Playing with Remainders Questions for discussion after the plays have been read.

“Round-up”.

1. Why did Tyler and Nikki have to round up their remainders each time in this story? 2. What are some situations in the real-world, where it would be appropriate to

“round-up”? 3. Write a good rule to help you know when you need to “round-up” the remainder.

“You Just Drop It” 1. Why did Shailee and Marisol have to drop their remainders each time in this story? 2. What are some situations in the real-world, where it would be appropriate to

“drop it”? 3. Write a good rule to help you know when you need to “drop” the remainder.

“Sharing is Very Important” 1. Why didn’t the remainders in this story need to be rounded up or dropped? 2. What are some situations in the real-world, where it would be appropriate to

“share the result”? 3. Why is it that when you have to “share” the remainder the answer is always a

fraction or decimal? 4. Write a good rule to help you know when you need to “share” the remainder.

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Remainder Stories

Answer each question with a complete sentence. Then tell how you used the remainder (whether you rounded up, dropped, or shared the remainder equally). Last, tell why you used the remainder the way you did. Each problem is worth four points (1 point = correct answer; 1 point = complete sentence; 1 point = correct use of remainder; 1 point = explanation for use of remainder). 1. Skyler is helping his mother plan a wedding breakfast for his older sister, Jessica. They are expecting 63 family members to attend, and they are using round tables that seat 8 guests each. How many tables will be needed to seat 63 people? 2. Skyler and his sister, Rylie, are preparing flower bouquets as centerpieces for each table at the wedding breakfast. They hope to have enough to decorate the table that is displaying the wedding cake as well. They have 67 carnations and wish to put 6 carnations in each bouquet. How many bouquets can they make with 67 carnations? 3. Rylie is going to the zoo for her 12th birthday party, and she is taking 9 friends. The zoo has a new baby giraffe, and groups of 3 children are allowed at a time in a special viewing room to see the giraffe and his mother. How many tours will it take for Rylie and her 8 friends to see the giraffe? 4. At Rylie’s 12th birthday party, she wants to give each of her friends a jar with a variety of candy from the candy store. She has 5 friends coming, and she has 113 individually wrapped pieces of candy. If she gives each person the same number of pieces of candy, how many pieces will each friend receive in her candy jar? 5. While Rylie is celebrating with her friends, Skyler’s mom gave him $10.00 to share equally with his three best friends so they could buy candy too. How much money do Skyler and his friends each get to spend? 6. Jessica is making curtains for her new apartment. She has 15 yards of material to make 2 sets of curtains. How much fabric can she use for each set? 7. Jessica’s mother is serving punch at the wedding reception. She has a punch bowl that holds 106 ounces of punch. How many 8-ounce servings can be poured from the punch bowl when it is full?

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The Remainder Game

Classroom Setup: Play this game with a partner. You will need a number Materials: eight-sided number cube (die) 20 small objects (e.g., buttons, paper clips, pennies, pieces of paper) recording score sheet

Directions:

1) To begin, a player rolls the number cube. The player needs to divide the 20 small objects into the number of groups shown on the number cube. For example, if a player rolls a 3, the player divides the 20 small objects into 3 groups.

2) If there is a remainder (there would be 2 leftover objects in the previous example), the player records the number of remaining objects on a recording score sheet.

Sample Score Sheet

3) Now the turn passes to the other player who rolls the number cube, makes equal groups, and records the remainder on his or her paper.

4) After each player has had 10 turns, the players add up the remainders on their

piece of paper. The player with the greater total wins the game.

Variations: Use a six-sided number cube for struggling students. Use a ten-sided number cube and a larger number of counters (instead of 20

change the dividend to 25, 30, etc….). Use a ten-sided number cube and create a spinner to have them spin for the

divisor. (See the page which follows the score sheet for a spinner.)

Game Wrap-Up and Possible Reflection Questions:

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1) After students have had time to play one game, have them bring their Score Sheet to the carpet for a wrap-up and reflection.

2) Begin a process chart. Ask students: “Who has a division sentence, from their game, that gave you a remainder of zero?” The teacher lists 5-6 of them on the process chart and then asks, “What do you notice about each of these division sentences?, “How do you know you’re not going to have a remainder? (When the divisor is a factor of the dividend.)

3) Ask students “Who has a division sentence, from their game, that gave you a remainder?” The teacher lists these on the process chart. “What strategies did you use to figure out the quotient and remainder? If you didn’t have counters how could you find the quotient and remainder?”

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The Remainder Game Score Sheet

Player 1: Player 2:

Division Sentence Remainder Division Sentence Remainder

20 ÷ 3 = 18 R 2 2 20 ÷ 4 = 5 0

Total Score Total Score

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Remainder Game Optional Dividend Spinner

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Sample Real-World Remainder Problems

Everyone in our school, which has 372 people, including teachers and students, is going on a field trip. Each bus holds 50 people. How many buses should be order? CDs are on sale for $12. I have $40 in my pocket. How many can I buy? Our school ordered 300 pounds of clap, and the clay needs to be distributed equally among 18 classrooms. How many pounds of clay should each classroom get? Your school is having an arts day. There are178 students who will attend, and a maximum of 15 students can work in each room. How many rooms will you need? The 178 students have a choice of art projects. They can choose painting, drawing, sculpture, weaving, or paper-making. If the painting project can have extra students, but the other projects must have an equal number of students, how many students will be working on the painting project? In one room of 15 students, there are 9 boxes of charcoal for drawing. How many additional boxes are needed? One box of charcoal for drawing costs $2. Jen has $11. How many boxes of charcoal can she buy?

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Open Ended Problems

An amusement park ride had a huge line that had to be divided into 2 smaller lines.

The same number of people ended up in each line. Since these lines were still too long, the ride operators cut off each line and had to ask 20 people in each line to come back another time. What do you know? What could you figure out mathematically?

Possible responses: If there were 1,000 people, there would be 500 in each line. If 29 people in each of these lines had to leave, then there were only 471 people in each line, and 942 people waiting for the ride.

Jake arranged some chairs into several rows of 8 chairs. When he was done, there were 3 chairs left. How many chair might have Jake arranged and how many rows might he have had?

Possible responses: If he had 11 chairs, he would only fill one row. Since it says rows, he probably has at least 19 chairs, which is 2 full rows and 3 extra chairs. He could have 83 chairs. You can just multiply any number (greater than 1) times 8 and add 3 to find a number of chairs that will work.

Mr. Wong has between 300 and 1,000 small prizes to divide evenly among his 19 students. He will give away as many prizes as possible. What is the greatest number of prizes that could be left over? Is it possible for each student to get 60 prizes?

Possible responses: 18 prizes because it 19 or more were left over, each student would get another prize. Since 19 is less than but close to 20, and 20 x 60 is 1,200, each student could not receive 60 prizes.

Suppose that ever day someone in your class helps the kindergartners at the crosswalk. A different student helps each day. How many times will each of you get to help?

Possible responses: There are 180 days in our school year. I divided 180 by 26, the number of students in our class, and got 6 and a remainder of 24. So, 6 turns per students x 26 students uses up 156 days, with 24 days left. On those 24 days, most of us could get a 7th turn.

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Make up two different division story problems that use 28 ÷ 8. Use one situation that calls for ignoring the remainder and the other that calls for including it as fraction or decimal.

Possible responses: Eight books fit in a box. If there are 28 books how many boxes will be filled? Ignore the remainder because the question asks about full boxes. If you just change the question to, “How many boxes will be used?” you can include the remainder as a fraction, so the answer will be 3 ½.

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Technology Links

Interpreting Remainders PowerPoint http://math4u.wicomico.wikispaces.net/file/view/Interpreting+Remainders+%233.pptx This is a PowerPoint that could be used with students to illustrate how to interpret remainders.

http://math4u.wicomico.wikispaces.net/file/view/Interpreting+Remainders+%233.pptx�

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Technology Links Continued

City Remainders Online Application http://www.goldridge08.com/fifthgames/fifthmath/9%203.swf This website has students read problems involving remainders and interpreting what they need to do with the remainder. This is a great independent activity for students to complete after reading and discussing the Remainder Plays.

http://www.goldridge08.com/fifthgames/fifthmath/9%203.swf�

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Exit Slip – 6.C.1.c

Name:

Mrs. Patel brought a box of 124 strawberries to the party. She wants to divide the strawberries evenly among 8 people.

1. How many strawberries will each person get? _________________

2. What should you do with the remainder in this problem? drop it round up share it Explain your thinking.


Name:

Mrs. Patel brought a box of 124 strawberries to the party. She wants to divide the strawberries evenly among 8 people.

1. How many strawberries will each person get? _________________

2. What should you do with the remainder in this problem? drop it round up share it Explain your thinking.

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Name:

The community center is offering a bus trip to a WNBA game. Each bus holds 46 passengers and 195 people sign up for the trip.

1. How many buses will be needed? _________________ 2. What should you do with the remainder in this problem? drop it round up share it Explain your thinking.


Name:

The community center is offering a bus trip to a WNBA game. Each bus holds 46 passengers and 195 people sign up for the trip.

1. How many buses will be needed? _________________ 2. What should you do with the remainder in this problem? drop it round up share it Explain your thinking.

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Name: If Ben and Jen take the Yellowhead Highway from Winnipeg to Edmonton and then travel south to Lake Louise, the total distance is 1910 km. If Ben and Jen travel at a more leisurely pace of 85 km a day, how many days will it take them to complete the trip?

1. How many days will it take them to complete the trip? _________________ 2. What should you do with the remainder in this problem? drop it round up share it Explain your thinking.


Name: If Ben and Jen take the Yellowhead Highway from Winnipeg to Edmonton and then travel south to Lake Louise, the total distance is 1910 km. If Ben and Jen travel at a more leisurely pace of 85 km a day, how many days will it take them to complete the trip?

3. How many days will it take them to complete the trip? _________________ 4. What should you do with the remainder in this problem? drop it round up share it Explain your thinking.

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Name:

There are 876 students at Chase Elementary School. The principal wants to have each class have 24 students. How many classes will be at Chase Elementary? Use what you know about discussion and remainders to explain how you found your answer.


Name:

There are 876 students at Chase Elementary School. The principal wants to have each class have 24 students. How many classes will be at Chase Elementary? Use what you know about discussion and remainders to explain how you found your answer.

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Name: Jumbo the elephant loves peanuts. His trainer has 525 pounds of peanuts. If he gives Jumbo 20 pounds of peanuts each day, how many days can he feed Jumbo peanuts?


Name: Jumbo the elephant loves peanuts. His trainer has 525 pounds of peanuts. If he gives Jumbo 20 pounds of peanuts each day, how many days can he feed Jumbo peanuts?

Grade 5 Unit 1 2011-2012 FINAL

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Transcript of Grade 5 Unit 1 2011-2012 FINAL