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About the MathProfessional Development
About the MathProfessional Development
Professional Development Videos
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LESSON AT A GLANCE
Progressto Algebra
173A Chapter 3
Interactive Student Edition
Personal Math Trainer
Math on the Spot Video
Animated Math Models
iTools: Counters
HMH Mega Math
Progress to AlgebraModel Using Ten FramesThe strategy of making ten helps children decompose and compose numbers to simplify addition. In the following example, children make a ten to solve 8 + 5. They represent 8 in the ten frame and then decompose 5 into 2 + 3 to complete the frame.
8 + 5 5 (8 + 2) + 3 3 10 + 3 3 13
Hands On • Make a 10 to Add
LESSON 3.8
Learning ObjectiveUse make a ten as a strategy to fi nd sums within 20.
Language ObjectiveChildren explain to two other children how you use the make a ten strategy to add.
MaterialsMathBoard, Workmat 7 (ten frame), Workmat 8 (ten frames) (see eTeacher Resources), two-color counters, red and yellow crayons
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. MP5 Use appropriate tools strategically.
F C R Coherence:Standards Across the GradesBeforeK.OA.A.1
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
F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 127J.
FOCUS COHERENCE RIGOR
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ENGAGE1
How do you use the make a ten
strategy to add?
Daily RoutinesCommon Core
1 23 4 Pages 38–39 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.
Lesson 3.8 173B
with the Interactive Student Edition
Essential QuestionHow do you use the make a ten strategy to add?
Making ConnectionsReview with children all the addition facts with a sum of ten. Have children practice the facts using a ten frame and two color counters.
Learning ActivityFocus on the cups on the table. Ask children:
Would it help to move the cups around as you try to solve the problem? Possible answer: It would help to put them in straight rows so I would not miscount the cups.
How would you place them? Possible answers: I would try to make a group of short rows.
Why would it help? Possible answer: I can see numbers more easily when I make short rows.
Literacy and MathematicsChoose one or both of the following activities.
Talk about “putting things in order” in terms of stories. Remind students that every story has a beginning, middle, and end. Have students retell the beginning, middle, and end of a story you have recently read together.
Have children write a story using a way to make 10.
1 23 4 Fluency BuilderMaterials 10-frames, number cards 11 to 20 (TR27, TR28), two-color counters
Have children work in pairs. Give each pair one 10-frame, and 20 counters. Tell children to use red counters to show 10 and yellow counters to show numbers less than 10.
Have one partner pull a number card. Have the other partner represent the number using the 10-frame and the counters. Have the first partner say what the model shows. For example: I see 10 red counters and 2 yellow counters. 10 + 2 = 12.
Have partners change roles and repeat the activity.
Problem of the Day 3.8Basic Facts Mrs. Morales baked 6 muffins. She gave 2 muffins away. How many muffins are left? 4 muffins are left.
Guide children through the process of drawing a picture to solve this problem.
Vocabulary make a ten
Common Core Fluency Standard 1.OA.C.6
Interactive Student EditionMultimedia Glossary e
EXPLORE2
Name
Make-a-Ten MatchDraw a line to match the addition. Then match the sum.
1.
5 + 6 10 + 4 12
2.
8 + 6 10 + 3 11
3.
9 + 7 10 + 1 16
4.
7 + 6 10 + 2 14
5.
6 + 6 10 + 6 13
Writing and Reasoning Explain how you matched the make-a-ten fact for Exercise 4.
Possible answer: Three more than 7 is 10 and
3 less than 6 is 3, so 7 + 6 = 10 + 3.
Lesson 3.8Enrich
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EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
3-20
1_MNLEAN342682_C03E08.indd 20 12/02/14 11:22 AM
Name
10+ 6
_
16
10+ 4
_
14
10+ 3
_
13
7
9
5
6
8
8
1.8+6
So,8+6= 14 —.
2.9+7
So,9+7= 16 —.
Makea10toAdd
Show8+5withcountersandatenframe.
Use . Makeaten.Add.
So,8+5=13—.
Draw toshowthesecondaddend.Makeaten.Add.
Lesson 3.8Reteach
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ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
3-19
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DifferentiatedInstruction1
2
3
Progressto Algebra
Listen and DrawListen and Draw
MATHEMATICAL PRACTICES 5MathTalk
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Chapter 3 one hundred seventy-three 173
Make a 10 to AddEssential Question How do you use the make a ten strategy to add?
What is 9 + 6? Use and the ten frame. Model and draw to solve.
HandsOn
FOR THE TEACHER • Ask children: What is 9 + 6? Have children use red and yellow counters to model. Then move one counter from the 6 to make a ten.
Use Tools Why do you start by putting 9 counters in the ten frame?
Lesson 3.8HANDS ON
Operations and Algebraic Thinking—1.OA.C.6 Also 1.OA.D.8
MATHEMATICAL PRACTICESMP2, MP5
Math Talk: Possible answer: I put 9 counters in the ten frame first because it is the greater addend. It is easier to make ten if I start with the greater addend.
Y Y Y
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173 Chapter 3
LESSON 3.8
Enrich 3.8Reteach 3.8
Listen and Draw Materials Workmat 7 (ten frame) or Workmat 8 (ten frames) (see eTeacher Resources), two-color counters, red and yellow crayons.
Read the following problem aloud to the class.How can you use a ten frame and counters to show the sum for 9 + 6?
Guide children to put 9 red counters inside the ten frame on the page and 6 yellow counters below the frame. • How can you rearrange the counters to
make it easier to add? I can make 10 by moving 1 yellow counter into the ten frame.
Guide children to move 1 of the yellow counters inside the ten frame so it is full. • What do you have now? I have 10 counters in
the ten frame and 5 counters outside the frame.
• What new addition fact does this model show? 10 + 5 = 15
• Is it easier to solve 9 + 6 or 10 + 5? Explain your reasoning. Possible answer: It is easier to solve 10 + 5. I can see right away that 10 and 5 is 15.
Demonstrate that you usually start with the greater addend in the ten frame, but you don’t have to; the sum is the same either way.
MathTalk
MP5 Use appropriate tools strategically. Use Math Talk to focus on children’s understanding of making a ten to add using a ten frame. Why is it helpful to make a ten to add? Possible answer: Once I make a ten, I can count on with the counters not in the 10-frame to fi nd the answer.
ELL Strategy: Model Concepts
Children can better understand what the ten frame is and how to use it when it is modeled.Guide children to solve a problem such as 8 + 5 = ___ using the ten frame. Point out that it is easiest to start with the greater addend.• How many counters remain when the ten
frame is fi lled? 3 Have children count on 3 from 10 to fi nd the sum. 13
HandsOn
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 2 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).
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EXPLAIN3
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Model and DrawModel and Draw
Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowMATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD
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174 one hundred seventy-four
Why do you show 8 in the ten frame to fi nd 4 + 8?
Put 8 in the ten frame. Then show 4 .
4 + 8
_
Draw to make a ten.Then write the new fact.
Use and a ten frame. Show both addends. Draw to make a ten. Then write the new fact. Add.
1. 9 + 5
_
2. 4 + 7
_
3. 9 + 8
_
B
10
+ B
1
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11
B
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+ B
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+ B
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b 10
1 b
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Quick Check
If
Rt I RR1
2
3
Then
COMMON ERRORS COMMON ERRORS
MATHEMATICAL PRACTICES
Advanced LearnersAdvanced LearnersAdvanced Learners Visual Partners
0
0 1 2 3 4 5 6 7 8
0 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 10
2 3 4 5 6 7 8 10 11
3 4 5 6 7 8 10 11 12
4 5 6 7 8 10 11 12 13
5 6 7 8 10 11 12 13 146 7 8 10 11 12 13 14 15
7 8 10 11 12 13 14 15 16
8 10 11 12 13 14 15 16 17
10 11 12 13 14 15 16 17 18
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9911 12 13 14 15 16 17 18 19 201010
Materials Addition Table (see eTeacher Resources), crayons
• Have one child name an addition fact with a sum greater than 10, such as 9 + 7 = 16. The child should color the space for the sum on the Addition Table.
• Have the partner tell how to use the strategy of making ten to rename the fact from 9 + 7 = 16 to 10 + 6 = 16. The partner should color the space for that sum on the Addition Table.
• Have partners repeat the activity using other appropriate facts.
Problem Type: Put Together/Take Apart • Total Unknown
Lesson 3.8 174
a child misses the checked exercises
Differentiate Instruction with • Reteach 3.8
• Personal Math Trainer 1.OA.6
• RtI Tier 1 Activity (online)
Model and DrawMP5 Use appropriate tools strategically. Work through the model with children using two-color counters on a ten frame. You might want to have children use their MathBoards. • In the model for 4 + 8, why do the
counters in the ten frame show 8 instead of 4? It is easier to start with the greater addend.
• In the model on the right, how do you know how many yellow counters to move into the ten frame? 2 to fi ll the ten frame
• How do the numbers in the fact change when you move the counters? One addend gets larger and the other addend gets smaller.
Share and Show MATHBOARDMATHBOARDMBOARDMMMMBOARDBOARDBOARDBOARDMATHATHABOARDMMMMAAAATHATHATHTHTHATHATHATHAATHAAAATHAAATHATHTHTHATHATHAAATHATHATHAAATHABOARDBOARDBOARDBOARD
Review addition facts for 10 before children begin the exercises. This will help them work with the ten frames.• How do you know your answers are
correct? I fi ll the ten frame and count on from 10.
Use the checked exercises for Quick Check.
Error Children make 10 but they may not subtract from the second addend.
Example For Exercise 1, children make 10 for 9 + 5 by writing 10 + 5.Springboard to Learning Have children write 9 + 5 on their MathBoards. Then have them cross out the 9 and write 10 above it and cross out the 5 and write 4 above it. Point out that whatever you add to one addend needs to be subtracted from the other.
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REMEMBER Start with
the greater addend.
Chapter 3 • Lesson 8 one hundred seventy-fi ve 175
MATHEMATICALPRACTICE 5 Use a Concrete Model
Use and a ten frame. Show both addends. Draw to make a ten. Then write the new fact. Add.
B
10
+ B
3
_
B
13
On Your OwnOn Your Own
5. SMARTER Andrew has visited Cedar Hill State Park 7 times. Cathy has visited the same park 9 times. How many times did they both visit the park?
Draw to make a ten. Write the missing number.
16 –– visits
4. 5 + 8
_
6. SMARTER What strategy would you choose to solve 7 + 8? Why?
Answers will vary. Accept reasonable explanations.
175 Chapter 3
On Your OwnMP5 Use appropriate tools strategically. If children answered Exercises 2 and 3 correctly, assign Exercises 4–6.
SMARTER
Exercise 5 requires higher order thinking skills. As children use the ten frame to model the problem, they may represent Cathy’s 9 visits first because they know 9 is closer to 10 than 7. The remaining visits are shown with 1 in the ten frame and 6 outside the ten frame. The missing number is 16 representing the 16 total visits.
SMARTER
Exercise 6 requires children to select a strategy to use to solve a basic fact and explain their reasoning. Emphasize that children may use any strategy that works best for them. To help children understand that some strategies are more efficient than others for certain facts, ask the following questions.• What addition strategies have you learned
so far? count on 1, 2, or 3; doubles; doubles plus one and doubles minus one; make a ten; add zero
• Would you use the counting on strategy to solve 7 + 8? Explain. No. None of the addends are 1, 2, or 3.
• How could you use doubles plus one or doubles minus one to solve 7 + 8? Possible answer: I could use doubles plus one. One addend is 7, and the other is 8, or 7 + 1. So, I can use the doubles fact 7 + 7 = 14 and add 1 more to get 15.
DEEPER
To extend thinking, have children generalize about what kinds of facts might be appropriate to use with the make a ten strategy. Some children may suggest to use it with facts in which one addend is a number close to 10, such as 7, 8, or 9. MP2 Reason abstractly and quantitatively. • How would you also use the make a ten
strategy to solve 11 + 3? Possible answer: I would make 11 to show 10 + 1, then I would add the 1 to the 3 to show 14.
4 ELABORATE
Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.
Math on the Spot Video TutorUse this video to help children model and solve this type of Think Smarter problem.
MATHEMATICAL PRACTICES
Math
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176 one hundred seventy-six
TAKE HOME ACTIVITY • Cut off 2 cups from an egg carton or draw a 5-by-2 grid on a sheet of paper to create a ten frame. Have your child use small objects to show how to make a ten to solve 8 + 3, 7 + 6, and 9 + 9.
Solve.
11. SMARTER The model shows 7 + 4 = 11.Write the 10 fact that has the same sum.
B + B = B
7. 10 + 8 has the same sum as 9 + 9 — .
8. 10 + 7 has the same sum as 8 + 9 — .
9. 10 + 5 has the same sum as 6 + 9 — .
10. DEEPER Write the numbers 6, 8, or 10 to complete the
sentence. 10 — + 6 — has the same sum as 8 — + 8.
Order of the addends 10 and 6 may vary.
10 1 11
EVALUATE5 Formative Assessment
MATHEMATICAL PRACTICES
Differentiated Centers Kit
DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD
Lesson 3.8 176
Children practice and review sums to 20.
Children read the book and add the number of hats made by Bunny.
Children complete orange Activity Card 16 by reviewing the problem-solving strategy of “making a ten.”
GamesNeighborhood Sums
LiteratureFunny Bunny Hats
ActivitiesMake a Ten to Add
Essential QuestionReflect Using the Language Objective Children explain to two other children how you use the make a ten strategy to add.How do you use the make a ten strategy to add? Possible answer: I can take numbers apart and put them back together in ways that make 10. Then it is easier to add 10 and the other number.
Math Journal Math
Use pictures or words to explain how you would use the make a ten strategy to solve 5 + 7.
Have children look at Exercises 7–10 and explain how they will solve the problems.
DEEPER
MP2 Reason abstractly and quantitatively. Exercise 10 requires children to use higher order thinking skills. If necessary, remind children that they can add in any order.
SMARTER
Exercise 11 assesses whether children understand how to use the make a 10 strategy. Children who write the wrong answer need additional practice. Intervene with further practice from lesson 3.8.
Problem Solving • Applications
Cross-Curricular
Problem SolvingProblem Solving©
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Chapter 3 one hundred seventy-seven 177
1. 5 + 7
_
2. 9 + 5
_
B
10
+ B
2
_
B
12
Make a 10 to Add
Use red and yellow and a ten frame. Show both addends. Draw to make a ten. Then write the new fact. Add.
Solve.
3. 10 + 6 has the same sum as 7 + 9 — .
4. Math Use pictures or words to explain how you would use the make a ten strategy to solve 5 + 7.
Practice and Homework
COMMON CORE STANDARD—1.OA.C.6 Add and subtract within 20.
Lesson 3.8
B
10
+ B
4
_
B
14
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Check children’s work.
177 Chapter 3
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 assorted seeds and beans, 2 cups of two kinds of beans or seeds
Display different kinds of beans or seeds, and discuss attributes such as size, shape, color, and texture.Give each child a handful (no more than 20) of two different kinds of beans or seeds. Have children sort them and tell how they sorted. Ask children to count how many beans or seeds are in each group. Then have them use the make a ten strategy to find how many in all.
Materials pictures of the White House, Statue of Liberty, or other historical locations
Display pictures of the White House, the Statue of Liberty, or other places associated with state and national history. Discuss their significance. Together, create story problems about people visiting these places. Children should use the make a ten strategy to solve the problems.
SOCIAL STUDIES
Personal Math Trainer
FOR MORE PRACTICE GO TO THE
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178 one hundred seventy-eight
Lesson Check (1.OA.C.6)
1. What sum does this model show? Write the number.
2. What addition sentence does this model show? Write the number sentence.
Spiral Review (1.OA.A.1, 1.OA.C.6)
3. What is the sum of 4 + 6? Write the sum.
10 —
4. There are 2 big flowers and 4 small flowers. How many flowers are there?
Write the number sentence and how many.
6 — flowers 2 — + 4 — = 6 —
B
10
+ B
5
_
B
15
B
10
+ B
4
_
B
14
Lesson 3.8 178
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.
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