FREEHOLD BOROUGH PUBLIC SCHOOLS … Borough Public Schools Curriculum Management System Grade 3...

FREEHOLD BOROUGH PUBLIC SCHOOLS Curriculum Management System

Mathematics Grade 3

Board Approved: August 2007

Freehold Borough Public Schools Curriculum Management System

Grade 3 Mathematics

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Freehold Borough Board of Education

Mr. James Keelan, President Mr. Ron Reich, Vice President

Mr. Andrew DeFonzo Mrs. Audrey Evans

Mr. Frank Gill Mrs. Annette Jordan

Dr. Eileen McGough Mrs. Victoria Muller

Mr. Adam Reich

District Administration

Mrs. Elizabeth O'Connell, Superintendent

Mrs. Veronica Wolf, Business Administrator

Mrs. Ronnie Dougherty, Director of Curriculum/Language Arts Supervisor

Mrs. Pat Rizzo, Director of Special Programs

Mr. Thomas Tramaglini, Director of Technology and Assessment

Mr. Jermaine Moore, Supervisor of Buildings & Grounds Ms. Janet Morales, Bilingual/ESL Supervisor/Community

Liaison

Curriculum Committee

Patricia Cundari Kathy Denison

Sharon Hennessy Juanita Jones Karen Kowalik

Lois Mann Sandra Shafi Elyse Smith

Judith Washburne


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Mission

We will inspire the creativity and imagination of all students

and empower them as knowledgeable, skillful, and confident learners who flourish and contribute willingly in a changing world.

Core Beliefs

We believe that:

• All people have inherent worth. • Life-long learning is basic to the survival and advancement of society. • The primary influence on the individual's development is the family in all its forms. • Valuing diversity is essential to individual growth and the advancement of society. • All individuals have strengths and human potential has no known limits. • Democracy thrives when individuals accept responsibility for their choices. • Being trustworthy builds trust. • Creativity and imagination are essential for society to flourish. • A safe environment is essential for the well-being of the individual and for society to flourish.


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Philosophy

The Freehold Borough Public Schools are committed to inspiring the creativity and imagination of all students and empowering them as knowledgeable, skillful, and confident learners who flourish and contribute willingly in a changing world. We believe that life-long learning is basic to the survival and advancement of society, as well as the notion that all individuals, especially our students, have strengths and human potential without limits.

The 2nd and 3rd grade mathematics program is one that strives to challenge children to make important decisions by employing integrated cross curricular experiences that foster practical meaningful real-life skills. Authentic lessons are designed to be conscious of the developmental stages of children and build logical reasoning skills with emphasis on utilizing multiple strategies for solving. Curricular experiences emphasize a concrete hands-on approach to mathematics which provides children a fun and motivating way to learn and apply concepts.

Goals

• Students will be provided with skills and concepts to use math effectively in their lives • Differentiated strategies to solve problems • Opportunities to communicate mathematical knowledge and experiences • Opportunities to use technology to enhance mathematical knowledge and capabilities • Fun and motivating experiences • Use assessment and data to drive instruction


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New Jersey Core Curriculum Content Standards for Mathematics

4.1. Number and Numerical Operations

A. Number Sense

B. Numerical Operations

C. Estimation

4.2. Geometry and Measurement

A. Geometric Properties

B. Transforming Shapes

C. Coordinate Geometry

D. Units of Measurement

E. Measuring Geometric Objects

4.3. Patterns and Algebra

A. Patterns and Relationships

B. Functions

C. Modeling

D. Procedures

4.4. Data Analysis, Probability, and Discrete Mathematics

A. Data Analysis (Statistics)

B. Probability

C. Discrete Mathematics--Systematic Listing and Counting

D. Discrete Mathematics--Vertex-Edge Graphs and Algorithms

4.5. Mathematical Processes

A. Problem Solving

B. Communication

C. Connections

D. Reasoning

E. Representations

F. Technology


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Scope and Sequence

Concepts

Quarter I

Number Sense • Place value concepts through hundred thousands • Compare and order whole numbers • Understand and use concepts of equals, less than, greater than to describe relationships

between numbers (=, <, >) • Odds/evens • Rounding

Numerical Operations – addition/subtraction • Addition whole numbers (3 digit numbers) and money (decimals to hundredths) • Subtraction whole numbers (3 digit numbers) and money • Estimations sums/differences – estimate without counting, whether a set has more/less/same

as a reference set • Use of calculators, mental math, paper/pencil • Check for reasonableness of results

Problem-Solving – (joining, separating, comparing) • Making change • Open-ended items • Follow, devise, and describe practical sets of directions • Estimation/check for reasonableness

Quarter II

Patterns • Recognize, describe, extend, and create • Whole number patterns that grow/shrink as a result of repeated operations (add/sub…) • Functions – use concrete and pictorial models to explore basic concept (input/output tables,

T-charts) • Construct and solve simple open sentences addition/subtraction (3+6=___; n+15-3; 16-c=7)

Data Analysis • Collect, generate, and display • Read, interpret, construct, analyze, generate questions, draw inferences (pictographs/bar


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graphs/tables) • Recognize and describe change in quantities – graphs representing change over time (e.g.

temperature/height) Numerical Operations

• Multiplication (concept) • Repeated addition, area/array • Properties – Commutative ( 3x7 = 7x3), Identify element for multiplication is 1 (1x8 = 8),

any number multiplied by zero equals zero • Develop proficiency with basic multiplication facts using a variety of strategies (skip

counting, counting up, doubles, near doubles, counting on) • Division (concept) – relate to multiplication • Repeated subtraction, sharing

Geometry • 2-D and 3-D figures (identify, classify, describe) • Symmetry and congruence – (identify, describe, and create) • Lines, segments, endpoints, angles • Transformations – reflection, rotation (slide, flip, turn) • Coordinate geometry – locate and name points in the first quadrant on a coordinate grid • Perimeter, area, volume – 2-D and 3-D figures

Quarter III

Fractions • Understand and name (denominators 2, 3, 4, 5, 6, 8, 10)

♦ parts of a whole ♦ subset of a set ♦ location on a number line

Probability and Discrete Math • Explore concepts of probability of events with chance devices (dice, coins, unevenly divided

spinners) • Predict outcomes (likely, unlikely, certain, impossible, more likely, less likely, equally

likely) • Collect data and use to make predictions • Represent and classify data according to attributes (shape, color, relationships) using Venn

Diagrams, numerical/alphabetical order • Represent all possibilities for simple counting situations (organized lists/charts)


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• Explore vertex-edge graphs (vertex, edge, path) • Find the smallest number of colors needed to color a map

Measurement • Select and use appropriate units, tools, and estimation • Length (fractions of an inch ¼, ½, inch) standard and metric units of measure • Area (square inch, square centimeter) • Weight (ounce pound, gram, kilogram) • Capacity (pint, quart, liter, fluid ounce, cup, gallon, milliliter) • Time (second, minute, quarter hour, half hour, hour, elapsed time) •

Quarter IV

Numerical Operations • Multiplication ( 2 digit x 1 digit) • Division facts (with remainder)

Fractions • Adding and subtracting • Equivalent • Ordering • Decimals

Embedded throughout

the year

Problem-solving Technology Vocabulary Development


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Freehold Borough Curriculum Management Grade Level/Subject Grade 3 Mathematics

Topic (s): Number Sense, Numerical Operations and Problem-Solving Timeline: Quarter I

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Concept New Jersey Core Curriculum Content Standard/Cumulative

Progress Indicator (CPI)

Specific Learning Objectives/ Essential Questions

The Students Will Be Able To:

Assessment

Instructional Tools / Materials / Technology / Resources /

Learning Activities / Interdisciplinary Activities /

Assessment Model

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a. Place value through hundred thousands

CPI: 4.1 A.2, .3

• Use place value chart to identify the value of a digit in a whole number

• Count, read and write whole numbers through 100,000

In the number 462, 579, what is the value of the 6?

a.) 6,000 b.) 60 c.) 600 d.) 60,000

. www.studyisland.com Place value models - Large Flip Chart Use ½ inch graph paper to write 6 digit numerals; circle commas as cue to say ‘thousand.’

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b. Compare and order whole numbers

CPI: 4.1 A.1, .6

• Order numbers from the greatest to least and least to greatest

• Compare and order numbers by looking at each digit’s value

Order the numbers from least to greatest. 4,328 ; 3,799 ; 4,337 a.) 4,328 ; 4,337 ; 3,799 b.) 3,799 ; 4,337 ; 4,328 c.) 3,799 ; 4,328 ; 4,337 d.) 4,337 ; 4,328 ; 3,799 •

• Place value models/charts - Use base ten blocks on place value mat. Tactile version of < or >

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c. Concepts and relationships (<, >, =) of numbers

CPI: 4.1 A.6 4.1 C.1 4.# D.2

• Create number sentences to show understanding of >,<, = signs

Which number sentence is true?

a.) 6 + 7 > 8+3 b.) 14 – 7 = 10 – 4 c.) 9 + 8 < 12 + 2 d.) 12 – 6 < 11 – 4

• < > = signs - Draw pictorial representations with numerals.


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d. Odd/even numbers CPI: 4.1 B. 5, .6

• Recognize patterns in even/odd numbers

• Demonstrate the place value of a given number

Using the digits 2, 6, and 7only once, what is the largest odd three digit number that can be made?

a.) 267 b.) 762 c.) 672 d.) 627

• number chart • place value chart - Use a chart numbered 1-100 and highlight ones digit. Change color of highlighters to note pattern.

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e. Rounding numbers CPI: 4.1 A .3

• Explain and understand the rules for rounding numbers to the nearest 10, 100, 1000

Round 462 to the nearest 10. a.) 500 b.) 400 c.) 460 d.) 470

• number line - Model low ten and high ten; find the nearest ten or hundred

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f. Addition and subtraction of whole numbers (3 digit numbers)

CPI:4.1 B.1, .3, .4

• Add/Subtract 3 digits with and without regrouping

• Orally explain the steps of regrouping

357 +539

• Graph paper • Place value manipulatives - Begin with tactile model and Step-by-step modeling. (Madeline Hunter) Students must ‘move’ the regrouped amount physically.

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g. Addition of Money (decimals to hundredths)

CPI: 4.1 B.6

• Count and add money • Apply place value and money

skills to real world situations

$ 46.39 +72.73 a.) $120.02 b.) $119.12 c.) $118.03 d.) $110.32

• www.moneyinstructor.com • place value chart • graph paper • money set

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h. Subtraction of Money (decimals to hundredths)

CPI: 4.1 B.5, .6

• Count money and make change

• Apply place value and money skills to real world situations

$2.57 - 1.63

• same as above - Flannel board numbers to demonstrate movement of decimal point.


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i. Estimate sums and differences

CPI: 4.1 C.2

• Explain and identify estimating sums, differences to the nearest 10, 100, 1000

58 + 88 a.) about 180 b.) about 160 c.) about 140 d.) about 120

• www.studyisland.com • number line - Use graph paper. Draw arrows from each addend, i.e. 58---->60

ongoing

j. Use of calculators, mental math strategies, paper/pencil

CPI: 4>1 C.3, .4

• Demonstrate / correctly use a calculator

• Identify math strategies to solve word problems

Distribute calculators John has 42 baseball cards. He buys 23 more cards. If his goal is to have 75 cards, has he met his goal? Explain how you know.

• Calculators • Read, Plan, Solve and Look

Back - Texas Instruments TI-108 overhead calculator for modeling.

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k. Check for reasonableness of results

CPI: 4.1 B.8 $.1 C .4

• Form conclusions about whether an answer is a reasonable estimate or not and explain

• Review and analyze examples of a reasonable estimation

There are 10 CDs in stack A. A B 10 CDs ? CDs Which is a reasonable estimate for the number of CDs in Stack B? a.) 25 b.) 50 c.) 100

• vocabulary chart


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d.) 500

ongoing

l. Problem-solving Joining, separating, comparing, Open-ended, devise and follow a practical set of directions CPI: 4.1 B.1 4.5 A.2

• Solve word problems using money and real life situations

• Explain and show the correct steps solving an open ended/ multi-step word problem

• Demonstrate prior knowledge of the value of coins and bills up to $ 20.00

Jose went to the store with $10.00. He bought a notebook for $2.99. What will be his change? Which answer is reasonable?

a.) About $13.00 b.) About $5.00 c.) About $7.00 d.) About $12.00 Follow the direction below to answer the problem. Be sure to answer all the parts of the problem. You go to the store and buy a book $2.29. You give the clerk $5.00. a.) What is the change? b.) Show the change using the

least number of coins possible. Put a circle around this.

c.) Show two other ways to make the change.

• www.mathpotd.org • Read, Plan, Solve , Look Back • Open ended Rubric • Coins/bills - At least one “Problem of the Day” (personalized) and modeled by teacher.


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m. • •


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Topic (s): Patterns, Data Analysis, Numerical Operations, Geometry Timeline: Quarter II

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Assessment

Instructional Tools / Materials / Technology /

Resources / Learning Activities / Interdisciplinary

Activities / Assessment Model

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a. Patterns CPI: 4.3 A.1 4.5 C.1

• Identify, recognize basic 2D and 3D shapes

• Recognize patterns in a series and identify what would come next

• Develop their own series of patterns and share with the class to determine the answer

Gary made pattern below with straws.

If Gary continues the same pattern, how many triangles will Gary make in Figure 8?

a.) 9 b.) 12 c.) 14 d.) 16

These squares follow a pattern.

Which square comes next in the pattern?

Tell what would come next. 2,4,3,5,4,6,5, ____

• Geometric 2D/3D shapes • Classroom objects - Household objects that resemble 3D shapes. Hold/manipulate and compare.


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a.) 10 b.) 7 c.) 8 d.) 9

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b. Functions CPI: 4.3 B.1

• Demonstrate the use of all four mathematical operations( - = x : )

• Explain the importance of a rule using one of the operations to solve and use an input/output chart

• Illustrate and develop an input/output chart

• Discuss with classmates the correct rules

Look at the two input/output tables below. Attached sheet Page 63 Input Output

5 12 3 10 7 14

Table A Input Output

7 4 10 7

3 0 Table B

What is the rule for Table A? Answer: _______________________________ What is the rule for Table B? Answer: _______________________________

If the number 24 were the input, which table

• Input/output model - Provide Visual on overhead and written steps. “What do I have to do to the input number to get to the output number?”


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would you use to get the greater output? Explain your answer:

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c. Part unknown - addition/subtraction sentences

CPI: 4.1 B.1 4.4 A.1

• Identify the missing data to complete and answer the problem

• Use addition/subtraction facts to solve word problems

• Look for key words to successfully solve the problem

Tina bought a pen for 45¢ she also bought a notebook for 75¢ which number sentence shows how much money Tina spent? a.) 75¢ ― 45¢ = n b.) 75¢ ― X = 45¢ c.) m + 45¢ = 75¢ d.) 75¢ + 45¢ = a

45¢

75¢

• Read, Plan, Solve, Look Back

• highlighter - Draw a pictorial representation of word problem; highlight key words.

On Going

d. Collect, generate, display data

CPI: 4.4 A.1, .2

• Interpret a table/graph by using data • Collect and organize data • Demonstrate knowledge of

coordinates on a graph

Complete the table and graph the points ▲― = 3 ▲ 7 1

0 4 5 9

4 7 3 0 9 8 5

• Input/Output model - Teacher models at overhead or on chart paper.


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e. Read, interpret, construct, analyze, generate questions, draw inferences - displays of data (pictographs, bar graphs, tables)

CPI: 4.4 A.1, .2

• Construct a pictograph, bar graph and line graph using information generated from a class topic

• Make conclusion and interpret given data from specific graphs

• Stress the importance of making a graph with the appropriate labels, key numbers and name

The graph below shows the color of tennis shoes the students wear in Brian’s gym class. Use the graph below to answer the next three questions.

1.) How many students wear red tennis shoes?

a.) 8 b.) 13 c.) 16 d.) 18

2.) How many more students wear white

• Graph paper • Modeling of different

graphs • Graphic organizers - Teacher models graphs on overhead or chart paper: Use different colors for sections of graph. Darken left side of graph.


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tennis shoes than blue tennis shoes? a.) 11 b.) 12 c.) 21 d.) 64

3.) Suppose Brian found 10 students wearing black tennis shoes. He wants to add a bar to the graph to represent these tennis shoes. Which statement describes the bar he will add?

a.) The new bar will be the shortest bar on the graph.

b.) The new bar will be the tallest bar on the graph.

c.) The new bar will be close to the same height as the bar for blue tennis shoes.

d.) The new bar will be skinnier than the other bars on the graph.

Students were asked to choose their favorite subject.

FAVORITE SUBJECT Social Studies ▲ ▲ ▲ ▲ ▲ ▲ ▲ Math ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ Social Studies ▲ ▲ ▲ ▲ ▲ ▲ Language Arts ▲ ▲ ▲ ▲ ▲ ▲

Key: Each ▲= 10 Students. = 5 Students

• How many students chose Social

Studies as their favorite subject? • How many more students chose


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Math than chose science? • How many students answered the

survey?

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f. Recognize and describe change in quantities (graphs representing change over time)

CPI: 4.3 C.1 4.4 A.2

• Explain and understand how to read , interpret and calculate changes on a specific graphs

• Recognize vocabulary : increase and decrease

The graph below shows the average temperature for five months.

Which sentence describes how the temperature changes from January to May?

a.) The Temperature stays the same. b.) The temperature becomes hotter. c.) The temperature becomes cooler. d.) There is no pattern to the

temperature change.

• Overhead activities • Thermometers • Graphs, etc. - Change colors of points. Use a straight edge or place marker.

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g. Multiplication (concept) Repeated addition, array CPI: 4.1 B.1, .10

• Explain how addition and multiplication are related

• Create an array of shapes/pictures to demonstrate knowledge of addition and multiplication

4+4+4+4+4 Which number sentence matches the addition sentence above?

a.) 6 X 4 = 24 b.) 3 X 4 = 12 c.) 5 X 4 = 20

• X chart • Flash cards • X bingo • Stickers, stamps - Begin with Unifix Cubes or colored plastic circles. Break into equal groups. Students


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d.) 4 X 4 = 16

then draw pictorial representations of sets and match to a number sentence.

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h. Properties – Commutative, identity element, zero property

CPI: 4.3 D.1

• Display an example of each property: Zero, Identity, Association and Commutative ( copy notes down in a notebook)

• Review and drill basic family of facts • Demonstrate the use of turn around

facts

Which property of multiplication does this number sentence show? 7 X 3 = 3 X 7

a.) Zero b.) Identity c.) Association d.) Commutative

Solve 4 X 0 = _______

a.) 4 b.) 0 c.) 3 d.) 6

Which is not an example of the Identity Property?

a.) 7 X 1 = 7 b.) 2 X 4 = 8 c.) 1 X 200 = 200 d.) 4 X 1 = 4

• www.coolmath.com • www.studyisland.com • games • Math Blaster • X chart • Flash cards • White boards - Draw pictorial representations of each property.

On Going

i. Develop proficiency – basic multiplication facts (multiple strategies)

CPI: 4.1 B.1, .2, .4, .10

• Display an understanding/knowledge of multiplication facts up to 12

4 X 6 = 3 X 9 = 5 X 8 = j.

• same as above - Allow to learn one set of facts at a time/daily drill and practice with audio-visual and repetition. Assess and move up to next fact. Chart progress.


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k. Division (concept) – relate to multiplication, repeated subtraction, sharing

CPI: 4.1 B.1, .10

• Display an understanding and knowledge of division facts and related family of facts

If 3 X 6 = 18, then 18 ÷ 6 = ___ • Same as above - Use Unifix Cubes or other manipulatives to show relationship.

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l. 2-D and 3-D figures

CPI: 4.2 A.2

• Recognize/ label 2D and 3D figures • (solid and plane figures)

Which shape is an octagon?

a.) b.) c.) d.)

Which shape has 12 edges?

a.) cylinder b.) rectangle c.) cube d.) sphere

• www.studyisland.com • geometric shapes • geo-boards • overhead shapes

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m. Symmetry/Congruence CPI: 4.2 A.3

• Identify, describe and draw symmetrical objects.

• Recognize, describe and draw congruent and similar shapes

• Label parallel and perpendicular lines on a figure

• Locate items in the classroom and at home that are symmetrical/congruent/similar

For 1 – 5, use the lettered shapes below.

1.) Which shapes have at least 1 line of symmetry? ___________

• tracing paper • protractors - Provide shapes/use rulers/scissors.


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2.) Which pairs of shapes are congruent? _____ and _____ _______and ______ ______and_______

3.) Which shapes are quadrilaterals? ____________ 4.) Which shapes have at least 1 right

angle? ____________ 5.) Which shapes have parallel lines

____________

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n. Lines, segments, endpoints angles

CPI: 4.2 A.4

• Identify, describe and classify lines, line segments, rays and angles

What is the part of a line that has two endpoints called?

I am part of line. I have one endpoint. I am straight and continue in one direction. What am I?

a. Line b. Ray c. Line segment d. Angle

What figure is shown?

a. Intersecting lines b. A ray c. An angle d. Parallel lines

• www.studyisland.com • toothpicks • rulers


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Which triangle is a right triangle? __________ Which triangle has three equal angles? __________

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o. Transformations (slide, flip, turn)

CPI: 4.2 B.2

• Investigate and predict the results of an object in motion

• Participate moving their own bodies to understanding the transformation skill

How should each white shape be moved so it fits on the gray shape?

Choose one of the exercises above. Describe how you decided if it was a slide, flip, or turn.

• Shapes • Tracing paper

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p. Coordinate Geometry CPI: 4.2 C.1, .2

• Determine the coordinates for the ordered pair

• Find the ordered pair that matches the coordinate

What is the ordered pair for point D?

• Battleship game • www.studyisland.com - Teacher models on overhead with variety of colors. Use “over and up” terminology.


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a. (4,5) b. (5,4) c. (3,1) d. (4,2)

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q. Volume CPI: 4.2 D.2

• Measure the amount of space taken up by a 3D object in cubic centimeters

• Label length, width and height • Make the connection with LX W X H • Build shapes using cubes • Create a different shape by using the

same number of cubes • Think: ice cubes

These boxes were built with the centimeter cubes. Fill in the measurements and the volume of each box.

Volume : __________cubic cm

• Connecting cubes • Place value blocks • Centimeter ruler • Overhead activities


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Topic (s): Fractions, Probability, Discrete Math and Measurement Timeline: Quarter III

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Assessment



Assessment Model

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a. Fractions (denominators 2,3,4,5,6,8,10) parts of a whole, subset location on number line

CPI: 4.1 A.1, .5

• Identify and label the numerator and denominator in a fraction

• Explain orally what a fraction is and list information

• Stress the shaded parts of a whole • Compare and order fractions • Apply knowledge of fractions to

solve word problems

What portion is shaded in the above figure?

a. 5/1 b. 1/6 c. 5/6 d. 3/6

Use the figures to help answer the question. Which of the following fractions is the smallest?

a. 5/7 b. 2/2

• www.studyisland.com • fraction bars/ strips • number lines • www.mathgoodies.com • www.coolmath.com • math.com • -Overhead fractional

bars/strips along with individual manipulatives.

• Use graph paper and darkened lines to differentiate numerator and denominator.

• Dictate fractional numerals and allow students to practice on white boards.


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c. 2/3 d. 4/5

Name the fraction shown by the point on the number line.

Write the fraction that names the shaded part of the group.

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b. Probability of events and chance devices

CPI:

• Apply probability to real world situations

• List possible outcomes and predictions

• Use and understand vocabulary: likely, unlikely, certain, impossible and most likely

The marbles are shown are put into the bag. You pick one without looking. Which best describes the likelihood of choosing a dotted marble?

a. Certain b. Likely c. Unlikely d. Impossible

• Marbles • Spinners • www.studyisland.com • Every day items in a sack.

List all outcomes on overhead. Allow students to randomly select objects.

• Probability vocabulary chart


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If the four spinner above are spun 100 times each, which spinner will most likely land on the number 3 the most times?

a. W b. Y c. X d. Z

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c. Predict probability of outcomes

CPI:

• Predict the number of times an event will occur in an experiment

• Group activities with spinners and marbles

The following chips are placed in a bucket: 3 red, 5 yellow, 1 blue, and 2 green. One chip is randomly selected from the bucket. What color chip has the best chance of being selected?

a. Red b. Blue c. Yellow d. Green

A class of 28 students is having a drawing. Each student’s name is placed on a piece of paper then placed in a hat. One name is randomly drawn from the hat. If there are 14 boys in the class, is the randomly selected name more likely to be a boy’s name or a girl’s?

a. It is equally likely to be a boy’s or girl’s

b. Girl’s c. Boy’s

• www.studyisland.com • probability vocabulary chart • hands on activities • marbles • spinners • Draw a probability tree;

pictorial representation of all outcomes. Visual required.


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Seven balls are placed in a bucket. The balls are numbered from 1 to 7. One ball is randomly selected from the bucket. Which ball is more likely to be selected, ball # 1, ball # 3, or ball # 6? It is Carmen’s turn to spin a spinner to choose an activity for her physical education class. Carmen will spin the spinner below to decide what the class will do.

What is the probability of Carmen landing on bowling? Show your work.

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d. Represent and classify data according to attributes

CPI:4.4 C.1

• Sole an open ended word problem using a tree diagram model (problem of the day)

• Use prior knowledge of x skills to explain the different combinations

What information on this Venn Diagram is true only for bicycles, but not skateboards? Explain your answer.

• Venn Diagram models • Tree diagram models • www.mathpotd.org • multiplication chart


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What could be placed in the overlapping area of this Venn diagram?

a. Have sides that are different lengths

b. Have no straight lines c. Made up of 4 sides d. Made up of three sides

Casey has 3 pairs of pants and 2 shirts. How many combinations of pants and shirts can she make using 1 pair of pants and 1 shirt? Show your work.

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e. Vertex-edge and graphs CPI: 4.4 D.3, .4

• Identify faces, edges, bases and vertices on figures

• Apply skills of possible outcomes in solving word problems

• Analyze data to make decisions

The graph below shows the outline of a field.

How many vertices are on this graph?

a. 3 b. 6 c. 4 d. 5

In the picture below what is the smallest

• Geometric shapes/figures • Common classroom objects • Cubes • Test Prep materials for the

NJASK


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number of colors that can be used so that sections that touch each other do not have the same color?

a. 4 b. 3 c. 1 d. 2

To color the following map you want to use as few colors as possible. What is the fewest number of colors you can use so that no areas that touch are the same color?

a. 2 b. 3 c. 4 d. 5


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f. Measurement (select and use standard units, tools and estimation to solve real-life problems)

CPI: 4.2 D.4

• Distinguish the correct tools of measurement in order to solve word problems using real life information/situations

Which of the following tools would you use to measure the length of a soccer field?

a. Measuring cup b. Yardstick c. Thermometer d. Scale

One Batch of Cookies

The recipe above is for one batch of chocolate chip cookies. If you want to make two batches of chocolate chips cookies, how much flour will you need? Explain how you got your answer.

• Hands on measurement tools • Ounces, pints, cups etc • Capacity, weight and height • Rulers, containers, measuring

tape, yard stick, scales and dry/wet materials

• Provide opportunity for self-measurements. i.e. own height, weight, length of arm or foot.

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g. Length (fractions of in ¼, ½, in, ft, yd, cm, m, mile, decimeter, kilometer)

CPI: 4.2 D.2 4.3 B.1

• Build conceptual understanding of customary and metric measurement

• Apply measurement to real world situations

• Identify units of measurement to the nearest inch/ centimeter

• Convert units of length, capacity and weight

Measure the ribbon to the nearest half inch. How long is the ribbon?

a. 1 ½ inches b. 2 inches c. 2 ½ inches d. 3 inches

Use your ruler. What is the length of the

• in/cm rulers • input/output chart • measuring tools • Mark rulers ahead of time

with permanent marker at any fractional point. Color-code (red ½, blue ¼)

2 c. flour 2 c. sugar 2 eggs 1 t. baking soda 6 oz. chocolate chips 4 T. butter


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pencil to the nearest ¼ inch?

a. 2 ¾ inches b. 3 inches c. 3 ¼ inches d. 3 ½ inches

Measure the eraser to the nearest centimeter.

a. 1 cm b. 2 cm c. 3 cm d. 4 cm

Josh and his father are building a new stand for his fish tank. The legs of the stand will be 3 feet high. Complete the table below to find out how many inches high the legs will be.

Feet 1 2 3 4

Inches

12 24 48

3

h. Area (sq in, sq cm) CPI: 4.2 D.2

• Estimate the area of a shape measuring in square units

• Think: tiles or a rug • Draw /shade an area by covering it

with square units

What is the area of the figure drawn on the grid?

• square cm/in grid sheet • graph paper • overhead activities


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a. 38 square units b. 39 square units c. 36 square units d. 41 square units

What is the area of the shape below?

1 cm a. 6 cm b. 9 cm c. 8 cm d. 11 cm

3

i. Weight (oz, lb, gram, kilogram)

CPI: 4.2 D.1, .2

• Estimate , measure, compare, and order weight in metric / customary units

• Hands on classroom activities

Which object weights about 5 pounds? a. Apple b. Box of cereal c. Watermelon d. Slice of bread

• Scales • Measuring tools • Measurement charts • Students hold objects that

weigh 1 pound, 5 pounds, etc.

3

j. Capacity (pt, qt, liter, fluid ounce, cup, gallon, milliliter)

CPI: 4.2 D.1, .2 4.3 B.1

• Estimate , measure, compare, and order capacity in metric/ customary units

• Hands on classroom activities • Use and make recipes to make the

concept more concrete • Show the relationship in everyday

activities and math skills

Use the information shown below, which amount of liquid is between 3 cups and 4 cups?

• galloon gal • hands on manipulatives • measurement charts

4 cups ----------------------32 oz 3 cups-----------------------24 oz 2 cups-----------------------16 oz 1 cup--------------------------8 oz


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a. 29 ounces b. 33 ounces c. 23 ounces d. 5 ounces

Complete the table below to show how many cups there are in different numbers of gallons.

Gallons 1 2 3 4 5 6

Cups 16 32 48

5 on

going

k. Time (second, minute,1/4 hr, 1/2 hr., hr., elapsed)

CPI: 4.2 D.1, .5

• Recognize and tells time to the nearest minute, ¼ hr,1/2 hr and hour

• Identify elapsed time using charts and relate it to real life situations

What is another way to read the time?

a. 42 minutes before 8 b. 18 minutes before 8 c. 18 minutes after 8 d. 15 minutes before 9

l.

• Judy clocks • “movie time” table • Timeline • Use individual miniature Judy

Clocks and provide on overhead. Students model after teacher.


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Topic (s): Numerical Operations and Fractions Timeline: Quarter IV

Sugg

este

d D

ays

of

Inst

ruct

ion





Assessment



Assessment Model

5

a. Multiplication (2 digit x 1 digit)

CPI: 4.1 B.4

• Use known facts to solve X problems

• Multiply multiples of 10, 100 and 1000

• Calculate and multiple 2digits by I digit with and without regrouping

• Identify the connection between using models and pencil and paper algorithms

• Estimate products by rounding to the nearest 10, 100, and 1000

• Solve X problems using 3 and 4 digits by I digit

Find the exact value of 87 x 6. a. 522 b. 523 c. 604 d. 642

70 X 4

a. 820 b. 740 c. 280 d. 208

• www.studyisland.com • wwww.mathpotd.org • Math Blaster • Flash cards • White Boards • Counters/ dry beans • Use a multiplication table.

Lesson modeled using Madeline Hunter/Step-by-step instruction (visual)

5

b. Division facts (with remainder)

CPI: 4.1B.4

• Use known facts in multiplication to assist in division

• Illustrate the distribution (sharing) process of division

• Demonstrate knowledge of division vocabulary: quotient, dividend, divisor and remainder

• Estimate quotients • Divide by 1 digit with and without

a remainder • Key: D, M, S, B ( divide, multiply,

subtract, bring down

Divide 7) 51

a. 6 R 5 b. 8 R 2 c. 9 R 1 d. 7 R 2

Divide and show your work.

• same as above • Unifix Cubes broken into

equal groups; find “left-overs.” • Model lesson with step-by-

step visual instruction.


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6) 40

3

c. Fractions – adding and subtracting

CPI: 4.1 B.9, .10

• Add/ Subtract fractions with like denominators

• Develop problem solving skills in division ( looking for key words)

• Identify the numerator and the denominator

• Identify the multiples of a number using x facts and skills to complete a fraction number line

• Write fractions in the simplest form

6/8 + 1/8 = _______

a. 5/16 b. 7/16 c. 5/8 d. 7/8

Emily completed ¼ of her homework before dinner and 2/4 after dinner. What part of her homework did she do in all? Explain how you found your answer.

a. 4 b. 2/4 c. 3/8 d. ¼

5/6 – 1/6 = _________

a. 4/12 b. 4/6 c. 6/6 d. 4/4

Pablo has ¾ of a pizza to share. Amy and Tim eat 2/4 of the pizza. How much pizza is left?

a. 1/8 b. ¼ c. 5/8 d. 2/4

• www.studyisland.com • www.math.com • fraction bars/strips • overhead activities and

manipulatives


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3

d. Equivalent Fractions CPI: 4.1 A.5

• Write fractions as equal parts of a group

• Identify equivalent fractions • Convert coins/dollars to represent

fractions and decimals

½ = ?/10

a. 1 b. 2 c. 5 d. 10

Which models show equivalent parts shaded?

• graph paper • fraction bars/circles • play money • number lines • counters • Using plastic fraction strips,

match to another fraction of equal size. Write out on graph paper.


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3

e. Ordering Fractions CPI: 4.1 A.6 4.3 D.2

• Apply their knowledge of fractions to show the order of least to greatest and greatest to least

• Apply fractions to real world situations

• List/Write ingredients needed to follow a recipe

• Display recipes and compare and discuss amounts needed

What group of fractions is in order from the least to greatest?

a. ½, 2/3, ¼ b. ¼ , ½, 2/3 c. ¼, 2/3, ½ d. 2/3, ½, 1/4

Linda is making cheese sauce.

Cheese Sauce 2 ½ cups milk

¼ pound butter

¾ cup Parmesan cheese

½ cup cheddar cheese

¼ cup mozzarella cheese

• Which type of cheese will she use the

least amount of? Which amount of cheese will she use the greatest amount of?

• Draw fraction bars to order the fractions

of cups of cheese from greatest to least.

• Class project (recipes) • Number line • Fraction strips • Fruit, pizza and goldfish


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5

f. Decimals – relationship to fractions

CPI: 4.1 A.1, .5

• Identify and explain the importance of the decimal point

• Understand the meaning of tenths and hundredths

• Compare and order decimals using real life situation i.e.; running, swimming, ERA in baseball

• Identify fractions and decimal that are equivalent

Which decimal does the shaded part of the model show?

a. 0.03 b. 0.07 c. 0.37 d. 0.70

What is the fraction for the decimal?

Ones • Tenths

0 • 4

a. 40/10 b. 10/40 c. ¼ d. 4/10

• cm graph paper • overhead activities • stop watch • play money • place value manipulatives

and charts • number line • base ten blocks and flannel

board to move a decimal point.

FREEHOLD BOROUGH PUBLIC SCHOOLS … Borough Public Schools Curriculum Management System Grade 3...

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