Third Grade Math-Third Six-Weeks Grade... · Web viewThe ability to break numbers apart in flexible ways is very important as they use invented strategies to solve multiplication

West-Orange Cove ISD 3rd Grade Mathematics – 3rd Six Weeks 2012 - 2013

Week 1 - 3

Nov 5 – 9

Nov 12 – 16

Nov 26 – 30

Learning Standards

4) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations. The student is expected to (A) learn and apply multiplication facts through 12 by 12 using [concrete] models [and objects];(B) solve and record multiplication problems (up to two digits times one digit); and(C) use models to solve division problems and use number sentences to record the solutions.

Major Concepts

Multiplication

Problem Solving

Processes: Problem Solving Model Thinking about learning and making

connections Use accountable talk by using the language of

mathematics

Instruction Resources Math StationsInterventions/Extensions

Assessment

Key Vocabulary – multiplication, division, equal groups, array, product, factor, horizontal, vertical, multiply, divide, divided by, input, output, fact family

The third six weeks is focused on multiplication and division. The first three weeks will be learning multiplication and the last three weeks, division. Students are expected to recognize and solve problems in multiplication and division situations.

Math background for teachers:

Multiplication may be thought of as repeated addition and involves joining equal groups.

An array involves joining equal groups and is another way to think of multiplication.

Two numbers can be multiplied in any order. Help students make connections to multiplication through skip

counting using number lines and hundreds charts. The ability to break numbers apart in flexible ways is very

important as they use invented strategies to solve multiplication. Teach the distributive property is an important concept. Teach

enVision Math –Topics 6, 7, 8, and 9

enVision Math Tools

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

http://express.smarttech.com/?url=http://exchangedownloads.smarttech.com/public/content/77/77c5bbc7-ecd1-4162-88dd-ecc7e8816a75/mutiplication.notebook#

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enVision Math multiplication games

Multiplication games using dice or cards

Problem Solving – word problems involving mixed operations including multiplication.

Journal writing – explain how multiplication is related to addition

Number of the week

Measurement Station

enVision Math Assessments

TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day Page 1

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students that they can solve 43 x 5 by breaking it into 40 x 5 + 3 x 5 then adding the results. Provide numerous opportunities for students to manipulate and apply strategies for solving.

Use number lines to solve multiplication problems. Students will not learn multiplication facts through “drill and kill” Students must learn to select ways to think about multiplication

that makes sense and are meaningful to them. Students tend to use three categories when solving multiplication:

(Van de Walle)o Complete-Number Strategies – These students are usually

not comfortable breaking numbers into tens and ones. For example 58 x 5. Students will do repeated addition and add 58 five times. When they could have multiplied 50 x 5 and 8 x 5 then added them together.

o Partitioning Strategies – (several examples of partitioning) 27 x 4 - 4 x 20 =80 4x7 = 28 46 x 3 double 46 = 92 + 46 = 138 27 x 4 = 10 x 4, 10 x 4, 7 x 4 then add the totals of

each to get 108 27 x 8 = 25 x 4, 25 x 8, 2 x 8 add the totals to get

216o Compensation Strategies –numbers are manipulated in a

manner the student is comfortable using. For example 27 x 4 may be seen as 27 + 3 = 30 x 4 = 120, 3 x 4 = 12, 120 – 12 = 108

Multiples of 10 and 100 – follows the familiar pattern of base 10 students are familiar with. Students will use 4 x 12 = 48 to solve 400 x 12 = 4,800. Students should not be taught to add zeros without understanding the concept of multiplying by 10 or 100.

Arrays are excellent models for concrete learning of multiplication. (This is a good time to connect arrays to finding area.)

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Foam Tiles

Counters

Dice

Playing Cards

Base 10

Interventions/Extensions

Often students “shutdown” when they hear the term multiplication. To help overcome this use egg cartons and counters to make the connection of multiplication being repeated addition. Pose fact problems to students such as 3 x 5. Students will put five counters in each of 3 compartments in the egg carton. Repeat several times then let students challenge each other.

GT: Students that are more familiar with multiplication and or know their facts can play a multiplication game. Student rolls two dice to get their first factor and write it down. Next they roll one die and multiply the 2 digit factor by it. Repeat 10 times, each time keeping a running total. Students then trade papers and check each other’s work. The student with the greatest ending total wins.

Products/project

Students will use newspaper or construction paper to make arrays for a given product

Students will work in groups to create and present visual representations of the properties of multiplication







There are four problem structures students should be familiar with to be efficient problem solvers.

1. Equal groups: Whole unknown. Jacob has 4 bags of oranges. There are six oranges in each

bag. How many oranges does Jacob have altogether? (Repeated addition.)

If oranges cost .10 each, how much will he pay for 5 oranges? (rate)

If He walked for 3 hours at 4 miles per hour, how far did he walk? (rate)

2. Comparison Problems – Product unknown. Susan picked 6 apples. Maria picked 4 times as many apples

as Susan. How many apples did Maria pick?3. Combinations Problems – Product Unknown.

Juan bought 4 pairs of jeans and 3 shirts and they can all be worn together. How many different outfits consisting of a pair of pants and a jacket does Juan have?

4. Area and other product-of-measures problems – the product is a different type of unit from the other two factors.

For example, length x width = area (usually square units.) (adapted from Van De Walle)

Again, the next five weeks are dedicated to multiplication. Begin with topic 6 – Multiplication meanings. Next introduce facts and strategies using patterns using topics 7 – 9.



Identify Patterns in Multiplication Facts

Use concrete objects, pictorial models, and technology to identify patterns in multiplication facts.

Example:Ms. Martin placed 4 vases on her desk. If there were 2 flowers in each vase, how many flowers were there all together?

Possible Answer: There are four vases, and each vase has 2 flowers. The number of flowers can be determined by 2 + 2 + 2 + 2 = 8 or2 4 = 8.

Example:Tamara purchased sheets of stickers for her sticker collection. Each sheet had 7 stickers on it. What are the possible numbers that Tamara could have said if she counted the stickers in groups of 7?



Possible Answers: The answers are multiples of 7. Possible answers are 7, 14, 21, 28 or 21, 28, 35, 42.

Example:

Ask the students, “What number sentence best represents the arrangement of the objects?”

Answer: 4 7

Example:

Albert placed the pencils from his pencil box in the arrangement shown below. How could you describe Albert’s pencil arrangement?



Possible Answers:

2 groups of 5 pencils, 2 equal groups of pencils with 5 pencils in each group, 2 rows and 5 columns, or 2 5

Example:

The pattern below shows a portion of the arrangement of stars in the floor tiles in Sharice’s room. Describe the arrangement of stars on Sharice’s floor tiles.

Possible Answers:

7 rows with 6 stars on each row,

6 columns with 7 stars in each column, 7 6, or 7 groups of 6 stars.


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Learn and Apply Multiplication Facts

Use concrete models to learn and apply multiplication facts through 12 by 12.

Example:Prompt the students to use concrete models such as color tiles to represent the array 3 5. Prompt the students to multiply the number of rows by the number of columns in order to determine the value of the array.

Answer:

Describe a pictorial representation of a multiplication fact with a number sentence.

Example:Ask the students, “How can this representation of a multiplication fact be described with a number sentence?”



Answer: There are 3 equal groups of 4 butterflies for a total of12 butterflies. 3 4 = 12.

Example:

While walking in the park, Jeremy saw 12 ladybugs. If each ladybug has 6 legs, how many ladybug legs did Jeremy see?

Prompt the students to use concrete models such as counters to solve the problem.

Answer: The product is 72.

6 12 = 72.



Multiplication

Solve and record multiplication problems.

Example:

There are 8 spiders in a jar. If each spider has 8 legs, how many spider legs are there all together?

Possible Solution Strategies:

Draw a picture, use concrete models, use repeated addition, or use multiplication.

Answer: The product is 64. 8+8+8+8+8+8+8+8=64 or 8 8 = 64.



Example:

James loads boxes on trucks for a shipping company. On Tuesday, James loaded 5 trucks with 52 boxes in each truck. How many boxes did James load on trucks on Tuesday?

Possible Solution Strategy:

Use base ten blocks in an area model.

Using partial products:

525

10 5 2 = 10+ 250 5 50 = 250

260

Answer: The product is 260.52 5 = 260.

Solve multiplication problems.

Example:

Jacquelyn’s choir had 95 members. Each member sang 3 solos for individual competitions during last month’s regional performance. How many solos did Jacquelyn’s choir sing all together?

Understanding the Problem:

Ask the students, “What are you trying to find out?”



Ask the students to restate the problem.

Possible Answer: “We need to find out how many total solos were sung by the 95 choir members.”

Making a Plan: Ask the students, “Are you joining equal sets or separating sets

of objects into equal groups?” Ask the students, “What is the important information in the

problem?”

Possible Answer: “We are joining equal sets, so we will multiply. The important information in the question is the number of choir members and the number of solos.”

Carrying out the Plan: Ask the students, “How did you solve the problem?”

Possible Answer: “We multiplied95 by 3.”

Evaluating for Reasonableness: Ask the students, “How do you know your answer is

reasonable?”

Possible Answer: “We knew that each choir member sang 3 solos, and there were 95 choir members. We estimated 95 as 100. So,100 3 = 300 and 300 is close to 285. We multiplied 95 by 3 to get our answer.”

Answer: 285 solos




Week 4 - 6

Dec 3 – 7

Dec 10 – 14

Dec 17 - 21

Learning Standards4) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations. The student is expected to (A) learn and apply multiplication facts through 12 by 12 using [concrete] models [and objects];(B) solve and record multiplication problems (up to two digits times one digit); and(C) use models to solve division problems and use number sentences to record the solutions.

Major Concepts

Division

Problem Solving

Processes: Problem Solving Model Thinking about learning and making

connections Use accountable talk by using the language of

mathematics

Instruction Resources Math StationsInterventions/Extensions

Assessment

Key Vocabulary – division, dividend, division, quotient, array, difference, fact family, factor, product

Math background for the teacher: Multiplication and division have an inverse relationship. Every division fact has a related multiplication fact. Students can use near facts to solve problems. There are two concepts of division:

o The partition or fair sharing – Tom has 360 Pokeman cards and he wants to share them equally with three friends. How many cards will Tom and each of his three friends have?

o The measurement or repeated subtraction – Spot’s master has a bag of 125 dog treats. Spot loves his dog treats and will do tricks to earn them. If spot’s master gives him 5 treats a day, how long will the bag of treats last?

Students must learn to solve both types of problems but you should start with the fair sharing because it is an easier concept for students to grasp and have success.

Fact families can be used to make connections to multiplication and division.

enVision Math -Topic 10

enVision Math Tools

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

http://express.smarttech.com/?url=http://exchangedownloads.smarttech.com/public/content/e7/e70adfb2-a7b4-4ce2-b830-49a8103fa3db/Division%20Lesson.notebook#

http://express.smarttech.com/?url=http://exchangedownloads.smarttech.com/public/content/c1/c14097a3-4d76-4dc2-a36c-3ecb946abc66/Fact%20Family(41).notebook#

enVision Math multiplication and division games

Multiplication games using dice or cards

Problem Solving – word problems involving mixed operations including multiplication and division.

Journal writing – explain how division is related to multiplication

Number of the week

Measurement Station

Interventions/Extensions

Students will use manipulatives to demonstrate fair sharing and repeated subtraction to solve problems.

GT: Students will write a letter to their grandmother

enVision Math Assessments

Products/project

Students will work in groups to create and present visual representations of division problems







https://www.pearsonsuccessnet.com/



Documents

Third Grade Math-Third Six-Weeks Grade... · Web viewThe ability to break numbers apart in flexible ways is very important as they use invented strategies to solve multiplication