lesson 4.4 progress correctionkey=d to algebra hands · pdf fileprogress to algebra teaching...

229A Chapter 4

LESSON 4.4

Hands On • Use 10 to Subtract

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LESSON AT A GLANCE

Progressto Algebra

Interactive Student Edition

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Math on the Spot Video

iTools: Counters

Progress to AlgebraTeaching for DepthRelating addition to subtraction is crucial for future work in algebra. Also, understanding that numbers can be composed and decomposed in different ways allows children to develop fl uency with numbers.

The make a ten strategy works well for subtraction facts in which the subtracted number is 8 or 9. In 16 − 9, children count up 1 to make 10, then count up 6 more to make 16. Children are relating 9 + 1 + 6 = 16 to 16 − 9 = 7. Tell children that they will be counting up to the number they start with. Counting up to 10 is the fi rst step.

• You just added 1. How do you know how many more to add?

• How does adding in two steps instead of one step make the problem easier?

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 207H.

Learning ObjectiveUse make a 10 as a strategy to subtract.

Language ObjectiveChildren model or draw, and then share with a partner how you can make a ten to help you subtract.

MaterialsMathBoard, Ten Frames (see eTeacher Resources), two-color counters

F C R Focus:Common Core State Standards

1.OA.C.6 Add and subtract within 20, demonstrating fl uency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 − 4 = 13 − 3 − 1 = 10 − 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 − 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP2 Reason abstractly and quantitatively. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP8 Look for and express regularity in repeated reasoning.

F C R Coherence:Standards Across the GradesBeforeK.OA.A.5

Grade 11.OA.C.6

After2.OA.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

FOCUS COHERENCE RIGOR

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Lesson 4.4 229B

How can you make a ten to help you

subtract ?

The Class Party

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

Children read the book and learn to read addition and subtraction number sentences.

Daily RoutinesCommon Core

Th Cl P

Problem of the Day 4.4Calendar Math Jill’s birthday is on the 11th. What was the date 2 days before her birthday? 9th

On the board, write 11 2 2 5 . Have children solve by using connecting cubes or counters. Then have them use the calendar to check their answers.

VocabularyInteractive Student EditionMultimedia Glossary e

1 23 4 Fluency BuilderMaterials two-color counters

Subtract With CountersWrite the following subtraction facts on the board.

10 2 2, 6 2 0, 5 2 1, 9 2 3, 7 2 5, 8 2 4

Have pairs find the difference using two-color counters. Then have volunteers say the subtraction sentence aloud.

with the Interactive Student Edition

Essential QuestionHow can you make a ten to help you subtract?

Making ConnectionsRemind children they have learned that an addition fact can help them to subtract.

What addition fact helps you solve 8 2 3? 3 + 5 = 8 What is the answer to the addition facts 8 1 2 and 9 1 1? 10

Learning ActivityFocus on the arrangement of acorns in the wagon. Connect the array to a 10 frame, helping children to visualize it that way. Ask the following questions.

• How many more acorns would fill up the ten frame? 1

• Someone found 1 acorn. How many acorns are still buried in the sandbox? 6

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

• Have children retell the story in their own words.

• Ask children to use adjectives to describe what they see on the screen.

Common Core Fluency Standard 1.OA.C.6

1 23 4 Pages 52–53 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Enrich 4.4Reteach 4.4

EXPLORE2

LESSON 4.4

Name

Write a ProblemWrite a problem for the number sentence. Then make a ten to solve the problem.

1. 17 – 8 = ? —

Problem:

Answer:

2. 15 – 6 = ? —

Problem:

Answer:

Writing and Reasoning Explain how you made a ten to solve the second problem.Possible answer: I found how many

I needed to add to 6 to make a ten.

Lesson 4.4Enrich

Answers may vary. Check children’s work.

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4-12 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Name Lesson 4.4Reteach

Use 10 to Subtract

Find 14 – 9.

Start with 9 cubes.

Make a 10.

Add cubes to make 14.

Count what you added.

You added 5  —.

So, 14 2 9 5 5  —.

Use . Make a ten to subtract. Draw to show your work.

1. 12 2 8 5 ? —

12 2 8 5

2. 15 2 9 5 ? —

15 2 9 5 4 6

Check children’s drawings.

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4-11 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 4MathTalk

red red red red

red red red red yellow

red

yellow yellow yellow yellow yellow

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HANDS ON

FOR THE TEACHER • Read the following problem. Austin puts 9 red counters in the first ten frame. Then he puts 1 yellow counter in the ten frame. How many more yellow counters does Austin need to make 15?

Use to show the problem.Draw to show your work.

Use 10 to SubtractEssential Question How can you make a ten to help you subtract?

Lesson 4.4

Chapter 4 two hundred twenty-nine 229

HandsOn

Operations and Algebraic Thinking—1.OA.C.6 Also 1.OA.D.8

MATHEMATICAL PRACTICESMP2, MP4, MP5

Represent How can your drawing help you solve 15 – 9?

Math Talk: Possible answer: There are 15 counters. 9 counters are red and 6 counters are yellow. So, 15 − 9 = 6.

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DifferentiatedInstruction1

2

3

Progressto Algebra

Problem Type: Put Together/Take Apart • Addend Unknown

229 Chapter 4

Listen and DrawMaterials two-color counters, Ten Frames (see eTeacher Resources)Read the following problem aloud.

Austin puts 9 red counters in the fi rst ten frame. Then he puts 1 yellow counter in the ten frame. How many more yellow counters does Austin need to make 15?

Guide children to model the problem using counters and the ten frames on the page. • How many red counters do you put in the

fi rst ten frame? 9 red counters

• How many yellow counters do you put in that ten frame? 1 yellow counter Why? Possible answers: to make 10; the problem says that Austin put 1 yellow counter in the ten frame.

• How many more yellow counters do you have to put in the bottom ten frame so that you have 15 counters? 5 yellow counters

MathTalk

MP4 Model with mathematics. Use Math Talk to focus on children’s understanding of how a drawing can help when making a ten to subtract.

ELL Strategy: Model Language

Children can learn correct pronunciation and sentence structure by listening to and repeating words and sentences modeled by the teacher.Write 15 − 9 = _____ on the board.Use counters and ten frames to model the subtraction sentence: • What is the fi rst step? I put 9 red counters

in the ten frame. What is the next step? I add 1 yellow counter to make a ten. What is the next step? I add more yellow counters to make 15. How do you fi nd the answer? I count the yellow counters.

Write other problems on the board. Have volunteers describe the steps to solve them.

MP5 Use appropriate tools strategically.• How does using counters in two colors help

you check your solution? Possible answer: I can see that 9 counters are red and 6 are yellow. If I take away the red ones, I have the yellow ones left.

1.OA.C.6 Add and subtract within 20, demonstrating fl uency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 −4 = 13 − 3 − 1 = 10 − 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 2 8 5 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

HandsOn


EXPLAIN3

Quick Check

If

Rt I RRR1

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3

COMMON ERRORS

Model and DrawModel and Draw

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

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Use and ten frames. Make a ten to subtract.Draw to show your work.

1. 12 − 8 = ? — 2. 11 − 9 = ? —

You can make a ten to help you subtract.

Start at 9.

Count up 1to make 10.

Count up 3more to 13.

Start at 8.

Count up 2 —

to make 10.

Count up 7 —

more to 17.

230 two hundred thirty

13 − 9 = 4 —

12 − 8 = 4 —

17 − 8 = 9 —

11 − 9 = 2 —

13 − 9 = ? — 17 − 8 = ? —

You counted up 4. You counted up 9 — .

MATHEMATICAL PRACTICES

EXPLAIN33 EXPLAIN3

Then

Lesson 4.4 230

Model and Draw MATHEMATICAL PRACTICES

MP4 Model with mathematics. Work through the model with children.• How do you know how many counters to

start with? Possible answer: I start with the number I am subtracting.

Put 9 red counters in a ten frame. Use yellow counters to show how many more are needed to make 13.• How do you know how many more

counters you need to make ten? Possible answer: I know 9 and 1 makes 10, so I put 1 more in.

• How many more counters make 13? 3• How many yellow counters are there? 4

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Guide children in using the models.• Why do you fill the first ten frame before

adding counters to the second ten frame? Possible answer: If I make a ten first, I can tell how many more counters I need to make the total number.

• How do you know your answers are correct? Possible answer: I see how many of each color and match the numbers.

Use the checked exercise(s) for Quick Check.

a child misses the checked exercise(s)

Differentiate Instruction with • Reteach 4.4

• Personal Math Trainer 1.OA.C.6

• RtI Tier 1 Activity (online)

Error Children may consider the counters used to count from 10 to the total number as the answer.

Example In Exercise 2, children write 11 - 9 = 1.Springboard to Learning Have children use red counters to show the number being subtracted and add yellow counters to make the total number. Then have them count all the yellow counters to find the difference.

15 − 8 = 7

Advanced Learners

Materials two-color counters, Ten Frames (see eTeacher Resources)

• Have partners work together to model and write subtraction facts within 20.

• One child uses two-color counters and Ten Frames to model a subtraction problem.

• The second child decides which subtraction fact the model shows and then records it, including the answer.

• Partners discuss whether or not the written problem is the same as the one shown by the model.

• Partners take turns with other subtraction facts.

Kinesthetic / VisualPartners

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MATHEMATICALPRACTICE 5 Use a Concrete Model

Use and ten frames. Make a ten to subtract. Draw to show your work.

Chapter 4 • Lesson 4 two hundred thirty-one 231

14 − 9 = 5 — 11 − 8 = 3 —

3. 14 − 9 = ? — 4. 11 − 8 = ? —

On Your OwnOn Your Own

Solve. Use the ten frames to make a ten to help you subtract.

5. SMARTER There are 14 flowers in the garden. 9 are red. The rest are yellow. How many flowers are yellow?

5 — yellow fl owers

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PROBLEM TYPE SITUATIONS

231 Chapter 4

On Your Own MP5 Use appropriate tools strategically. If children answered Exercises 1 and 2 correctly, assign Exercises 3–5.

DEEPER

MP5 Use appropriate tools strategically. Have children write related addition facts for Exercises 3–5, using ten frames and counters to represent them. To extend thinking and encourage discussion, mention to children that the strategy they use in this lesson is sometimes called the “counting up” strategy. Ask children to discuss why that name may be a good way to describe the strategy. In the discussion, encourage children to refer to their ten frames and to use their own words to tell what happens when they use the strategy to subtract.MP2 Reason abstractly and quantitatively.• How does a ten frame model help you see

the count up strategy? I look at the number I’m subtracting and see those circles. Then count up to the total.

SMARTER

Exercise 5 requires children to use higher order thinking skills as they start with 9 counters and determine how many more counters are needed to make 14.

4 ELABORATE

Addition and Subtraction

Take From • Start Unknown Exercise: 7

Put Together/Take Apart • Addend Unknown Exercises: 5, 6


Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

MathMath

MATHEMATICAL PRACTICES COMMUNICA C


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TAKE HOME ACTIVITY • Ask your child to explain how he or she solved Exercise 6.

6. DEEPER Mia has 18 beads. 9 are red and the rest are yellow. How many beads are yellow?

232 two hundred thirty-two

9 — yellow beads

16 — stickers

7. SMARTER John had some stickers. He gave 9 to April. Then he had 7. How many stickers did John start with?


8. SMARTER Which shows a way to make a ten to subtract?

● ● ● ●

17 − 8 = ? —

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

MATHEMATICAL PRACTICES

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

Lesson 4.4 232

Children practice subtraction facts to 12.

Children read the book and learn to read addition and subtraction number sentences.

Children complete blue Activity Card 5 by modeling subtraction problem

GamesUnder the Sea

LiteratureThe Class Party

ActivitiesRunaway Squares

EVALUATE5 Formative Assessment

Essential QuestionReflect Using the Language Objective Have children model or draw, and then share with a partner to answer the Essential Question.How can you make a ten to help you subtract? Possible answer: After I make a ten, I can see how many more I need to make the total number. Then I can count how many counters I added.

Math Journal Math

Draw ten frames and counters to show how to solve 18 − 9 = .

MP5 Use appropriate tools strategically. For Exercise 6, have counters and Ten Frames available for children to use to model the problem.

SMARTER

Exercise 7 requires children to use higher order thinking skills to reverse the process and add to find the unknown start.

Personal Math Trainer SMARTER

Be sure to assign Exercise 8 to children in the Personal Math Trainer. It features an animation to help them model and answer the problem. This exercise assesses whether children understand how to use a ten frame to model subtraction. Remind children to first use counters to show the number being subtracted. Then have them count on to 17, filling the rest of the ten frame and part of another one with yellow counters. The number of yellow counters is the answer to the subtraction.

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

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Chapter 4 two hundred thirty-three 233


3. Marta has 15 stickers.8 are blue and the rest are red. How many stickers are red?

7 — stickers

1.

12 − 9 = ? —

12 − 9 = 3 —

2.

12 − 8 = ? —

12 − 8 = 4 —

Lesson 4.4Use 10 to Subtract

Use and ten frames. Make a ten to subtract. Draw to show your work.

COMMON CORE STANDARD—1.OA.C.6 Add and subtract within 20.

4. Math Draw ten frames and counters to show how to solve 18 – 9 = — .

Practice and Homework

Check children’s drawings.

233 Chapter 4

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.

Materials two egg cartons cut to have 10 sections each, connecting cubes

• Discuss chicken eggs. Explain that female chickens, or hens, may lay many eggs in one year. A hen may lay one or two eggs per day.

• Show children a cut egg carton. Tell them that eggs usually come in groups of 12, but this carton has 10 sections.

• Have children work together to use two cut egg cartons and connecting cubes to make a ten to solve 12 2 8 and 12 2 9.

Materials Ten Frames (see eTeacher Resources), two-color counters

• Mention that some cities or counties have sports leagues for children. Say that in one city, soccer teams have 15 players and baseball teams have 13 players. If fewer than that number of children sign up, more children are needed to fill up the team.

• Present this problem to children. Invite children to use ten frames and two-color counters to solve.

Laura and 7 of her friends want to form a baseball team. A full team has 13 players. How many more children do they need to make a full team? 5 children

SOCIAL STUDIES


FOR MORE PRACTICE GO TO THE

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Lesson Check (1.OA.C.6)

234 two hundred thirty-four

1. Look at the model. Write the subtraction sentence that the model shows.

13 — − 9 — = 4 —

Spiral Review (1.OA.C.6)

2. What number sentence does this model show?

7 — 4 — 11 —

3. This ten frame shows 5 + 8. Draw to make ten. Then write the new fact.

+ =

B

10

+ B

3

__

B

13

Answers may vary.

Lesson 4.4 234

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 4.4 progress correctionkey=d to algebra hands · pdf fileprogress to algebra teaching...

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