Grade 2nd Six... · Web viewIn training for a marathon, Arturo must run 105 miles each week. If he...

West-Orange Cove ISD 4th Grade Mathematics – 2nd Six Weeks 2012 - 2013

Week 1Oct. 1 - 5

Learning Standards:4.4 Multiply and divide to solve meaningful problems involving whole numbers.4.5 Estimate to determine reasonable results.4.6 Use patterns in multiplication and division.4.7 Use organizational structures to analyze and describe patterns and relationships.4.14 Apply Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.4.15 Communicate about Grade 4 mathematics using informal language.4.16 Use logical reasoning.Reporting Category 1

Major Concepts: Multiplication Relationship between

addition and multiplication

Multiplication is a pattern

Processes: Properties of Multiplication Problem solving model Use accountable talk by using the language

of mathematics Multiplication can be represented by

modeling the factors (arrays)

Learning Standard Instruction Resources Math Stations Assessment

4.4BRepresent multiplication anddivision situations in picture,word, and number form.

Key Vocabulary: array, product, factors, multiple, Commutative Property of Multiplication, Zero Property of Multiplication, Identity Property of Multiplication, Distributive Property, column, row

Represent Multiplication Situations using pictures, words, and numbers.

Prompt the students to use pictures, words, and numbers to represent multiplication situations.

Example:Ask the students, “How can this multiplication situation be represented with pictures, words, and numbers?” Frank is arranging his toys on bookshelves. He puts 4 toys on each shelf. If he fills 3 shelves with toys, how many toys does Frank have altogether? Pictorial Representation of possible answer

Word Representation Possible Answer:

enVision Topic 7, Lessons 1 - 5

Internet link for teaching multiplication facts using the finger method:http://www.metacafe.com/watch/891715/math_trick_for_your_fingers_easy_multiplication/

Technology: Pearson enVision link for animated introduction, journal writing, and review – copy and paste this link:

https://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=toc&newServiceId

Manipulatives: dice, cards, counters

Multiplication fact drills/chart

Multiplication games using dice or cards

Problem Solving – word problems involving mixed operations including multiplication. Problem solving strategies make an organized list, missing or extra information, drawing a picture, and looking for a pattern.

Journal writing – Write a reflection of when you have or could have used multiplication in your everyday life.

Number of the week

Measurement Station

Formal enVision Math Assessment – Profile, set goals, and use data for intervention groups

Readiness Standards = Red Supporting Standards = Green All other Standards = Blue




http://www.metacafe.com/watch/891715/math_trick_for_your_fingers_easy_multiplication/




4.14B Solve problems that incorporateunderstanding the problem,making a plan, carrying out theplan, and evaluating the solutionfor reasonableness

There are 3 groups with 4 toys in each group. There are a total of 12 toys.

Numerical RepresentationPossible Answer: 3 × 4 = 12

Create a number sentence that represents a multiplication situation.

In training for a marathon, Arturo must run 105 miles each week. If he runs the same number of miles each week, what number sentence can be used to find the number of miles Arturo will run in 7 weeks?

Understanding the Problem:• Ask the students to restate the content of the problem in their own words.• Ask the students, “What are we trying to find out?”Possible Answer: “We are trying to find out how many miles Arturo will run in 7 weeks.

Making a Plan:Ask the students, “How will thinking about groups help us make a plan to solve this problem?”

Ask the students, “What are the groups suggested in this problem? How many groups are there?”

Possible Answer: “The number of miles Arturo runs each week are equal groups. The number of weeks is the number of groups. When combining equal groups of a quantity, we need to multiply to find a total number of miles.”

Carrying out the Plan:Ask the students, “How are you going to solve the problem?”

Possible Answer: “We can add 105 seven times, or we can multiply 105 x 7.”

Evaluating for Reasonableness:

Interventions/ExtensionsBased on student needs

Work with students in small groups to make arrays by providing them with a product and they discover all the factors by making arrays using tiles or other counters.

Extension: Students will write 2 multiplication sentences for the number 36,000. Students will then represent their sentences in a drawing and write an explanation explaining why it is reasonable and how they solved the problem.

GT: Students will solve the following problem from Van de Walle: Yesterday as we planned for the school’s Fall Festival, we discovered that it took 7 yards of paper to cover the bulletin board in the front lobby of the school. There are 25 more bulletin boards in the hallways and classrooms around the school. How many yards of paper will we need if we help to cover all the bulletin boards in the school?

Products/project

Concept map

Draw an array showing the number of desks in the classroom

Write a multiplication word problem for a partner to solve.



4.4D Use multiplication to solve problems (no more than two digits times two digits without technology).

4.14D Use tools such as real objects, manipulatives, and technology to solve problems.

Ask the students, “Have we answered the question that the problem asked?”

Ask the students, “How do we know that our answer is reasonable?”

Possible Answer: “We wrote the number sentence 105 x 7 = ____ because the problem can be solved with multiplication.”

Multiply Whole Numbers (up to 2-digitnumbers x 2-digit numbers)

• Develop strategies to use with multiplication.

Use base ten blocks to represent a 2-digit times 2-digit multiplication problem.



4.14BSolve problems that incorporateunderstanding the problem,making a plan, carrying out the


West-Orange Cove ISD 4th Grade Mathematics – 2nd Six Weeks 2012 - 2013plan, and evaluating the solutionfor reasonableness

Use a problem-solving model to solve multiplication problems.

Example:Diego has 24 boxes to fill with cans of soup. Each box holds 36 cans of soup. How many cans of soup will he pack in 24 boxes?

Understanding the Problem:• Ask the students to restate the problem in their own words.• Ask the students, “What are we trying to find out?”

Possible Answer: “We are trying to figure out the number of cans of soup that Diego can pack in 24 boxes.”

Making a Plan:• Ask the students, “Are we putting things together, or are we separating them?”• Ask the students, “How can thinking about groups help us solve this problem?”

Possible Answer: “We are putting groups of 36 cans of soup in each box, and we have 24 boxes to pack. Since we are combining equal groups, we can add 36 twenty-four times, or we can multiply 36 x24 to get the answer.

Carrying out the Plan:•Ask the students, “How are you going to solve the problem?”

Possible Answer: “We can draw 24 squares to represent the boxes and put 36 in each box to represent 36 cans of soup in each box. Then we can add the 24 groups of 36 or multiply 36 × 24.”

Answer: 864 cans of soup

Evaluating for Reasonableness:• Ask the students, “How do you know that your answer is reasonable?”

Possible Answer: “We can use rounding to estimate our


West-Orange Cove ISD 4th Grade Mathematics – 2nd Six Weeks 2012 - 2013product. Twenty-four rounds to 20, and 36 rounds to 40. Then we multiply 20 × 40 and we get 800. This estimate is close to our actual answer.”



Week 2Oct 8 – Oct. 125 Instructional

Days

Learning Standards:4.4 Multiply and divide to solve meaningful problems involving whole numbers.4.5 Estimate to determine reasonable results.4.6 Use patterns in multiplication and division.4.7 Use organizational structures to analyze and describe patterns and relationships.4.14 Apply Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.4.15 Communicate about Grade 4 mathematics using informal language.4.16 Use logical reasoning.RC – 1,6

Major Concepts: Division is the inverse of

multiplication Division is separating items

into equal groups Division facts make up half

of a fact family. (Each fact family for multiplication/division have 4 facts – 2 multiplication and 2 division)

Processes: All of the facts are

conceptually related. You can figure out new or unknown facts from those you already know (Van de Walle.)

Students should be encouraged to use inventive strategies in problem solving

Accountable talk – using the language of mathematics

Problem solving model

Note: Forms and templates are in the

curriculum documents file.

Learning Standards

Instruction Resources Math Stations Assessment

4.6AUse patterns and relationships todevelop strategies to rememberbasic multiplication and divisionfacts (such as the patterns inrelated multiplication and divisionnumber sentences (fact families)such as 9 9 = 81 and 81 9 =9

Key Vocabulary: round, estimate, reasonable, quotient, division, divisor, factor, multiple, fact family, product, dividend, divisibility rules, remainder

This week division is introduced and taught. Students in 4th

grade are expected to have the skills to divide one-digit divisors and three-digit dividends.

Introduce the concept using either the literature connection with follow up lesson plan or technology. Use enVision Math lessons 4-1 and 4-2

Students must make the connection between multiplication and division. Ask, “what thought process do you use to recall facts such as 48/6 or 36/9? Students should be encouraged to think about what they are thinking and to verbalize it to a partner using a think/pair/share strategy.

There are two basic kinds of division problems and students should be familiar with both types. They are sharing and measurement problems. The first, sharing means to partition equally. Example: There are 125 gumballs in a bag. Maria and 4 friends want to share them equally. How

enVision Math Texas – Topic 4

Counters

Technology: Pearson enVision link for animated introduction, journal writing, and review – copy and paste this link:https://www.pearsonsuccessnet.com/

enVision eTools

Literature – “The Doorbell Rang” by Pat Hutchins

http://www.lessonplanspage.com/printables/PMathLAMultiplicationDivisionUsingTheDoorbellRang23.htm

Number fluency – addition , subtraction, multiplication, division

Problem Solving – word problems and problem solving strategies.

Journal Writing – Write a news article explaining the connection between multiplication and division.

Number of the week

Measurement Station

Teacher observation

Journal entry





https://www.pearsonsuccessnet.com/



4.4EUse division to solve problems(no more than one-digit divisorsand three –digit dividends without technology

many gumballs will Maria and her friends get?

The other kind of division problem is measurement based. For example: Duke loves milk bones. If his owner gives him 4 bones each day, how many days will a box of 94 bones last?

Although we are encouraging students to use inventive strategies for problem solving be sure to teach them two traditional algorithms. The first is the standard and the second is the partial quotient method. Provide students with a reference to remember the steps in long division. There are many examples available on the Internet. The campus mnemonic strategy is: DMSCBR (Does McDonalds Serve Cheeseburgers which means - divide, multiply, subtract, check, bring down, repeat

http://www.youtube.com/watch?v=UVE6ZIV7tv

Multiplication Chart

Interventions/Extensions

Use the below level task on P. 90F for struggling students. In this task students practice division using manipulatives.

Use a completed multiplication chart to explore patterns.

Extension:Students write and illustrate several divisibility rules.

GT: Illustrate different algorithms for multiplication and division for your Math Project Book.

Product/ProjectFrayer ModelConcept MapReal life problem solving illustrations

Students will solve and write their explanation:

6 x 7 =

In assessing, this problem, look for specific strategies like double and double again, or 6 x 5, or 3 x 7 + 3 x 6. You are looking for number fluency and the students’ ability to decompose and compose numbers in a systematic method. Based on student responses, pose advancing questions to stretch their thinking.





Another method some students may prefer is the :

Next use lessons 4-3 through 4-5 to provide students multiple opportunities to explore problem solving and fact families


West-Orange Cove ISD 4th Grade Mathematics – 2nd Six Weeks 2012 - 2013Week 3 and

Week 4Oct 15 – 19 and Oct 21 - 269 instructional days, 1 day for assessment and profiling

Learning Standards:4.4 Multiply and divide to solve meaningful problems involving whole numbers.4.5 Estimate to determine reasonable results.4.6 Use patterns in multiplication and division.4.7 Use organizational structures to analyze and describe patterns and relationships.4.14 Apply Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.4.15 Communicate about Grade 4 mathematics using informal language.4.16 Use logical reasoning.RC – 1,6

Major Concepts: Basic math facts and place value

patterns can be used to divide multiples of 10 and 100 by one digit numbers

Remainders must be less than the divisor

Processes: All of the facts are conceptually related.

You can figure out new or unknown facts from those you already know (Van de Walle.)

Students should be encouraged to use inventive strategies in problem solving



Learning Standards

Instruction Resources Math Stations Assessment

4.5ARound whole numbers to thenearest ten, hundred, orthousand to approximatereasonable results in problemsituations.

4.14AIdentify the mathematics ineveryday situations.

Key Vocabulary - round, estimate, reasonable, quotient, division, divisor, factor, multiple, fact family, product, dividend, divisibility rules, remainder, compatible

The next two weeks will be a continuation of multiplication and division and making the connection. It is very important students master their facts before moving into the next segment of learning objectives.

Round Whole Numbers To Estimate Quotients - • Estimate to determine reasonable results.

Example:

Mr. Benavente’s fourth-grade class is collecting sweaters for the local charities. They have collected 183 sweaters to share evenly among the 9 local charities. About how manysweaters will each charity receive? Prompt the students to round 183 to 180, and then divide 180 by 9.

Answer: About 20 sweaters

enVision Math -Topic 8 and reteach of Topic 3,4, 5, 6, & 7 as needed

Technology: Pearson enVision link for animated introduction, journal writing, and review – copy and paste this link:https://www.pearsonsuccessnet.com/

enVision eTools

Manipulatives - counters, base ten

Number fluency – addition , subtraction, multiplication, division

Problem Solving – word problems and problem solving strategies.

Journal Writing - Explain how knowing your multiplication facts will help you solve division problems.

Number of the week

Measurement Station

Formal - Test –Curriculum Based Assessment #3 and profiling



West-Orange Cove ISD 4th Grade Mathematics – 2nd Six Weeks 2012 - 20134.14 CSelect or develop an appropriateproblem-solving plan or strategy,including drawing a picture, looking for a pattern, systematicguessing and checking, acting it out, making a table, working asimpler problem, or workingbackwards to solve a problem.

4.5BUse strategies including roundingand compatible numbers toestimate solutions tomultiplication and divisionproblems.

4.4BRepresent multiplication and division situations in picture, word, and number form.

Use compatible numbers to estimate solutions.

Example:

Millie read 249 pages of her novel in 5 days. If she read about the same number of pages each day, about howmany pages of her book did she read each day?Prompt the students to determine that they are dividing pages read into groups of pages read per day. Promptthe students to determine that 249 is close to 250 and that 250 is easily divisible by 5. 250 ÷5 =50 pages

Solution: 50 pages is a reasonable estimate of the number of pages that Millie read each day.

Represent Division SituationsRepresent division situations using picture, word, andnumber form.

Example:Ask the students, “How can this division situation be represented with pictures, words, and numbers?”

Intervention/ExtensionStudents that are still struggling with learning their multiplication facts should continue to learn them using real world problems in addition to practice in stations. Continue letting struggling students use their multiplication chart and or a calculator for problem solving.

Extension: Students that have mastered their facts can conduct a survey of their favorite local animal. Students spend 20 minutes a day outside for one week and count the number of times they spot their animal. At the end of the week they display their data in a table. Challenge students to then calculate how many times their animal would be spotted in a month, three months, 6 months, 9 months, and 1 year. (modified from P 175 enVision Math)

GT: Divide 583/4. After solving this problem, write a paragraph explaining how to solve the problem without using the words “goes into”.

Product/ProjectConcept Map – Multiplication/DivisionJournal entryProblem solving illustrations



4.15BRelate informal language tomathematical language and symbols

Shilo has 12 star stickers to share equally among herself and her 2 sisters. How many star stickers will each sister get?

Pictorial Representation (possible answer)

Word Representation (Possible Answer):12 star stickers divided equally into 3 groups equals 4 star stickers in each group.

Numerical RepresentationAnswer: 12 ÷3 = 4 star stickers• Create a number sentence that represents a division situation.

Example:Mrs. Lopez is rearranging the jars on her spice rack. If Mrs. Lopez has 54 jars and 6 shelves, how many jars can she put on each shelf?Answer: 54 6 = 9 jars

4.14BSolve problems that incorporateunderstanding the problem,making a plan, carrying out theplan, and

Use a problem-solving model to solve division problems.

Example:Joseph has 115 marbles to divide into 3 bags. If each bag needs to have an equal number of the marbles, how many marbles will be in each bag?

Understanding the Problem:• Ask the students to restate the problem using their own


West-Orange Cove ISD 4th Grade Mathematics – 2nd Six Weeks 2012 - 2013evaluating the solution for reasonableness

4.7ADescribe the relationshipbetween two sets of related datasuch as ordered pairs in a table.

words.• Ask the students, “What are we trying to find out?”Possible Answer: “We are supposed to find out how many marbles each bag contains after the marbles have been evenly divided.Making a Plan:• Ask the students, “Which operation will be most useful inhelping us determine the answer?”Possible Answer: “We have a total of 115 marbles and 3 bags. We will use division to separate the marbles intoequal groups.”Carrying out the Plan:• Ask the students, “How are you going to solve the problem?”Possible Answer: “We can divide 115 by 3, and get 38 marbles in each bag with 1 marble remaining.”Evaluating for Reasonableness:• Ask the students, “How can we be sure that the answer wehave is correct?” • Ask the students, “How do we know our answer is reasonable?Possible Answer: “We can evaluate the solution for its reasonableness by estimating. Since 38 is close to 40 andthere are 3 bags with 40 marbles, we will have a total of 120, which is close to the original number of marbles westarted with. Thus, the solution is reasonable.

Describe Relationships in TablesExample:What is the relationship between the numbers in Column B and the corresponding number in Column A?

Column A Column B7 114 221 328 435 5

Answer:


West-Orange Cove ISD 4th Grade Mathematics – 2nd Six Weeks 2012 - 2013The number in column B is the number in Column A divided by 7, or the number in Column B is 1/7the number in column A.


West-Orange Cove ISD 4th Grade Mathematics – 2nd Six Weeks 2012 - 2013Week 5Oct 29 - Nov 25 instructional days

Learning Standards4.2 Describe and compare fractional parts of whole objects or sets of objects.4.10 Recognize the connection between numbers and their properties and points on a line.4.14 Apply Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.4.15 Communicate about Grade 4 mathematics using informal language.4.16 Use logical reasoning.

Major Concepts Each whole numbers,

decimals, and fraction can be associated with a specific point on a number line.

You can use a number line to compare whole numbers, fractions, and decimals

The more fractional parts used to make a whole, the smaller the parts.

Processes: Locating fractions and decimals on a number

line provides a visual reference to understand the values of fractions/decimals

Information in a problem can be represented by a picture or diagram to help solve a problem



Learning Standard Instruction Resources Math Stations Assessment4.10ALocate and name points on a line using whole numbers, fractionssuch as halves and fourths, anddecimals such as tenths.

Key Vocabulary: number line, fraction, whole number, mixed number, numerator, denominator, equivalent fraction. Simplest form, improper fraction

The next three weeks is dedicated to teaching fractions. Begin by reviewing and connecting all new vocabulary terms. Add fractions to your concept map.

Once students have a firm grasp of how decimals and fractions are connected to the place value system begin teaching them to locate fractions and decimals on a number line. This is covered in Topic 13

Locate and Name Points on a Number Line:

Locate and name points on a number line using fractions.

Example:Which point on the number line best represents 2 ½?

enVision Math – Topic 13

Technology: Pearson enVision link for animated introduction, journal writing, and review – copy and paste this link:https://www.pearsonsuccessnet.com

Manipulatives: Fraction circles Cuisenaire rods Fraction strips/bar Paper Plates

Number fluency – addition, subtraction, multiplication, and division – use a mix of timed drills and computation

Problem Solving – word problems involving multi-steps

Journal writing - how do you use fractions in your everyday life?

Number of the week

Measurement Station

.Informal or formal – students are able to draw a number line and locate specific fractions on it.





4.2AUse concrete objects and pictorialmodels to generate equivalentfractions.4.14DUse tools such as real objects,manipulatives, and technology tosolve problems.

Interventions/ExtensionsBased on student needs

Intervention: Use real world objects such as pizza or a Hershey candy bar to demonstrate fractions parts of a whole.

Extension: Solve the following problem using a model: Four children are sharing 10 brownies so that each one will get the same amount. How much can each child have?

GT: Students will draw a number line and label points 0, ½, 1. Next students will label 3 additional points between 0 and ½ and three additional points between ½ and 1. Students will then write and justify their thinking for the points on their number line.

Continue working on Math Book Project.

Products/Project

Frayer Model – fraction

Students will model parts of a whole for halves, thirds, fourths, sixths, and eights using a paper plate.



4.2AUse concrete objects and pictorialmodels to generate equivalentfractions.4.14DUse tools such as real objects,manipulatives, and technology

Equivalent Fractions

Example:Prompt the students to name a fraction equivalent to ½

.Prompt the student to use concrete models such as fraction bars to create a model that represents ½

.



4.16AMake generalizations frompatterns or sets of examples andnonexamples.

4.16BJustify why an answer isreasonable and explain thesolution process.

Ask the student, “Can you explain how you got your answer and how you know that it is reasonable? Possible answer: “I was able to generate fractions equivalent to ¾ by creating a model of ¾ and then dividing the parts of the model into smaller equal-sized pieces and writing a fraction to describe the new model. I know that my fractions are equivalent because the amount of the model that was shaded did not change. I know that my model of 1/3 is not equivalent to ¾ because the shaded portions of the models are a different size.


Grade 2nd Six... · Web viewIn training for a marathon, Arturo must run 105 miles each week. If he...

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