Professional Development

Professional Development

Professional Development Videos

Progress to AlgebraWhy Teach ThisThe conceptual understanding of two-digit numbers takes time to develop. For example, some children will be able to say that 53 has 5 tens and 3 ones without a clear understanding of what the number represents. Continue to have children group single objects into tens and ones and break apart tens and ones into single objects.

Having children count out tens and ones with base-ten blocks reminds them that numbers represent countable things, and can be decomposed in useful ways, such as tens and ones. This understanding builds a solid foundation for more advanced computation skills.

LESSON AT A GLANCE

Progressto Algebra

367A Chapter 6

Hands On • Tens and Ones to 100

LESSON 6.7

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Base-Ten Blocks

HMH Mega Math

About the Math

Learning ObjectiveGroup objects to show numbers to 100 as tens and ones.

Language ObjectiveChildren work in teams to discuss and decide how best to show numbers to 100 as tens and ones.

MaterialsMathBoard, base-ten blocks, connecting cubes

F C R Focus:Common Core State Standards

1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP2 Reason abstractly and quantitatively. MP4 Model with mathematics.MP6 Attend to precision.

F C R Coherence:Standards Across the GradesBeforeK.NBT.A.1

Grade 11.NBT.B.2

After2.NBT.A.1

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your Own, Practice and HomeworkLevel 3: Applications..................................Think Smarter and Go Deeper

F C R For more about how GO Math! fosters Coherencewithin the Content Standards and Mathematical Progressions for this chapter, see page 327J.

FOCUS COHERENCE RIGOR

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=D

ENGAGE1Daily Routines

Common Core

hundred

Interactive Student EditionMultimedia Glossary e

Lesson 6.7 367B

How can you show numbers to 100 as

tens and ones?

Vocabulary BuilderMaterials connecting cubes, Vocabulary Card hundred (see eTeacher Resources), small classroom items

Hundred CountOne at a time, display ten 10-cube trains as you count with children from 0 to 100 by tens. Write 100 on the board and display the Vocabulary Card. Read the word hundred aloud, and tell children that one hundred is equal to 10 tens or 100 ones.

Display groups of small classroom items such as 15 crayons and 100 paper clips. Ask children which group they think shows 100. Let volunteers count the objects and report their findings in a sentence, such as I counted one hundred paper clips.

with the Interactive Student Edition

Essential QuestionHow can you show numbers to 100 as tens and ones?

Making ConnectionsRemind children that they have learned to look for patterns to count forward.

Look at 115, 116, 117. What are the next 3 numbers? 118, 119, 120

Look at 142, 144, 145. What number is missing? 143

Learning ActivityWhat is the problem children are trying to solve? Connect the story to the problem. Ask questions like the following.

• How many tens are there in 100? 10

• How can you say a number like 108 using the words “tens” and “ones”? 108 has 10 tens and 8 ones

Literacy and MathematicsView the lesson opener with the children. Then choose one or more of the following activities.

• Have children write and illustrate a word problem about ten tens and some ones.

• Have children retell the story in their own words.

Problem of the Day 6.7Calendar Math Chin and his family are going on a trip for 5 days. They leave on the 8th day of the month. On what date do they return? Possible answer: They return on the 13th day of the month.

Help children find the 8th on the calendar and then count, in unison, to the 13th.

Vocabulary hundred

EXPLORE2

Name

Riddles to 100Write a number to solve.

1. I am greater than 57.

I am less than 60.

I have 9 ones.

59 —

2. I am greater than 72.

I am less than 76.

The ones are not 3 or 5.

74 —

3. I am less than 40.

I have 8 ones and 2 tens.

28 —

4. I am less than 100.

I have no tens. I am greater than 0 and less than 2.

1 —

5. I am greater than 35.

I am less than 45.

I have 2 ones.

42 —

6. I am greater than 80.

I am less than 90.

I have 1 one.

81 —

Writing and Reasoning Write a riddle for the number 62.

Lesson 6.7Enrich

I am less than 65. I have 2 ones.

Possible answer: I am greater than 59.

DO NOT EDIT--Changes must be made through "File info"CorrectionKey=A

6-18 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

1_MNLEAN342712_C06E07.indd 18 2/15/14 11:50 PM

Tens Ones

Name 

There are 9 tens.There are 8 ones.The number is 98.

Tens and Ones to 100

If you know the tens and ones, you can write the number.

9 tens 8 ones = 98  —

Use your MathBoard and to show the tens and ones. Write the numbers.

1.

5 tens 9 ones = 59  —

2.

6 tens 3 ones = 63 —

3.

7 tens 7 ones = 77 —

4.

8 tens 2 ones = 82 —

Lesson 6.7Reteach

DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A

6-17 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

1_MNLEAN342712_C06R07.indd 17 2/15/14 11:56 PM

1

2

3 DifferentiatedInstruction

Progressto Algebra

Listen and DrawListen and Draw

25

50

52

HandsOn

MATHEMATICAL PRACTICES 2MathTalk

Name

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Chapter 6 three hundred sixty-seven 367

Tens and Ones to 100Essential Question How can you show numbers to 100 as tens and ones?

Use to model the number.Draw a quick picture to show your work.

Number and Operations in Base Ten—1.NBT.B.2

MATHEMATICAL PRACTICESMP.2, MP.4, MP.6

Lesson 6.7HANDS ON

FOR THE TEACHER • Ask children to use base-ten blocks to show how many tens and ones there are in 25, 50, and 52.

Reasoning How did you figure out how many tens and ones are in 52?

Math Talk: Possible answer: I looked at the number 52. The 5 in 52 means there are 5 tens. The 2 in 52 means there are 2 ones.

Possible answers shown.

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=A

1_MNLESE341906_C06L07.indd 367 2/13/14 6:35 PM

367 Chapter 6

Listen and DrawMaterials base-ten blocks, connecting cubesIn the previous lesson, children made the transition from connecting cubes to using base-ten blocks. Continue to have connecting cubes available for children to use if theyneed to.Read the following directions aloud.

Use base-ten blocks to show how many tens and ones there are in 25, 50, and 52.

Have children model the numbers and draw quick pictures of tens and ones to represent their models.• How many tens and ones did you draw to

show 25? Possible answer: I drew 2 lines for the 2 tens and 5 circles for the 5 ones.

• What does the 0 in 50 mean? There are no ones.

• All three numbers have a 5. Does the 5 mean the same thing in each number? Explain. No. The 5 in 25 means 5 ones. The 5 in 50 and 52 means 5 tens.

MathTalk

MP2 Reason abstractly and quantitatively. Use Math Talk to focus on children’s understanding of how to show a two-digit number as tens and ones.When you look at a two-digit number, what do you know about every two-digit number? Possible answer: The number on the left tells me how many groups of tens there are and the number on the right tells me how many ones there are.

ELL Strategy: Illustrate Understanding

Children may illustrate their understanding of tens and ones by drawing a quick picture.Ask children to show the number 33 using base-ten blocks. Remind children that lines represent tens and circles represent ones. Ask children to draw a quick picture for 33. Repeat with different numbers. Encourage children to ask and answer questions about how they can show numbers.MP6 Attend to precision. • What do a base-ten block, a ten-cube train,

and a quick draw line have in common? They all represent one group of ten.

LESSON 6.7

HandsOn

1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.

Enrich 6.7Reteach 6.7

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=D

EXPLAIN3

Advanced Learners

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

Model and DrawModel and Draw

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

368 three hundred sixty-eight

Draw quick pictures to show 99 and 100.

The number just after 99 is 100.10 tens is the same as 1 hundred.

1. 2.

Use your MathBoard and to show the tens and ones. Write the numbers.

3. 4.

9 — tens 9 — ones = 99 — 10 — tens 0 — ones = 100 —

7 — tens 9 — ones = 79 — 5 — tens 4 — ones = 54 —

6 — tens 3 — ones = 63 — 8 — tens 7 — ones = 87 —

COMMON ERRORS

Quick Check

If

Rt I RRR1

2

3

Then

Lesson 6.7 368

Model and Draw MATHEMATICAL PRACTICES

MP2 Reason abstractly and quantitatively. Have children trace the numbers as you read aloud to discuss 99 and 100. • What does it mean that 100 is just after 99?

Possible answers: When you count to 100, you say 100 right after you say 99; 100 is one more than 99.

• How is 100 different from 99? There are 10 tens in 100 and only 9 tens in 99; there are 10 tens zero ones in 100, and 9 tens 9 ones in 99.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children complete the exercises and use their MathBoards to explain their thinking. Make sure children notice the ones blocks are shown before the tens in Exercises 2 and 4.• How do you know your answer is correct?

Possible answer: My answer has two numbers. The number on the left tells how many tens and the number on the right tells how many ones. My answer matches the drawings.

Use the checked exercises for Quick Check.

Error Children may have difficulty differentiating the tens and ones.

Example For Exercise 1, children write 9 tens 7 ones.Springboard to Learning Have children draw vertical lines through the tens as they count each picture. Then have children draw dots on the ones as they count them. Tell children to watch for cubes with space between them to indicate ones.

a child misses the checked exercises

Differentiate Instruction with • Reteach 6.7

• Personal Math Trainer 1.NBT.B.2

• RtI Tier 1 Activity (online)

Materials base-ten blocks, Workmat 3 (see eTeacher Resources)

• Have children take turns thinking of a number from 50 to 100 and giving their partner a clue for the number, such as, “My number has more than 6 tens but fewer than 8 tens.”

• The partner tries to guess the number by modeling it with base-ten blocks on the workmat. If the guess is incorrect, the first child gives another clue, such as, “The tens are correct, but my number also has some ones.”

• Clues are given until the partner models the correct number. Children then switch roles and repeat.

Auditory / KinetheticPartners

4 ELABORATE On Your OwnOn Your Own

Name

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

MATHEMATICALPRACTICE 2 Reason Quantitatively Write the numbers.

Chapter 6 • Lesson 7 three hundred sixty-nine 369

5.

6.

7.

9.

8.

9 — tens 6 — ones = 96 —

6 — tens 9 — ones = 69 —

8 — tens 4 — ones = 84 —

7 — tens 2 — ones = 72 —

10 — tens 0 — ones = 100 —

90 — 63 —

10. DEEPER What number is the same as 7 tens and 20 ones?

11. DEEPER What number is the same as 5 tens and 13 ones?

369 Chapter 6

On Your Own MP2 Reason abstractly and quantitatively.If children answered Exercises 3 and 4 correctly, assign Exercises 5–11.

DEEPER

Exercises 10 and 11 require children to use higher order thinking skills to apply what they know about tens and ones. You may wish to have children use base-ten blocks to model the problems and demonstrate how tens and ones can be traded.• How many ones can you trade for 1 ten?

Explain. 10 ones; 10 ones are equal to 1 ten.

• So, 20 ones can be traded for how many tens? Explain. Possible answer: If I have 20 ones and trade 10 of them for 1 ten, then I will have 10 ones left and I can make another trade for 1 ten. So, 20 ones can be traded for 2 tens.

MP6 Attend to precision. • For Exercise 11, how does thinking of 13 as 1

ten and 3 ones help you solve the problem? Possible answer: I can take one ten from 13 and add it to my 5 tens to get 60. Once I have 60, I see I have 3 ones left. I can’t make any more tens so I know my answer is 63.

DEEPER

To extend thinking, have children write addition expressions using tens and ones that show the solutions for Exercises 10 and 11. Have children share their solution strategies and explain their reasoning. Being able to decompose a problem into steps and explain the steps to others is a valuable exercise in critical thinking skills.A sample solution strategy might be: 5 tens + 13 ones 5 tens + 1 ten + 3 ones 6 tens + 3 ones 63

EVALUATE5 Formative Assessment

Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

Math

MATHEMATICAL PRACTICES

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

• Im

age

Cred

its: (

bl) ©

Phot

oDis

c/Ge

tty Im

ages

370 three hundred seventy

Draw a quick picture to show the number. Write how many tens and ones there are.

12. Edna has 82 stamps.

13. Amy has 79 beads.

14. SMARTER Moe has a group of 70 red feathers and 30 brown feathers.

8 — tens 2 — ones

10 — tens 0 — ones

7 — tens 9 — ones

TAKE HOME ACTIVITY • Give your child numbers from 50 to 100. Ask your child to draw a picture to show the tens and the ones in each number and then write the number.

16 —

15. SMARTER Read the problem. Write a number to solve.

I am greater than 14. I am less than 20. I have 6 ones.

Other answers are possible, such as 7 tens 30 ones.

Also accept other ways to show 82.

Also accept other ways to show 79.

Lesson 6.7 370

GamesTens and Ones Race

LiteratureStrawberries

ActivitiesTen and Up

Children practice decomposing numbers into tens and ones.

Children read the book and use place value to find the number of strawberries.

Children complete purple Activity Card 14 by reviewing place value and numbers from 10 to 50.

Essential QuestionUsing the Language ObjectiveReflect Have children work in teams and discuss to answer the Essential Question.How can you show numbers to 100 as tens and ones? Possible answer: I can use base-ten blocks to show tens and ones. If I know the tens and ones I can write the number.

Math Journal Math

Use words and pictures to show 59 and 95.

MATHEMATICAL PRACTICES

MP4 Model with mathematics.Make sure that children understand that the first digit in a two-digit number represents the tens, and the second digit represents the ones. Some children may find it helpful to model the problem to see the tens and ones or to check their answers.

SMARTER

MP2 Reason abstractly and quantitatively. Exercise 14 requires children to use higher order thinking skills. They need to add the group of 7 tens to the group of 3 tens to make 10 tens.

SMARTER

In Exercise 15, children use logical thinking and understanding of tens and ones to answer a number riddle. Children who answer incorrectly may have difficulty differentiating between tens and ones. Some children may use a Number Chart to circle the numbers between 14 and 20, circle all numbers that have 6 ones, and then select the only number that is in both sets of circled possibilities.

Math on the Spot Video TutorUse this video to help children model and solve this type of Think Smarter problem.

Problem Solving • Applications

Cross-Curricular

Problem SolvingProblem Solving

Name

© H

ough

ton

Mif

flin

Har

cour

t Pub

lishi

ng C

omp

any

Chapter 6 three hundred seventy-one 371

1.

9 — tens 8 — ones = 98 —

2.

8 — tens 9 — ones = 89 —

3.

7 — tens 5 — ones = 75 —

Draw a quick picture to show the number. Write how many tens and ones there are.

4. Inez has 57 shells.

5 — tens 7 — ones

Tens and Ones to 100

Write the numbers.

COMMON CORE STANDARDS—1.NBT.B.2 Understand place value.

Lesson 6.7Practice and Homework

5. Math Use words and pictures to show 59 and 95.

Also accept other ways to show 57.

Check children’s work.

371 Chapter 6

Practice and HomeworkUse the Practice and Homework pages to provide children with more practice of the concepts and skills presented in this lesson. Children master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine children’s understanding of content for this lesson. Encourage children to use their Math Journals to record their answers.

SOCIAL STUDIES

Materials base-ten blocks

• Discuss the significance of the Declaration of Independence and ways Americans celebrate their freedom on July 4th. Allow children to share their family or community traditions.

• Tell children that 56 leaders signed the Declaration of Independence. Have children use base-ten blocks to show the number 56 as tens and ones.

Materials collection of 20–50 rocks

• Provide a collection of about 30 rocks for children to examine. Have children describe how the rocks are alike and different. Discuss where rocks are found, concluding that they are found on Earth’s surface.

• Have children count the rocks in the collection by putting them in groups of tens and ones. Ask them to tell how many tens and ones there are and then name the number.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

© H

ough

ton

Mif

flin

Har

cour

t Pub

lishi

ng C

omp

any

372 three hundred seventy-two

Lesson Check (1.NBT.B.2)

1. What number has 10 tens 0 ones?

100 —

2. What number doesthe model show?Write the numbers.

7 — tens 4 — ones = 74 —

Spiral Review (1.OA.B.3, 1.OA.C.5)

3. Barry knows that 6 + 5 = 11. What other addition fact does he know? Write the new fact.

5 — + 6 — = 11 —

4. Count on to solve 2 + 6.Write the sum.

2 + 6 = 8 —

Lesson 6.7 372

Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage children in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.