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Progress to AlgebraIf Children AskIn previous lessons, children made a ten by connecting 10 cubes to make a cube train. In this lesson, children use base-ten blocks to represent tens and ones. Base-ten blocks are pregrouped models that are effi cient to use, but children cannot take them apart or put them together to show number relationships.

Continue to provide access to connecting cubes for the upcoming lessons. Some children will benefi t from having the opportunity to continue making tens to reinforce their transition to base-ten blocks.

LESSON AT A GLANCE

Progressto Algebra

361A Chapter 6

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

iTools: Base-Ten Blocks

HMH Mega Math

Hands On • Tens and Ones to 50

LESSON 6.6

About the Math

Learning ObjectiveGroup objects to show numbers to 50 as tens and ones.

Language ObjectiveChildren group cubes and then draw and label them in their Math Journal to show a number as tens and ones.

MaterialsMathBoard, connecting cubes, base-ten blocks

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.)MP4 Model with mathematics. MP5 Use appropriate tools strategically.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

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ENGAGE1Daily Routines

Common Core

1 23 4 Pages 46–47 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

How can you group cubes to show a number

as tens and ones?

Lesson 6.6 361B

with the Interactive Student Edition

Essential QuestionHow can you group cubes to show a number as tens and ones?

Making ConnectionsAsk children to think about how they could arrange themselves to show a number.

Have children draw pictures to show the number of children in class. Share and discuss the pictures with the class.

Learning ActivityDiscuss using models to show tens and ones.

• How could you use counters or cubes to show the number of baseballs in the treehouse? Possible answer: I could use one counter or cube to show each baseball.

• How does using a model help you to count the number of baseballs? Answers will vary.

• If you didn’t use tens and ones to help you count, what other groups could you use? Explain. Answers will vary.

Literacy and MathematicsChoose from one or more of the following activities.

• Help children write a class story that uses a number up to twenty.

• Have children draw more than ten of one kind of object. Ask them to circle the ten in their pictures and explain their drawings.

1 23 4 Fluency BuilderMaterials Basic Facts (See eTeacher Resources)

Mental MathPresent word problems like the ones below. Have children use mental math to solve.

• Pam made cupcakes for the bake sale. She put 10 cupcakes on each tray. She filled 4 trays. How many groups of ten are there? 4 tens How many cupcakes are there in all? 40 cupcakes

• There are 2 rows of cars in the parking lot. Each row has 10 cars. How many groups of ten are there? 2 tens How many cars are there in all? 20 cars

Problem of the Day 6.6Words of the Day make a ten Lindsay makes a ten to find 6 + 7. What two numbers does Lindsay add? 10 + 3

Remind children to start with the greater number, 7, and add on to make a 10. They then add the remaining 3.

VocabularyInteractive Student EditionMultimedia Glossary e

Strawberries

Literature ConnectionFrom the Grab-and-Go™ Differentiated Centers Kit

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

Common Core Fluency Standard 1.OA.C.6

EXPLORE2

Name

Ones and Tens CrossoutCross out the box that does not match.Then write the missing number.

1.

242 tens 4 — ones

— tens 2 ones

2.

48

8 tens — ones

4 — tens 8 ones

3.

36

— tens 3 ones

3 tens 6 — ones

Writing and Reasoning How can you draw to show that Exercise 3 is correct?

Lesson 6.6Enrich

I can draw 3 groups of ten and 6 ones. I can

count to find 36.

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6-16 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Tens Ones

Name 

Tens and Ones to 50

You can use tens and ones to show a number.

4 tens 2 ones = 42  —

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

1.

1 ten 8 ones = 18  —

2.

2 tens 5 ones = 25 —

3.

4 tens 7 ones = 47 —

4.

3 tens 6 ones = 36 —

There are 4 tens.There are 2 ones.This shows 42.

Lesson 6.6Reteach

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6-15 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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1

2

3 DifferentiatedInstruction

Progressto Algebra

Tens Ones

MATHEMATICAL PRACTICES 4MathTalk

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Chapter 6 three hundred sixty-one 361

Use to model the number.Draw to show your work.

Tens and Ones to 50Essential Question How can you group cubes to show a number as tens and ones?

Listen and DrawListen and DrawHands

On

FOR THE TEACHER • Ask children to use 23 cubes and show them as tens and ones.

Model How did you figure out how many tens and ones are in 23?

HANDS ONLesson 6.6

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

MATHEMATICAL PRACTICESMP4, MP5, MP6

Math Talk: Possible answer: I made two groups of ten and had 3 cubes left over. The two groups of ten show there are 2 tens. The 3 cubes left are the ones.

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361 Chapter 6

LESSON 6.6

Listen and Draw Materials connecting cubes, base-ten blocks

Read the following aloud.Use 23 connecting cubes and show them as tens and ones. Then draw your models.

• What have you learned about making a ten that can help you show 23 as tens and ones? I know that 10 ones are equal to 1 ten. So I can make tens, and the leftover cubes are the ones.

Have children model with connecting cubes in the place value chart on the page. After children represent their work, allow them to share their pictures. If children have made 1 ten with 13 ones leftover, encourage them to make as many tens as possible.• What did you draw in the chart? Possible

answer: I drew 2 tens cube trains in the tens column and 3 squares in the ones column; I drew 2 lines to show 2 tens and 3 circles to show the ones.

Distribute tens and ones base-ten blocks. Show children how to use base-ten blocks to model the number 23. Discuss how this new model compares with the model that used connecting cubes.Have children explore showing the numbers 18, 31, and 27 as tens and ones.

MathTalk

MP4 Model with mathematics. Use Math Talk to focus on children’s understanding of how to count and organize objects to show two-digit numbers as tens and ones.• Why is the tens column on the left in the

model? When I write a two-digit number, the tens are on the left, just like in the model.

ELL Strategy: Identify Relationships

Children identify the relationship between different ways of showing tens and ones. Show children 13 cubes connected into a 10-cube train and 3 extra cubes. Then show children a quick picture of 1 ten and 3 ones.

• This is another way to show the number 13. How are the cubes and the picture alike? How are they different? They both show 13. They look different.

Repeat with different numbers through 19.

HandsOn

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

Enrich 6.6Reteach 6.6

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EXPLAIN3

Tens Ones

Advanced Learners

Tens Ones Tens Ones

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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

2 — tens 4 — ones = 24 — 4 — tens 2 — ones = 42 —

1. 2.

3. 4.

3 — tens 5 — ones = 35 —

4 — tens 3 — ones = 43 — 1 — ten 4 — ones = 14 —

2 — tens 9 — ones = 29 —

The 2 in 24 means 2 tens. The 2 in 42 means 2 ones.

COMMON ERRORS

Quick Check

If

Rt I RRR1

2

3

Then

Lesson 6.6 362

Error Children may reverse the digits when writing the numbers.

Example In Exercise 1, children write 3 tens 5 ones as 53.Springboard to Learning To help connect 3 tens 5 ones to 35, suggest that children work from left to right, recording the number of tens first, and then the number of ones.

Model and Draw MATHEMATICAL PRACTICES

MP5 Use appropriate tools strategically. Work through the model with children. For 24, have children count the tens and trace the number. Have children count the ones and trace the number. Repeat for the model of 42.• What do the two digits in the number 24

stand for? 2 tens and 4 ones

• Is the value of the digit 2 the same in both 24 and 42? No Explain. In 24, the 2 has a value of 2 tens, or 20. In 42, the 2 has a value of 2 ones, or 2.

• How do you know that 42 has 4 tens? Possible answer: The 4 is on the left and the 2 is on the right, so 42 has 4 tens and 2 ones.

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Have children complete the exercises using the Tens and Ones workspace on the MathBoard.• How do you know your answer is correct?

Possible answer: I compared my model to the picture.

Use the checked exercises for Quick Check. Children should use MathBoards to show their solutions.

a child misses the checked exercises

Differentiate Instruction with • Reteach 6.6

• Personal Math Trainer 1.NBT.B.2

• RtI Tier 1 Activity (online)

Materials base-ten blocks, Numeral Cards 21–50, Workmat 3 (see eTeacher Resources)

• Partners shuffle the cards and distribute them equally (15 cards each, facedown).

• Have children take turns choosing a card from their own pile and telling their partner how to model it on the workmat, without saying the number. For example: Put 2 tens on the mat under Tens. Put 4 ones on the mat under Ones.

• Have the child making the model tell the number that it shows—in this example, 24.

• Repeat as time allows.

Visual / AuditoryPartners

4 ELABORATE

Tens Ones Tens Ones

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Chapter 6 • Lesson 6 three hundred sixty-three 363

9. DEEPER Mary drew tens and ones to show 32. She made a mistake. Draw a correct quick picture to show 32. Write the numbers.

MATHEMATICALPRACTICE 6 Make Connections

Write the numbers.

3 — tens 3 — ones = 33 —

5 — tens 0 — ones = 50 —

4 — tens 6 — ones = 46 —

0 — tens 5 — ones = 5 —

5. 6.

7. 8.

3 — tens 2 — ones = 32 —

On Your OwnOn Your Own

Possible answer shown.

363 Chapter 6

On Your Own MP6 Attend to precision. If children answered Exercises 3 and 4 correctly, assign Exercises 5–9. Check to make sure children put the zero in the correct place in Exercises 7 and 8.

DEEPER

Exercise 9 requires children to use higher order thinking skills to identify the error and draw a correct answer. You might have them model the number in the same way as Mary, using 2 tens and 3 ones.• What do you think Mary did wrong? Possible

answer: She does not know which digit means the tens and which digit means the ones.

• How can you correct the mistake Mary made? Possible answer: I draw to show 32 as 3 tens and 2 ones. The sentence will read 3 tens 2 ones equals 32.

DEEPER

To extend thinking, ask children why, when writing a number such as 32, it makes a difference whether they write the 3 in front of or after the 2. Have them explain their reasoning with words, pictures, or base-ten blocks.Children should recognize that the first digit (on the left) in a two-digit number represents the tens, and the second digit (on the right) represents the ones. Lead children to conclude that they should write the 3 first because it represents the tens.MP6 Attend to precision. • To model 42, what do you need to show?

Possible answer: I need to show 4 groups of ten and two ones. How does your model change to show 24? Possible answer: My model changes to show 2 groups of tens and 4 ones. Why does it matter in which order you write the numbers in a two-digit number? Possible answer: In a two-digit number, the number on the left is the tens and the number on the right is the ones. If I write the numbers in the wrong order, I will be showing the wrong number of tens and ones.

MATHEMATICAL PRACTICES

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

Math

MATHEMATICAL PRACTICES

Personal Math Trainer

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Solve. Write the numbers.

10. I have 46 cubes. How many tens and ones can I make?

11. I have 32 cubes. How many tens and ones can I make?

12. I have 28 cubes. How many tens and ones can I make?

13. SMARTER I am a number less than 50. I have 8 ones and some tens. What numbers could I be?

4 — tens 6 — ones

3 — tens 2 — ones

2 — tens 8 — ones

28, 38, 48 ———

TAKE HOME ACTIVITY • Write a two-digit number from 20 to 50, such as 26. Ask your child to tell which digit names the tens and which digit names the ones. Repeat with different numbers.

14. SMARTER There are 35 . Jun says that there are 3 ones and 5 tens. Rob says that there are 3 tens and 5 ones. Who is correct? Circle the name.

Jun Rob

How can you draw to show 35?

Possible answers shown.

Check children’s explanations or drawings.

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

Lesson 6.6 364

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.

GamesTens and Ones Race

LiteratureStrawberries

ActivitiesTen and Up

Essential QuestionReflect Using the Language Objective Have children model and then draw their model in their Math Journal to answer the Essential Question.• How can you group cubes to show a

number as tens and ones? Possible answer: Make as many groups of ten as you can and the leftovers are ones.

Math Journal Math

Write a number from 20 to 50 that has both tens and ones. Use pictures and words to show the tens and ones.

Encourage children to look at the place of the digits in each number to determine how many tens and ones there are.

SMARTER

MP1 Make sense of problems and persevere in solving them. For Exercise 13, encourage children to make a list of numbers less than 50 that have 8 ones, and then examine the list to determine which of those numbers also have some tens.

Personal Math Trainer SMARTER

Be sure to assign Exercise 14 to children in the Personal Math Trainer. It features an animation to help them model and answer the problem. Children must use logic to compare how the opinions are the same and different, assess who is correct, and then justify their thinking by drawing a picture or writing an explanation.

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

Problem Solving • Applications

Mathematical Practices in Your Classroom PROFESSIONALDEVELOPMENT

Problem SolvingProblem Solving

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1.

3 — tens 6 — ones = 36 —

2.

0 — tens 8 — ones = 8 —

Tens and Ones to 50

Write the numbers.

Solve. Write the numbers.

3. I have 43 cubes. How manytens and ones can I make?

4 — tens 3 — ones

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

Lesson 6.6Practice and Homework

4. Math Write a number from 20 to 50 that has both tens and ones. Use pictures and words to show the tens and ones.

Check children’s work.

365 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.

CCSS.Math.Practice.MP5 Use appropriate tools strategically. Children extend previous work with one ten and some ones as they identify and model the tens and ones in two-digit numbers to 50. In this lesson, children represent tens and ones with paper and pencil for quick pictures and with concrete models in the form of base-ten blocks.

Ask children to name all of the available tools for identifying tens and ones, but allow them to decide which are appropriate. Remind them of online resources such as iTools.

Discuss the advantages and disadvantages of different models to show numbers to 50.

• What can you use to model tens and ones? Possible answers may include: bundles of 10 sticks and single sticks, quick picture of lines and dots, connecting cubes, base-ten blocks, iTools

• Why would you use base-ten blocks instead of connecting cubes to show tens and ones? Possible answers: It takes more time to count out and connect 10 connecting cubes. The base-ten tens blocks are just counted as ten, so it is quicker; You can miscount the cubes when making tens. Then you will get the wrong number of tens and ones.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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1. What number does the model show?Write the numbers.

2 — tens 9 — ones = 29 —

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

4 — tens 7 — ones = 47 —

Spiral Review (1.OA.A.1, 1.OA.C.6)

3. Write the sum.

4. Show taking from. Circle the part you take from the group.Then cross it out.Write the difference.

6 – 4 = 2 —

Lesson Check (1.NBT.B.2)

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+ 39

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.

Lesson 6.6 366