Go Math 2012 Common Core

Program Overview Grades K–6

GO Math! is built for the COMMOn COre

READ ME FIRST

Common Core Instruction ��6

Instructional Support ��8

Digital Path ��10

Differentiated Instruction ��12

Response to Intervention ��14

Assessment ��16

• It’s New

• It’s Common Core

• It’s Built for Student Success

Table of Contents

COMMOn COre editiOn

Here’s a glimpse of what you will find in

Children record, represent, solve, and explain as they discover and build new understandings, right in their student books.

Every lesson is four pages to ensure students are learning mathematics at a deeper level of understanding.

It’s New!It’s coMMoN coRE It’s Built for Student Success

NEW Write-In Student Edition

Since GO Math! was built for the Common Core, all the Mathematical Practices are completely embedded in the lessons.

NEW Ways to Engage

MATHEMATICALPRACTICES

COMMON CORE

4 5

NEW Color Coding for Critical Areas

NEW Common Core State Standards Practice Book

NEW MathBoards

© Houghton Mifflin Harcourt School Publishers

Side ALado A

1180489 0-15-385878-8 9780153858789

Read the Problem Lee el problema

Solve the Problem Resuelve el problema

What do I need to find?¿Qué debo hallar?

What information do I need to use?¿Qué información necesito usar?

How will I use the information?¿De qué manera usaré la información?

Show how to solve the problem.Muestra la manera de resolver el problema.

Soluciona el problema

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6 7

Teacher Materials Student Materials

Student Edition• Write-In student interactive text

• Organized around the Common Core State Standards Critical Areas

• Special color-coding for Critical Areas

• Mathematical Practices embedded in the lessons

Planning Guide• Chapter Planners

• Common Core Correlations

• Additional planning resources for end of year

Classroom Manipulatives Kit• Enough materials for 30 students

• Pre-packaged in handy zipper bags

• Available for each grade, K–6

MathBoard• Write-on/wipe-off, available for each grade, K–6

• Helps students organize their thinking

• Enables students to engage in the Mathematical Practices

• Supports the emphasis on Math Talk


COMMON CORE


COMMON CORE

To view all of the Chapter Teacher Editions, go to

hmheducation.com/gomath

Teacher Edition• Separate Chapter Books

• Organized and flexible

• Color-coded by Critical Area

packaged with the

Student editionStandards Practice Book• Full page of practice for each

lesson

• Full page of spiral review every day

• Getting Ready lessons for the following grade level

• Multi-day projects for each Critical Area

Comm

on Core Instruction

8 9

Instructional Support

Grab-and-Go!® Differentiated Centers Kit• Ready-made activities, games, and literature for each lesson

• Available for each grade, K–6

• Actual size when open: 42” x 25”

Differentiated Instruction

Assessment Guide


COMMON CORE

1461037

3 E D I T I O N

PROVIDES Tier 1 Intervention for Every Lesson

www.hmhschool.com

Reteach Book

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Tier 1

1516680

E D I T I O N

1

2

3

www.hmhschool.com 3

Strategic Intervention Teacher Activity Guide

Response to Intervention

TIER 2 ACTIVITIES

INCLUDES:• Diagnostic Practice for Prerequisite Skills• Activities for Students Needing Tier 2

Instructional Intervention• Copying Masters

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Enrich Book Available for each grade, K–6

Reteach Book Available for each grade, K–6

ELL Activity Guide Available K–2 and 3–6 online only Tier 2 Tier 3

ELL Activity Guide

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E D I T I O N

1

2

3

3www.hmhschool.com

Intensive Intervention Teacher GuideResponse to Intervention

TIER 3 ACTIVITIES

INCLUDES:• Diagnostic Practice for Prerequisite Skills• Activities for Students Needing Tier 3

Instructional Intervention• Copying Masters

Inten

sive Interven

tion

Teach

er Gu

ide

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diagnoStic Formative Summative

Assessment Guide includes:• Prerequisite Skills Inventory

Beginning–of-Year, Middle-of-Year, and End-of-Year Benchmark Tests

• Diagnostic Interview Assessments

• Chapter Tests in Multiple Choice and Mixed Response Formats

• Performance Assessments

• Getting Ready for Next Year Tests

• Individual and Class Record Forms

1

2

3


Instructional Support

10 11

PLAN1 ENGAGE2

TEACH ASSESS43

• Information and communication skills• Higher-order thinking skills• Problem-solving skills• Independent learners• Real-world connections

GO Math! Digital Path provides the opportunity for lifelong learning skills for students in the 21st century by developing:

To view sample iwB lessons, go To


Response to Intervention1

2

3


Soar to Success Math

Tier 1 On-Level Intervention

Tier 2 Strategic Intervention

Tier 3 Intensive Intervention

PLAN1ENGAGE2

Tier 1 On-Level Intervention

Tier 2 Strategic Intervention

Tier Intensive Intervention3

Response to Intervention1

2

3

PLAN1ENGAGE2

TEACH3 ASSESS4TEACH3 ASSESS4

Digital Path PG15

Program Overview

Animated Math Models

HMH Mega Math• Provides additional lesson

practice with engaging activities that include audio and animation

• Carmen Sandiego™ characters introduce lesson activities with audio and animation

• Concepts are modeled and reinforced with feedback

Soar to Success Math• Diagnose and prescribe

interactive intervention lessons for all RtI Tiers

Go Math! Digital Path provides the opportunity for lifelong learning skills for students in the 21st Century by developing:

• Information and communication skills• Higher order thinking skills• Problem solving skills• Independent learners• Real-world connections

• Includes audio, graphics, and animation

Multimedia eGlossary

• Includes all Student Edition pages for student access at school or home

• Provides audio reinforcement for each lesson

• Features point-of-use links to Animated Math Models

eStudent Edition Online Assessment System• Receive instant results,

including prescriptions for intervention

• Includes a variety of reports to track student progress

• Create customized tests

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• Provides rich and engaging learning experiences

• Encourages active participation throughout the lessons

• IWB lesson for every GO Math! lesson

• Solve problems with interactive digital manipulatives

• Model and explore math lesson concepts

Interactive Whiteboard Lessons

To preview the technology

offerings, go to


iTools

CARMEN SANDIEGO™ Math Detective Activities for Grades 3–6

• Engaging activities

• Solve math problems with real-world themes

• Provides additional lesson practice with engaging activities that include audio and animation

Mega Math

Chapter ePlanner

Math Practices Videos

Professional Development Podcasts

• Daily Digital Path links to all online resources for each lesson

• Create customized planning calendar

• View and assign online activities and lessons to students

• Download video

podcasts with

strategies for teaching

math practices

• View on hand-held

device or computer

• Download podcasts with strategies for teaching concepts and skills

• View on hand-held device or computer

eStudent Edition• Includes all Student Edition

pages for student access at school or home

• Provides audio reinforcement for each lesson

• Features point-of-use links to Animated Math Models

• Also available on tablets

eTextbook also available

eTextbook also available

• Receive instant results, including prescriptions for intervention

• Includes a variety of reports to track student progress

• Create customized tests

Online Assessment System

• Diagnose and prescribe interactive intervention lessons for all RtI Tiers

eTeacher Edition• Access all Teacher Edition

pages at school or home

Animated Math Models

Real World Videos• Show motivating videos

of real-world settings to introduce lessons in Grades 3–6

Multimedia eGlossary

• Curious George® (K–2) and Carmen Sandiego (3–6) characters introduce lesson activities with audio and animation.

• Concepts are modeled and reinforced with feedback

• Includes audio, graphics, and animation

PROBLEM SOLVING

Name

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What information do I need to use?

What do I need to find?

Lesson 2.11

Show how to solve the problem.Model the numbers. Draw quick pictures of your models.

Chapter 2

ninety-seven 97

HOME CONNECTION • Your child used base-ten blocks to represent the numbers in the problem. These models were used as a tool for comparing numbers to solve the problem.

Children bought 217 cartons of chocolate milk and 188 cartons of plain milk. Did they buy more cartons of chocolate milk or plain milk?

Problem Solving • Compare Numbers Essential Question How can you make a model to solve a problem about comparing numbers?

217 — cartons of chocolate milk 188 — cartons of plain milk

if the children bought more —

cartons of chocolate milk ——————

or plain milk ——

The children bought more cartons of chocolate ——— milk.

COMMON CORE STANDARD CC.2.NBT.4Understand place value.

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Digital Path

Technology

12 13


Differentiated InstructionDiD

Small GroupWhole Group Whole Group

SUMMARIZEPRACTICE

QUICK CHECK TEACH AND TALK

ENGAGE SPRACTICE

QUICK CHECK TEACH AND TALK

ENGAGE 43

2

1

Enrich

• HMH Mega Math

• iTools

OnlineGO

On Level

• HMH Mega Math

• iTools

OnlineGO

Extra Support

• Strategic Intervention Guide

• Soar to Success Math• Intensive Intervention Guide

OnlineGO

0 to 1 correct

INTERVENEThese students need

lesson support.

2 correct

ON LEVELThese students are ready

to begin independent practice.

Advanced

ENRICHThese students are

ready for enrichment.

• RtI Activities

• Reteach Book

• Activity ELL

• Standards Practice Book

• Cross-Curricular Activities

• Activity ELL

• Enrich Activity

• Enrich Book

• Extend the Project

• Activity ELL

Rt I RR1

2

3

Differentiated Centers Kit

WHAT ARE THE OTHER STUDENTS DOING?

Multiplication Facts and Strategies 131F

The kit provides literature, games, and activities for use every day.

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Differentiated Instruction Activities

Tier 2Tier 1Reteach

EnrichLanguage SupportELL

1

2

3


1

23

4

56

7

8

9

Lesson 4.1 133B

Materials counters, large sheet of paper

• Draw 4 circles on a large sheet of paper. Tell students that each circle represents one group.

• Ask students to place 2 counters in each circle. Guide them to write an addition sentence to show the total number of counters.

2 1 2 1 2 1 2 5 8

• Four groups of 2 equals 8. Guide students to write the multiplication sentence, 4 3 2 5 8.

Kinesthetic / Visual Small Group

Materials square tiles

• Have partners each make 2 rows of 3 tiles each.

• What multiplication sentence can you write to show how many tiles you have in all? 2 3 3 5 6

• Then have partners join their rows to form 4 rows in one group. Ask students to write a multiplication sentence to show how many tiles they have in all. 4 3 3 5 12

• How does knowing 2 3 3 5 6 help you fi nd 4 3 3? I can double the product for 2 3 3 to fi nd the product for 4 3 3: 6 1 6 5 12.

• Have partners repeat the activity with different numbers of tiles in 2 equal rows.

Logical / MathematicalPartners

Materials Digit Cards (see eTeacher Resources)

• Have students shuffl e a set of cards (1–9) and place them facedown in a pile.

• One partner selects a card, keeping it hidden, and then mentally fi nds the product of that number and 2 and says the product aloud.

• The other partner names the number that was multiplied by 2 to get the given product.

• Partners reverse roles and repeat the activity until all the cards have been used.

• Then have partners repeat the activity with 4 as the factor.

Strategy: DrawMaterials paper, color pencils

• Students can draw pictures to reinforce vocabulary.

• Read aloud this sentence: “Each of the 3 students has 2 costumes.” Have students draw pictures to show what this means. (Make sure students understand that a costume is a special set of clothes.)

• Point to the fi rst fi gure in a drawing. How many costumes does this student have? 2 How do you know he has 2 costumes? Accept all reasonable responses that describe the drawing.

See ELL Activity Guide for leveled activities.

VisualSmall Group

Auditory / KinestheticWhole Class / Small Group

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No student will feel left out with GO Math!

Reaching All Students Practical, point-of use support is built into each lesson so all learners–early finishers, gifted and talented students, and those needing extra support or intervention–can all achieve success.

1461037

3 E D I T I O N

PROVIDES Tier 1 Intervention for Every Lesson

www.hmhschool.com

Reteach Book

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Enrich Book Reteach Book ELL Activity Guide


14 15


Comprehensive Support for RtI Improves Learning

2

4

6

8

Objective: Skip count by tens Materials: hundred chart (see eTeacher Resources), crayons

• Ask the student to find 10 on the hundred chart and color the box. Then ask him or her to color the box that shows 10 more and say the number. 20

• Have the student continue in a similar manner until 50. Ask questions such as: What number are you on? 30 How many tens are in 30? 3

• Summarize by comparing the numbers the student has colored. They all have a 0 in the ones place.

• Look for the student to accurately identify the number that is 10 more than the one he or she starts with.

Objective: Add equal groupsMaterials: red, yellow, and blue connecting cubes

• Give the student red, yellow, and blue connecting cubes.

• Have the student count 4 red cubes and make a train. Repeat with the 4 blue and 4 yellow cubes. Ask: How many groups do you have? 3 How many cubes are in each group? 4

• Have the student join the red and blue cubes. How many cubes are there now? 8 Now add the last 4 cubes and have the student count the number of cubes in all. Repeat with equal groups of different sizes.

• Look for the student to add the number of cubes accurately.

Objective: Count by twos Materials: stick-on dots, paper

• Give the student stick-on dots to arrange in groups of two on paper.

• Have the student skip count by two and write numbers under each set of dots.

• The student can use the dot pairs to practice counting by twos.

• Look for the student to increase the number of dots by two and to count the dots accurately.

Activity 5

Activity 4

Activity 3

Grade 3Intensive Intervention User Guide© Houghton Mifflin Harcourt Publishing Company

6

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Differentiated Instruction ActivitiesDifferentiated Instruction ActivitiesDifferentiated Instruction Activities

Tier 2Tier 1Reteach

1

2

3


Language SupportELL Enrich

3 3 3 3

12

2 2 2 2

8 beads

Lesson 3.4 111B

Problem Solving • Model Multiplication

VisualSmall Group

• Display and read aloud the following problem:

Toshi has 3 boxes of rocks. There are 4 rocks in each box. How many rocks are there in all?

• Have students draw a picture to represent the problem.

• Reread the problem. Demonstrate how to draw and use a bar model to solve the problem.

• Present the following problem to students:

Mai has 4 rings. There are 2 beads on each ring. How many beads are there in all?

• Discuss with students what they need to fi nd and what information they will use. the total number; 4 rings, 2 beads on each of 4 rings

• Guide students to draw a bar model to help solve the problem.

VisualWhole Class / Small Group

Strategy: Model LanguageMaterials counters, color pencils

• Students repeat sentences to learn correct pronunciation.

• Arrange 24 counters into 4 rows of 6 counters.

• Have students draw diagramsof the model. As students drawtheir diagrams, say and have themrepeat sentences such as these:I am drawing a diagram. My diagramhas 4 rows.

• Be sure to speak slowly and clearly as you model the sentences.


• Draw the following diagram on the board.

• Have students write a word problem that can be solved using the diagram. For example: Flora put 3 pictures on each of 4 pages in her photo album. How many pictures did Flora put in her album? 12 pictures

• Students exchange papers and solve the word problem, checking that the problem matches the diagram.

VisualPartners

Visual / AuditorySmall Group

4 4 4

12 rocks

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Differentiated Instruction ActivitiesDifferentiated Instruction ActivitiesDifferentiated Instruction Activities

Tier 2Tier 1Reteach

1

2

3


Language SupportELL Enrich

3 3 3 3

12

2 2 2 2

8 beads

Lesson 3.4 111B

Problem Solving • Model Multiplication

VisualSmall Group

• Display and read aloud the following problem:

Toshi has 3 boxes of rocks. There are 4 rocks in each box. How many rocks are there in all?

• Have students draw a picture to represent the problem.

• Reread the problem. Demonstrate how to draw and use a bar model to solve the problem.

• Present the following problem to students:

Mai has 4 rings. There are 2 beads on each ring. How many beads are there in all?

• Discuss with students what they need to fi nd and what information they will use. the total number; 4 rings, 2 beads on each of 4 rings

• Guide students to draw a bar model to help solve the problem.

VisualWhole Class / Small Group

Strategy: Model LanguageMaterials counters, color pencils

• Students repeat sentences to learn correct pronunciation.

• Arrange 24 counters into 4 rows of 6 counters.

• Have students draw diagramsof the model. As students drawtheir diagrams, say and have themrepeat sentences such as these:I am drawing a diagram. My diagramhas 4 rows.

• Be sure to speak slowly and clearly as you model the sentences.


• Draw the following diagram on the board.

• Have students write a word problem that can be solved using the diagram. For example: Flora put 3 pictures on each of 4 pages in her photo album. How many pictures did Flora put in her album? 12 pictures

• Students exchange papers and solve the word problem, checking that the problem matches the diagram.

VisualPartners

Visual / AuditorySmall Group

4 4 4

12 rocks

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Program Overview PG11

Program Overview

New Interactive Interventions for RtI

Intensive InterventionStrategic InterventionOn-Level Intervention

3 O

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S F

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Te

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Pri

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Act

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Within every lesson, activities and materials for all levels of RtI, engage learners with focused hands-on activities, print support, and a comprehensive online intervention solution. This way, teachers can select instructional strategies and resources to specifically align with student’s level of understanding and preferred learning style.

3_MNLAEPG590936_PO 11 6/2/11 11:46:36 PM

TIER 2 TIER 3

Grade Pre-K Grade K Grade 1

Before Grade 3 AfterBefore Grade 4 After

Before Grade 4 After

405

8

4 80 12 16

1

2

3

TIER 2TIER 2 TIER 3TIER 3

131G Chapter 4

Common Core Standards Across the Grades

3 3 4 5 12

2 3 6 5 12

Write It!Objective Write multiplication word problems to match given models.

Have students write a word problem that can be solved by using each of the models shown. Provide sentence frames as needed. Draw these models on the board. Have a volunteer count aloud how many jumps there are. 3Then have another student count how many marks on the number line are included within each jump. 4 Explain that 3 and 4 are the factors. As needed, guide students to understand that 3 groups of 4 are equal to 12.

Draw It!Objective Draw a fast array to model and fi nd the answer to basic multiplication facts.

Materials MathBoards

Draw a fast array for 5 3 8 on the board.

Point out that in a fast array you draw only one row and one column.

Ask:

• How could you use a fast array to find 5 3 8? Possible answer: I know that 2 3 8 5 16, so I can double 16 and add 1 more 8.

Write “40” in the box. Have students think of two basic facts they do not know and draw fast arrays to find the products.

Have volunteers share their fast arrays and methods for solving the problems with the class.

Multiplication Facts and StrategiesChapter 4

See A page of each lesson for Common Core Standard text.

Domain: Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.CC.4.OA.2, CC.4.OA.3Generalize and analyze patterns. CC.4.OA.5

Domain: Number and Operations in Base Ten

Use place value understanding and properties of operations to perform multi-digit arithmetic.CC.4.NBT.5, CC.4.NBT.6

Domain: Operations and Algebraic ThinkingRepresent and solve problems involving multiplication and division.CC.3.OA.3Understand properties of multiplication and the relationship between multiplication and division.CC.3.OA.5Multiply and divide within 100.CC.3.OA.7Solve problems involving the four operations, and identify and explain patterns in arithmetic. CC.3.OA.8, CC.3.OA.9

Domain: Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.CC.2.OA.1Work with equal groups of objects to gain foundations for multiplication.CC.2.OA.3, CC.2.OA.4

Domain: Number and Operations in Base Ten

Understand place value.CC.2.NBT.2

Use counters to provide support for individual students or small groups as needed. Guide them to count the rows of counters (2) and how many counters there are in each row (6) to get the factors for the multiplication problem.

Have volunteers share their problems and discuss the multiplication situations they wrote.

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Three Options for Intervention for Each Tier1. Print support

2. Focused hands-on activities

3. Comprehensive online intervention solutions

1517895

E D I T I O N

1

2

3

3

www.hmhschool.com

Intensive Intervention

Teacher Guide


TIER 3 ACTIVITIES

INCLUDES:

• Diagnostic Practice for Prerequisite Skills

• Activities for Students Needing Tier 3

Instructional Intervention

• Copying Masters

Inten

sive Interven

tion

Teach

er Gu

ide

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Intervention

16 17

TIER 1 TIER 2 TIER 3 ENRICHMENT

On-Level Intervention Strategic Intervention Intensive Intervention Independent Activities

Intervention Options Response to Intervention1

2

3

WITHTM

INTERVENE

INTERVENE

If NO...then

INTERVENE

If YES...then use

INDEPENDENTACTIVITIES

GOOnline

Assessment Options: Soar to Success Math

WITHTM

Check your understanding of important skills.

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Stephen needs to use these clues to find a buried time capsule. • Start with a number that is the product of 3 and 4.• Double the product and go to that number.• Add 2 tens and find the number that is 1 less than the sum.Be a Math Detective to help him find the time capsule.

Chapter 4 131

Multiplication Facts and Strategies

→ Doubles and Doubles Plus One Write the doubles and doubles plus one facts.

1.

2.

→ Equal Groups Complete.

3. 4.

_ groups of _ _ groups of _

_ in all _ in all

Name

_ 1 _ 5 _

_ 1 _ 5 _ _ 1 _ 5 _

_ 1 _ 5 _4

2

4 5

12 10

3 2

4

2

5

3

9

5

4

2

8

4

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• eStudent Edition • Multimedia eGlossaryGOOnline

• eStudent Edition • Multimedia eGlossaryOnline

Vocabulary Builder

• eStudent Edition • Multimedia eGlossaryGOGOOnline

1 3 4 5 4

Property ofMultiplication



(4 3 2) 3 3 5 4 3 (2 3 3)

3 3 2 5 2 3 3 • • •• • •• •• •• •

Identity Associative Commutative

arraysproductfactors

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→ Visualize ItComplete the tree map by using the words with a 3.

→ Understand VocabularyComplete the sentences by using the preview words.

1. The ___ Property of Multiplication states that when the grouping of factors is changed, the product is the same.

2. A ___ of 5 is any product that has5 as one of its factors.

3. The ___ Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

Example: 2 3 8 5 2 3 (4 1 4)

2 3 8 5 (2 3 4) 1 (2 3 4)

2 3 8 5 8 1 8

2 3 8 5 16

Multiplication Properties

Review Words

3 arrays

3 Commutative Property

of Multiplication

even

3 factors

3Identity Property

of Multiplication

odd

3 product

Preview Words

3 Associative Property

of Multiplication

Distributive Property

multiple

Distributive

Associative

multiple

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Use Show What You Know, Lesson Quick Check, and Assessments to diagnose students’ intervention levels.

131 Chapter 4

In this Math Detective, students decipher clues using math vocabulary knowledge and fact skills. Review with students the terms sum and product before they start the activity.

Ask:

• Can 15 be the answer to the fi rst clue? Explain. No; 15 is not the product of 3 and 4.

• How can you double 12? I can think 12 1 12 5 24.

• Which number marks the location where the time capsule is buried? 43

Assessing Prior KnowledgeUse Show What You Know to determine if students need intensive or strategic intervention.

Chapter 4

GOOnline

CARMEN SANDIEGO™ Math Detective Activities

Use to determine if students need intervention for the chapter’s prerequisite skills.

Show What You Know • Diagnostic Assessment

Use the Enrich Book or the independent activities in the Grab-and-Go™Differentiated Centers Kit.


SkillMissed More

Than

Doubles and Doubles Plus One

0

Equal Groups 0

TIER 3

TIER 2

TIER 2

InterveneWith

Soar to Success Math

Intensive Intervention Skill 8; Intensive Intervention User Guide Activity 4

Warm-Up 10.19

Strategic Intervention Skill 9

Warm-Up 12.18

Were students successful withShow What You Know?

For Diagnostic Interview Tasks for Show What You Know skills, see Assessment Guide.

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INDEPENDENT ACTIVITIES

Differentiated InstructionMath Talk in Action

PROFESSIONALDEVELOPMENT

COMMON CORE

Quick Check

If

Rt I RR1

2

3

Then


3 1 2 3 4 5 6 7 8 9

2

4

2 4 6 8 10 12 14 16 18

8 12 16 20 24 28 32 36

10

20

404

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Chapter 4 • Lesson 1 135

Name

9.

_ 3 _ 5 _

10.

_ 3 _ 5 _

11. 10 3 4

_

12. 2 3 9

_

13. 4 3 6

_

14. 7 3 2

_

15. 2 3 0

_

Find the product. Use your MathBoard.

21.

Algebra Complete the table for the factors 2 and 4.

Algebra Write the unknown number.

23. 4 3 8 5 16 1 _ 24. 20 5 2 3 _ 25. 8 3 2 5 10 1 _

16. 4 3 3

_

17. 2 3 8

_

18. 4 3 4

_

19. 10 3 2

_

20. 4 3 5

_

On Your OwnWrite a multiplication sentence for the model.

Write a multiplication sentence for the model.

Find the product.

2.

_ 3_ 5_

3.

_ 3_ 5_

4. 6 3 2

_

5. 9 3 4

_

6. 2 3 7

_

7. 8 3 4

_

8. 5 3 2

_

22.

12

40

44 3 12 82

16 10 6

18 024 14

16 2016 20

3 4 122 2 4

12 36 14 32 10

Untitled-2676 135 4/6/2011 9:22:03 AM

Model • Reason • Make SenseMATHEMATICALPRACTICES

Play Tickets

Brandon

Haylie

Elizabeth

Key: Each = 2 tickets sold.

Name Tickets Sold

UNLOCK the Problem

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c. Show the steps you used to solve the problem.

d. Complete the sentences.

Brandon sold _ tickets.

Haylie sold _ tickets.

Together, Brandon and Haylie sold

_ tickets.

a. What do you need to find?–

b. Why should you multiply to find the number of tickets shown? Explain.–

26. Ms. Peterson’s class sold tickets for the class play. How many tickets in all did Brandon and Haylie sell?

27. Suppose Sam sold 20 tickets to the school play. How many tickets should be on the picture graph above to show his sales? Explain.

28. Test Prep Lindsey, Louis, Sally, and Matt each brought 5 guests to the school play. Which number sentence shows their total number of guests?

A 4 1 5 = 9 C 4 3 4 = 16

B 5 1 4 = 9 D 4 3 5 = 20

FOR MORE PRACTICE:Standards Practice Book, pp. P67–P68

Possible explanation: there should be

10 pictures of tickets to show 20 tickets;

10 3 2 5 20.

Possible explanation: each ticket shown stands for 2 tickets sold, so you multiply by 2

to � nd how many tickets each student sold.

Brandon: 4 3 2 5 8 Haylie: 7 3 2 5 14 8 1 14 5 22

8

14

22

how many tickets in all Brandon and Haylie sold

Untitled-2676 136 4/6/2011 9:22:06 AM

135 Chapter 4

On Your Own • Independent Practice

Remind students that the multiplication table for Exercises 21 and 22 looks like the addition tables they have used to fi nd sums. Review the rows and columns and discuss how to use the table to multiply and write a product.• How do you fi nd where to write the product

for 2 and 7? Possible answer: follow across the row for 2 and down the column for 7. I write the product in the box where the row and column meet.

See the Math Talk in Action below for a discussion about multiplying by 2 and 4 and patterns in the multiplication table.

Go DeeperHave students connect what they know about modeling repeated addition to fi nd unknown factors in multiplication sentences. Suggest that students draw a quick picture of the situation to help fi nd the unknown factors for 4 3 5 24 and 3 7 5 14.

c

The teacher is leading a discussion about Exercises 21 and 22.

Teacher: What patterns do you see in the multiplication table you completed?

Jared: If you look across the fi rst row, it is like skip counting by 2.

Teacher: What do the numbers in the second row look like?

Dora: Skip counting by 4.

Linda: It’s like adding 4. Each number is 4 more than the number before it.

Teacher: Does anyone see any patterns in the columns of the table?

Lee: Each number is double the number above it. Like in the fi rst column, you have 1, and double 1 is 2. Double 2 and you get 4.

Teacher: Is that true for all the columns?

Lee: Yes.

Teacher: How can you use doubles to multiply 4 3 8?

Emilio: I can double 8 and that is 16.

Teacher: What multiplication fact is that the answer to?

Emilio: 2 3 8 5 16. I need to double 16 to fi nd 4 3 8. 16 1 16 5 32. So, 4 3 8 5 32.

Teacher: Well done!

a student misses Exercises 3 and 8

Differentiate Instruction with • RtI Tier 1 Activity, p. 133B

• Reteach 4.1

Soar to Success Math 12.21, 12.25

Use Exercises 3 and 8 for Quick Check.

Untitled-48 135 5/2/2011 11:38:05 PM

1

2

3

Data-Driven Decision Making

Mid-Chapter Checkpoint

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Chapter 4 153

Vocabulary

Choose the best term from the box to complete the sentence.

1. A ____ of 4 is any product that has 4 as one of its factors. (p. 137)

2. This is an example of the ____ Property.

3 3 8 5 (3 3 6) 1 (3 3 2)

This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. (p. 145)

Concepts and Skills

Write one way to break apart the array. Then find the product. (CC.3.OA.5)

→

→

3.

4.

Vocabulary

Commutative Property

of Multiplication


multiple

Find the product. (CC.3.OA.3, CC.3.OA.7)

9. 2 3 1

_

10. 6 3 6

_

11. 8 3 7

_

12. 6 3 0

_

13. 3 3 8

_

5. 3 3 1 5 _ 6. 5 3 6 5 _ 7. 7 3 7 5 _ 8. 2 3 10 5 _

multiple

Distributive

Possible answers are given.

3 30 49 20

362 56 0 24

5 3 (3 1 4) or (2 1 3) 3 7

or (2 3 7) 1 (3 3 7); 35

4 3 (5 1 4) or (2 1 2) 3 9

or (2 3 9) 1 (2 3 9); 36

Untitled-5424 153 3/17/2011 12:01:35 PM

PREPTESTPREPTEST

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14. Lori saw 6 lightning bugs. They each had 6 legs. How many legs did the lightning bugs have in all? (CC.3.OA.3)

A 36

B 24

C 12

D 6

15. Zach gave his dog 2 dog biscuits a day, for 5 days. How many biscuits did Zach give to his dog in all? (CC.3.OA.3)

A 3

B 7

C 10

D 30

16. Annette buys 4 boxes of pencils. If there are 8 pencils in each box, how many pencils doesshe have in all? (CC.3.OA.3)

A 32

B 24

C 16

D 12

17. Shelly can paint 4 pictures in a day. How many pictures can she paint in 7 days? (CC.3.OA.7)

A 3

B 11

C 28

D 32

Fill in the bubble for the correct answer choice.

Untitled-5424 154 3/17/2011 12:01:36 PM

*CCSS—Common Core State Standards Key: R—Reteach Book; TE—RtI Activities

Based on the results of the Mid-Chapter Checkpoint, use the following resources to strengthen individual or whole class instruction.

Item Lesson *CCSS Common Error Intervene With Soar to Success Math

3, 4 4.4 CC.3.OA.5 May not understand how to fi nd a product by breaking apart an array R—4.4; TE—p. 145B 12.50

5–13 4.1–4.3, 4.5CC.3.OA.3CC.3.OA.7

May fi nd an incorrect product when multiplyingR—4.1–4.3, 4.5;TE—pp. 133B, 137B, 141B, 149B

12.21, 12.22, 12.23, 12.25, 12.26, 12.28,

12.31

Formative AssessmentUse the Mid-Chapter Checkpoint to assess students’ learning and progress in the fi rst half of the chapter. The formative assessment provides the opportunity to adjust teaching methods for individual or whole class instruction.

153 Chapter 4

LESSONS 4.1 TO 4.5

Untitled-1111 153 5/10/2011 7:22:53 PM

1

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3


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Chapter 4 153

Vocabulary


1. A ____ of 4 is any product that has 4 as one of its factors. (p. 137)

2. This is an example of the ____ Property.

3 3 8 5 (3 3 6) 1 (3 3 2)

This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. (p. 145)

Concepts and Skills

Write one way to break apart the array. Then find the product. (CC.3.OA.5)

→

→

3.

4.

Vocabulary

Commutative Property

of Multiplication


multiple


9. 2 3 1

_

10. 6 3 6

_

11. 8 3 7

_

12. 6 3 0

_

13. 3 3 8

_

5. 3 3 1 5 _ 6. 5 3 6 5 _ 7. 7 3 7 5 _ 8. 2 3 10 5 _

multiple

Distributive


3 30 49 20

362 56 0 24

5 3 (3 1 4) or (2 1 3) 3 7

or (2 3 7) 1 (3 3 7); 35

4 3 (5 1 4) or (2 1 2) 3 9

or (2 3 9) 1 (2 3 9); 36

Untitled-5424 153 3/17/2011 12:01:35 PM

PREPTESTPREPTEST

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14. Lori saw 6 lightning bugs. They each had 6 legs. How many legs did the lightning bugs have in all? (CC.3.OA.3)

A 36

B 24

C 12

D 6

15. Zach gave his dog 2 dog biscuits a day, for 5 days. How many biscuits did Zach give to his dog in all? (CC.3.OA.3)

A 3

B 7

C 10

D 30

16. Annette buys 4 boxes of pencils. If there are 8 pencils in each box, how many pencils doesshe have in all? (CC.3.OA.3)

A 32

B 24

C 16

D 12

17. Shelly can paint 4 pictures in a day. How many pictures can she paint in 7 days? (CC.3.OA.7)

A 3

B 11

C 28

D 32

Fill in the bubble for the correct answer choice.

Untitled-5424 154 3/17/2011 12:01:36 PM


Based on the results of the Mid-Chapter Checkpoint, use the following resources to strengthen individual or whole class instruction.


3, 4 4.4 CC.3.OA.5 May not understand how to fi nd a product by breaking apart an array R—4.4; TE—p. 145B 12.50

5–13 4.1–4.3, 4.5CC.3.OA.3CC.3.OA.7

May fi nd an incorrect product when multiplyingR—4.1–4.3, 4.5;TE—pp. 133B, 137B, 141B, 149B

12.21, 12.22, 12.23, 12.25, 12.26, 12.28,

12.31

Formative AssessmentUse the Mid-Chapter Checkpoint to assess students’ learning and progress in the fi rst half of the chapter. The formative assessment provides the opportunity to adjust teaching methods for individual or whole class instruction.

153 Chapter 4

LESSONS 4.1 TO 4.5

Untitled-1111 153 5/10/2011 7:22:53 PM

Diagnostic Formative

Show What You Know• Identifies students’ level of preparation for

the chapter content

• Determines if students need intensive or strategic intervention

• Special intervention and challenge resources link to the “Show What You Know Diagnostic Assessment” chart

• Monitor students’ understanding in every lesson

• Adjust instruction accordingly

• Assess students’ learning and progress in the first half of the chapter

• Adjust teaching methods for individual or whole class instruction

Assessment

Assessment

Core Student Materials

• Student Edition Package (Student Edition and Standards Practice Book)

• eStudent Edition• MathBoard

Core Teaching Materials

• Teacher Edition Collection with Planning Guide

• eTeacher Edition• Assessment Guide• Reteach Workbook• Enrich Workbook• Grab-and-Go! Differentiated

Centers Kit• Grab-and-Go! Manipulatives Kit• Online Teacher Resource Center

Additional Teaching Resources

• Strategic Intervention Guide• Intensive Intervention Kit• ExamView® Common Core Test

Generator CD-ROM

Online Teacher Resource Center

• Student Edition• Standards Practice Book with Teacher

Edition• Teacher Edition Collection with

ePlanner• Concept Readers• ELL Activity Guide• Teacher Resource Book• Reteach Workbook with

Teacher Edition• Enrich Workbook with Teacher Edition• Lesson Transparencies• Assessment Guide• Grab-and-Go! Differentiated Centers

Teacher Guide and Activities• Professional Development Podcasts• Math Practices Videos• Interactive Whiteboard Lessons• iTools• Animated Math Models• Carmen Sandiego™ Math Detective

Activities for Grades 3–6• Real World Videos Grades 3–6• Multilingual eGlossary• Mega Math• Soar to Success Math Intervention

(Tiers 1, 2, and 3)• Online Assessment• Bilingual MathBoards• Strategic Intervention Teacher Guide• Intensive Intervention User Guide• Intensive Intervention Skills Pack• Intensive Intervention Teacher Guide

program Components

available in english and spanish

Performance Indicators

Performance Task Scoring RubricPerformance Task Scoring Rubric

1

2

3


PREPTESTPREPTEST

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Chapter 4 177

26. James made an array with 6 rows of 8 blocks. Which number sentence shows one way to break apart his array to find the product? (CC.3.OA.5)

A 6 3 8 5 (6 1 4) 1 (6 1 4)

B 6 3 8 5 (6 3 4) 1 (6 3 4)

C 6 3 8 5 (3 3 4) 1 (3 3 4)

D 6 3 8 5 (6 3 8) 1 (6 3 8)

27. Zach and his dad baked some cupcakes for his class. They put 6 cupcakes on each of 8 plates. How many cupcakes did they put on the plates? (CC.3.OA.7)

A 12

B 14

C 24

D 48

28. Sydnee’s class is studying animals that hibernate, or go into a sleep-like state during the winter. A black bear’s heartbeat slows to about 9 beats per minute during hibernation. About how many times will a black bear’s heart beat in 5 minutes? (CC.3.OA.7)

A 45

B 36

C 18

D 9

Untitled-185 177 4/15/2011 3:45:14 PM

PREPTESTPREPTEST

176

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Fill in the bubble for the correct answer choice.19. Which number sentence is an example of the

Distributive Property? (CC.3.OA.5)

A 5 3 9 5 (5 3 5) 1 (5 3 4)

B (3 3 2) 3 5 5 3 3 (2 3 5)

C 5 3 9 5 9 3 5

D 5 3 9 5 45

20. Adel needs 5 pieces of ribbon, each 8 centimeters long. How much ribbon does she need altogether? (CC.3.OA.3)

A 13 centimeters C 35 centimeters

B 32 centimeters D 40 centimeters

21. When Chloe finds the multiplication facts for 2, which digit will NOT be in the ones place of the products? (CC.3.OA.9)

A 8 C 4

B 6 D 3

22. Vicky went to the store and bought 3 pairs of shorts. They each cost $8. How much did she spend? (CC.3.OA.7)

A $3 B $8 C $21 D $24

23. A honeybee is an insect. It has 6 legs. How many more legs do 7 honeybees have than 5 honeybees? (CC.3.OA.3)

A 5 C 12

B 6 D 30

24. Jody has bags of shells. Each bag has 6 shells. She gives 3 bags to each of 2 friends. How many shells did Jody give away? (CC.3.OA.5)

A 36 B 18 C 12 D 6

25. The camping club rents 4 rafts. Each raft can hold 6 people. How many people can 4 rafts hold? (CC.3.OA.3)

A 16 B 20 C 24 D 30

Untitled-125 176 10/18/2011 12:33:51 PM

GOOnline

Assessment OptionsChapter Test

Chapter 4 Review/Test

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Chapter 4 175

Vocabulary


1. The ___ Property of Multiplication states that when the grouping of factors is changed, the product is the same. (p. 155)

2. A __ of 9 is any product that has 9 as one of its factors. (p. 137)

Concepts and Skills

Use arrays to show each property. (CC.3.OA.5)

→

→

3. Distributive Property

Break apart the array to show 8 3 6 5 (4 3 6) 1 (4 3 6).

4. Associative Property of Multiplication

Circle groups to show 3 3 (2 3 3).


Vocabulary

Associative Property

of Multiplication


multiple

11. 9 3 0 5 _ 12. 7 3 8 5 _ 13. 4 3 8 5 _ 14. 2 3 6 5 _

15. 9 3 9 5 _ 16. 3 3 4 5 _ 17. 5 3 10 5 _ 18. 7 3 3 5 _

5. 6 3 8

_

6. 10 3 4

_

7. 5 3 9

_

8. 6 3 3

_

9. 5 3 8

_

10. 8 3 8

_

Associative

multiple

48 40 45 18 40 64


0

81

56

12

32

50

12

21

Untitled-185 175 4/15/2011 3:45:12 PM

175-176 Chapter 4Performance Task may be used for portfolios.

3

Generally accurate, complete, and clear: All parts of the task are successfully completed. The student demonstrates sound reasoning and an understanding of the key concepts and procedures. Explanations are complete and clear with no meaningful errors.

2Accurate results without suffi cient support: All parts of the task are completed. While correct answers may indicate some understanding of the key concepts and procedures, explanations are lacking in reasoning and mathematical justifi cation.

1Partially accurate: Part of the task is successfully completed while other parts may be attempted, but not successfully completed. The student demonstrates minimal understanding of key concepts and procedures.

0Not accurate, complete, and clear: No part of the task is completed with any success. There is little, if any, evidence that the student understands key concepts and procedures.



3, 4 4.4, 4.6 CC.3.OA.5 May use the wrong property R—4.4, 4.6; TE—p. 145B, 155B 12.49, 12.50

5–18, 20 4.1–4.3, 4.5, 4.8, 4.9

CC.3.OA.3CC.3.OA.7

May fi nd an incorrect product

R—4.1–4.3, 4.5, 4.8, 4.9;TE—p. 133B, 137B, 141B, 149B, 163B, 167B

12.21, 12.22, 12.23, 12.25, 12.26, 12.28, 12.29, 12.30,

12.31

19, 26 4.4 CC.3.OA.5 May incorrectly break apart a factor R—4.4; TE—p. 145B 12.50

22, 27 4.8 CC.3.OA.7 May multiply the wrong numbers R—4.8; TE—p. 163B 12.29

21 4.7 CC.3.OA.9 May incorrectly identify the pattern R—4.7; TE—p. 159B 12.38

23 4.3 CC.3.OA.3 May not subtract the products R—4.3; TE—p. 141B 12.26, 12.28

24 4.6 CC.3.OA.5 May multiply by only 2 numbers R—4.6; TE—p. 155B 12.49

25 4.3 CC.3.OA.3 May use an incorrect rule R—4.3; TE—p. 141B 12.26, 12.28

28 4.9 CC.3.OA.7 May multiply 9 by the wrong number R—4.9; TE—p. 167B 12.30

Based on the results of the Chapter Review/Test, use the following resources to review skills.

Summative AssessmentUse the Chapter Review/Test to assess students’ progress in Chapter 4.

You may want to review with students the essential question for the chapter.

Chapter Essential QuestionWhat strategies can you use to multiply?

Ask the following questions to focus students’ thinking:

• How are patterns and multiplication related?

• How can multiplication properties help you fi nd products?

• What types of problems can be solved by using multiplication?

Chapter 4

Review/Test

Untitled-397 176 10/20/2011 2:27:20 PM

Performance Indicators

Performance Task Scoring RubricPerformance Task Scoring Rubric

1

2

3


PREPTESTPREPTEST

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Chapter 4 177

26. James made an array with 6 rows of 8 blocks. Which number sentence shows one way to break apart his array to find the product? (CC.3.OA.5)

A 6 3 8 5 (6 1 4) 1 (6 1 4)

B 6 3 8 5 (6 3 4) 1 (6 3 4)

C 6 3 8 5 (3 3 4) 1 (3 3 4)

D 6 3 8 5 (6 3 8) 1 (6 3 8)

27. Zach and his dad baked some cupcakes for his class. They put 6 cupcakes on each of 8 plates. How many cupcakes did they put on the plates? (CC.3.OA.7)

A 12

B 14

C 24

D 48

28. Sydnee’s class is studying animals that hibernate, or go into a sleep-like state during the winter. A black bear’s heartbeat slows to about 9 beats per minute during hibernation. About how many times will a black bear’s heart beat in 5 minutes? (CC.3.OA.7)

A 45

B 36

C 18

D 9

Untitled-185 177 4/15/2011 3:45:14 PM

PREPTESTPREPTEST

176

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Fill in the bubble for the correct answer choice.19. Which number sentence is an example of the

Distributive Property? (CC.3.OA.5)

A 5 3 9 5 (5 3 5) 1 (5 3 4)

B (3 3 2) 3 5 5 3 3 (2 3 5)

C 5 3 9 5 9 3 5

D 5 3 9 5 45

20. Adel needs 5 pieces of ribbon, each 8 centimeters long. How much ribbon does she need altogether? (CC.3.OA.3)

A 13 centimeters C 35 centimeters

B 32 centimeters D 40 centimeters

21. When Chloe finds the multiplication facts for 2, which digit will NOT be in the ones place of the products? (CC.3.OA.9)

A 8 C 4

B 6 D 3

22. Vicky went to the store and bought 3 pairs of shorts. They each cost $8. How much did she spend? (CC.3.OA.7)

A $3 B $8 C $21 D $24

23. A honeybee is an insect. It has 6 legs. How many more legs do 7 honeybees have than 5 honeybees? (CC.3.OA.3)

A 5 C 12

B 6 D 30

24. Jody has bags of shells. Each bag has 6 shells. She gives 3 bags to each of 2 friends. How many shells did Jody give away? (CC.3.OA.5)

A 36 B 18 C 12 D 6

25. The camping club rents 4 rafts. Each raft can hold 6 people. How many people can 4 rafts hold? (CC.3.OA.3)

A 16 B 20 C 24 D 30

Untitled-125 176 10/18/2011 12:33:51 PM

GOOnline

Assessment OptionsChapter Test

Chapter 4 Review/Test

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Chapter 4 175

Vocabulary


1. The ___ Property of Multiplication states that when the grouping of factors is changed, the product is the same. (p. 155)

2. A __ of 9 is any product that has 9 as one of its factors. (p. 137)

Concepts and Skills

Use arrays to show each property. (CC.3.OA.5)

→

→

3. Distributive Property

Break apart the array to show 8 3 6 5 (4 3 6) 1 (4 3 6).

4. Associative Property of Multiplication

Circle groups to show 3 3 (2 3 3).


Vocabulary

Associative Property

of Multiplication


multiple

11. 9 3 0 5 _ 12. 7 3 8 5 _ 13. 4 3 8 5 _ 14. 2 3 6 5 _

15. 9 3 9 5 _ 16. 3 3 4 5 _ 17. 5 3 10 5 _ 18. 7 3 3 5 _

5. 6 3 8

_

6. 10 3 4

_

7. 5 3 9

_

8. 6 3 3

_

9. 5 3 8

_

10. 8 3 8

_

Associative

multiple

48 40 45 18 40 64


0

81

56

12

32

50

12

21

Untitled-185 175 4/15/2011 3:45:12 PM

175-176 Chapter 4Performance Task may be used for portfolios.

3

Generally accurate, complete, and clear: All parts of the task are successfully completed. The student demonstrates sound reasoning and an understanding of the key concepts and procedures. Explanations are complete and clear with no meaningful errors.

2Accurate results without suffi cient support: All parts of the task are completed. While correct answers may indicate some understanding of the key concepts and procedures, explanations are lacking in reasoning and mathematical justifi cation.

1Partially accurate: Part of the task is successfully completed while other parts may be attempted, but not successfully completed. The student demonstrates minimal understanding of key concepts and procedures.

0Not accurate, complete, and clear: No part of the task is completed with any success. There is little, if any, evidence that the student understands key concepts and procedures.



3, 4 4.4, 4.6 CC.3.OA.5 May use the wrong property R—4.4, 4.6; TE—p. 145B, 155B 12.49, 12.50

5–18, 20 4.1–4.3, 4.5, 4.8, 4.9

CC.3.OA.3CC.3.OA.7

May fi nd an incorrect product

R—4.1–4.3, 4.5, 4.8, 4.9;TE—p. 133B, 137B, 141B, 149B, 163B, 167B

12.21, 12.22, 12.23, 12.25, 12.26, 12.28, 12.29, 12.30,

12.31

19, 26 4.4 CC.3.OA.5 May incorrectly break apart a factor R—4.4; TE—p. 145B 12.50

22, 27 4.8 CC.3.OA.7 May multiply the wrong numbers R—4.8; TE—p. 163B 12.29

21 4.7 CC.3.OA.9 May incorrectly identify the pattern R—4.7; TE—p. 159B 12.38

23 4.3 CC.3.OA.3 May not subtract the products R—4.3; TE—p. 141B 12.26, 12.28

24 4.6 CC.3.OA.5 May multiply by only 2 numbers R—4.6; TE—p. 155B 12.49

25 4.3 CC.3.OA.3 May use an incorrect rule R—4.3; TE—p. 141B 12.26, 12.28

28 4.9 CC.3.OA.7 May multiply 9 by the wrong number R—4.9; TE—p. 167B 12.30

Based on the results of the Chapter Review/Test, use the following resources to review skills.

Summative AssessmentUse the Chapter Review/Test to assess students’ progress in Chapter 4.

You may want to review with students the essential question for the chapter.

Chapter Essential QuestionWhat strategies can you use to multiply?

Ask the following questions to focus students’ thinking:

• How are patterns and multiplication related?

• How can multiplication properties help you fi nd products?

• What types of problems can be solved by using multiplication?

Chapter 4

Review/Test

Untitled-397 176 10/20/2011 2:27:20 PM

summative

• Determine whether students have achieved the chapter objectives

• Use Data-Driven Decision Making chart to provide intervention to students

Assessment

18

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