## Envision Math Common Core 2nd Grade Answers Key Topic 6 Fluently Subtract. Within 100

Essential Question:
What are strategies for subtracting numbers to 100?

enVision STEM Project: Finding Water and Finding Differences
Find Out Use globes, maps, books, and other sources to find out where water, snow, and ice can be found on Earth. Make a list of different names of bodies of water and names of bodies of snow and ice.
Journal: Make a Book Show what you learn in a book. In your book, also:

• Tell about how globes are models that show where water is found on Earth.
• Tell about how to use a subtraction model to find differences.

Review What You Know

Vocabulary

Question 1.
Break apart 56 into tens 1 and ones. Draw place value blocks to show the parts.
56 = _______ + ________

Question 2.
Complete the drawing to show how to regroup 1 ten as ones.

Question 3.
Complete the bar diagram to model 64 – 31 = ?

Open Number Lines
Question 4.
Find 40 – 25 by counting back on an open number line. Show your work.

40 – 25 = _______

Question 5.
Find 45 – 22 by adding up on an open number line. Show your work.

45 – 22 = _________

Math Story
Question 6.
Lea has 30 cookies. She gives 17 cookies to her friends. How many cookies does Lea have now?

Pick a Project

PROJECT 6A
Do snakes lay eggs?
Project: Make a Model of a Snake and Its Nest

PROJECT 6B
How are schools different around the world?
Project: Compare and Contrast Classroom Sizes

PROJECT 6C
How long does it take to drive from a large city to nearby places?
Project: Draw a Map of Some State Places

PROJECT 6D
What stories are in the night sky?
Project: Perform a Skit About Constellations

### Lesson 6.1 Subtract 1-Digit Numbers Using Models

Solve & Share
How can you use tens and ones to find 23 – 6? Use place-value blocks to help you. Show your work.
I can … use place value and models to subtract I-digit numbers.

Visual Learning Bridge

Convince Me! In the first example above, why were 4 ones taken away first?

Guided Practice

Subtract. Use place-value blocks. Draw blocks to show your work.
Question 1.
63 – 2 = ___

Question 2.
44 – 9 = _______

Question 3.
32 – 8 = _______

Independent Practice

Subtract. Use place-value blocks. Draw blocks to show your work.
Question 4.
29 – 1 = _______

Question 5.
50 – 7 = _______

Question 6.
61 – 4 = _______

Question 7.
43 – 5 = _______

Question 8.
86 – 9 = _______

Question 9.
39 – 3 = _______

Question 10.
56 – 8 = _______

Question 11.
21 – 6 = _______

Question 12.
Higher Order Thinking Which one-digit numbers can you subtract from 74 without first regrouping? Explain how you know.

Problem Solving

Solve each problem below.
Question 13.

Question 14.
Make Sense Kate has 45 marbles. She gives 3 marbles to her brother. How many marbles does Kate have now?
_______ marbles

Question 15.
Higher Order Thinking Sammie has 9 fewer rings than Emilio. Sammie has 7 more rings than Sara. Emilio has 34 rings. Complete the sentences below. Draw a picture to explain your work.
Sammie has _______ rings.
Sara has ________ rings.

Question 16.
Assessment Practice Draw place value blocks to find 34 – 8. Which is the difference?

A. 22
B. 26
C. 28
D. 46

### Lesson 6.2 Subtract 2-Digit Numbers Using Models

Solve & Share
You have 42 pipe cleaners. You use 19 of the pipe cleaners. How many pipe cleaners do you have now?
I can … use place value and models to subtract 2-digit numbers.

_________ pipe cleaners

Visual Learning Bridge

Convince Me! How are the two ways shown above alike? How are they different?

Guided Practice

Subtract. Use place-value blocks. Draw blocks to show your work.
Question 1.
52 – 13 = _________

Question 2.
46 – 25 = ________

Question 3.
65 – 37 = _______

Independent Practice

Subtract. Use place-value blocks. Draw blocks to show your work.
Question 4.
56 – 31 = _______

Question 5.
63 – 24 = _______

Question 6.
72 – 46 = _______

Question 7.
57 – 15 = _______

Question 8.
25 – 19 = _______

Question 9.
84 – 27 = _______

Question 10.
41 – 13 = _______

Question 11.
90 – 38 = _______

Question 12.
Algebra Write numbers to complete the equations. Draw pictures to help if needed.

Question 13.
Number Sense Do these models show the same value? Explain.

Problem Solving

Solve each problem.
Question 14.
Model Anita has $63. She spends$24 and saves the rest. How much does Anita save?

\$ ________

Question 15.
Higher Order Thinking Write a subtraction story about 36 – 17. Explain how to solve the problem.

Question 16.
Assessment Practice Draw place-value blocks to find 70 – 11. Which is the difference?

A. 59
B. 49
C. 47
D. 11

### Lesson 6.3 Subtract Using Partial Differences

Solve & Share
Ari has 72 stickers. He puts 25 of his stickers in a scrapbook. How many stickers are left? Draw place-value blocks to help you solve the problem.
I can … subtract using place value and partial differences.

Visual Learning Bridge

Convince Me! The example above shows one way to find 64 – 36 using partial differences. Could you begin by subtracting the ones instead of the tens? Explain.

Guided Practice

Subtract. Use place-value blocks to find partial differences. Record your work.
Question 1.
34 – 15 = _______

Question 2.
63 – 48 = _______

Independent Practice

Subtract. Use place-value blocks to find partial differences. Record your work.
Question 3.
52 – 36 = _______

Question 4.
94 – 54 = _______

Question 5.
41 – 25 = _______

Question 6.
33 – 28 = _______

Question 7.
65 – 42 = _______

Question 8.
70 – 48 = _______

Question 9.
96 – 37 = _______

Question 10.
87 – 45 = _______

Solve. Draw a model to help.
Question 11.
Higher Order Thinking Tia’s basketball team scored 61 points. They won by 23 points. How many points did the other team score?
_______ points

Problem Solving

Solve each problem.
Question 12.
Model Don has 72 marbles. Josie has 56 marbles. How many more marbles does Don have than Josie?
Can you use drawings of place-value blocks to show partial differences?
__________ more marbles

Question 13.
Higher Order Thinking Write a subtraction story using two 2-digit numbers. Then solve the problem in your story.

Question 14.
Assessment Practice Which numbers will complete this partial differences problem for 44 – 17?
Choose all that apply.

### Lesson 6.4 Continue to Subtract Using Partial Differences

Solve & Share
Show two different ways to find 53 – 28.

Visual Learning Bridge

Convince Me! Find 73 – 45. Andy says he can subtract 3. then 2, and then 40 to find the difference. Do you agree? Explain.

Guided Practice

Subtract. Use partial differences. Break apart the number you are subtracting. Show your work.
Question 1.

Question 2.

Independent Practice

Subtract. Use partial differences. Break apart the number you are subtracting. Show your work.
Question 3.
_______ = 32 – 13

Question 4.
74 – 28 = _______

Question 5.
_______ = 61 – 47

Question 6.
84 – 46 = _______

Question 7.
59 – 17 = _______

Question 8.
_______ = 95 – 38

Question 9.
Higher Order Thinking Tina found 53 – 27 by breaking apart 27 into 23 and 4. Does Tina’s way work?
Show another way you could break apart 27 to find 53 – 27. Then find the difference.

Problem Solving

Solve each problem. Show your work.
Question 10.
en Vision® STEM Kate had 32 ice cubes. She put 14 of them in the sun and they melted. How many ice cubes does Kate have now?
________ ice cubes

Question 11.
Make Sense Mark has 27 stamps. Sam has 82 stamps. Lena has 42 stamps. How many more stamps does Sam have than Mark?

________ more stamps

Question 12.
Higher Order Thinking Allison found 51 – 34 using partial differences. She broke apart 34 into 31 + 3.
Write equations to show how Allison could have found the difference.

Question 13.
Assessment Practice Can you use the equations to find 63 – 45? Choose Yes or No.

### Lesson 6.5 Practice Subtracting

Solve & Share
Find 82 – 56. Use any strategy you have learned or your own strategy. Show your work. Explain why your strategy works.
I can … subtract 2-digit numbers using any strategy I’ve learned and explain why the strategy works.

Visual Learning Bridge

Convince Me! Could you solve 72 – 24 using a different strategy? Explain.

Guided Practice

Use any strategy to subtract. Show your work. Draw blocks if needed. Explain why the strategy works.
Question 1.
67 – 39 = ________

Question 2.
78 – 42 = ________

Independent Practice

Question 3.
73 – 4 = ________

Question 4.
78 – 25 = ________

Question 5.
83 – 46 = ________

Question 6.
36 – 27 = ________

Question 7.
98 – 51 = _______

Question 8.
65 – 7 = ________

Question 9.
86 – 19 = ________

Question 10.
7 – 8 = ________

Question 11.
85 – 23 = ________

Algebra Find the missing number.

Question 12.
34 – 8 = 35 – ______

Question 13.
27 – 9 = 28 – ________

Problem Solving

Make Sense Make a plan. Solve each problem. Show your work.
Question 14.
A hardware store has 32 hammers in stock. The store sells 16 hammers on Saturday. How many hammers are left?
________ hammers

Question 15.
A barber does 15 haircuts on Monday. He does 28 haircuts on Friday. How many more haircuts does he do on Friday than on Monday?
________ more haircuts

Question 16.
Vocabulary Complete each sentence. Use two of the words below.
equation
difference
sum
93 – 53 = 40 is an ________
40 is called the ________ of 93 and 53.

Question 17.
Higher Order Thinking Fill in the missing digits of this subtraction problem.
☐ ☐ – 23 = 29

Question 18.
Assessment Practice Circle the problem that you can use regrouping to solve. Then use a strategy to find both differences. Show your work.
56 – 38 = ________
74 – 52 = ________

### Lesson 6.6 Solve One-Step and Two-Step Problems

Solve & Share
Trevor made 20 apple muffins for the bake sale. Ryan made 15 banana muffins. They sold 23 muffins in all. How many muffins are left to sell? Solve any way you choose. Show your work.
I can … use models and equations to solve word problems.

Visual Learning Bridge

Convince Me! Look at the example above. How does the bar diagram show that you can add to find the answer?

Guided Practice

Solve the problem. Show your work.
Question 1.
Kyla’s goal is to walk her dog 50 blocks on Friday, Saturday, and Sunday. On Friday, she walked 16 blocks. On Saturday, she walked 18 blocks. How many blocks does she need to walk on Sunday to meet her goal?

________ blocks

Independent Practice

Use a bar diagram to solve each problem. Show your work.
Question 2.
Some balls are in the closet. Mr. Thomas takes out 15 balls for class. Now there are 56 balls in the closet. How many balls were in the closet in the beginning?

________ balls

Question 3.
Corey buys a box of 96 paper clips from the store. He uses 34 paper clips. How many paper clips does Corey have left?

_______ paper clips

Question 4.
A.J. counts 44 acorns in his yard. He picks up 27 acorns. Then 16 more acorns fall from the tree. How many acorns are in the yard now? Show your work.

_______ acorns

Problem Solving

Make Sense Make a plan. Solve each problem. Show your work. Then check your work.
Question 5.
27 people are at a picnic. 14 people eat hamburgers. The rest eat hot dogs. How many people eat hot dogs?

________ people eat hot dogs

Question 6.
Some pumpkins are in a patch. 41 pumpkins are picked. Now there are 33 pumpkins in the patch. How many pumpkins were in the patch at the start?

________ pumpkins

Question 7.
Higher Order Thinking Lauren has a stamp collection. She gives Kristen 12 stamps and Ethan 15 stamps. Lauren has 22 stamps left. How many stamps did she have at the start?

________ stamps

Question 8.
Assessment Practice Lance buys 48 eggs. He uses 24 of them for baking. Then he buys 12 more eggs. How many eggs does Lance have now? Which set of equations can you use to solve this problem?
A. 48 + 24 = 72
72 – 12 = 60

B. 48 – 24 = 24
24 + 12 = 36

C. 48 + 24 = 72
72 + 12 = 84

D. 48 – 24 = 24
24 – 12 = 12

### Lesson 6.7 Problem Solving

Reasoning
Solve & Share
Farmer Davis has 52 chickens. Farmer Phil has 15 fewer chickens. How many chickens does Farmer Phil have? Do you add or subtract to solve this problem? Explain why. Solve. Show your work.
I can … reason about word problems, and use bar diagrams and equations to solve them.

Visual Learning Bridge

Convince Me! Why can you subtract 45 – 17 to solve 45 – ? = 17?

Guided Practice

Reason about the numbers in each problem. Complete the bar diagram and write an equation to solve. Show your work.
Question 1.
Wendy has 38 cents to spend on a snack. She buys an apple that costs 22 cents. How many cents does Wendy have left?

Question 2.
Joe has 46 crayons. Tamila has 18 more crayons than Joe. How many crayons does Tamila have?

________ _______ _________ crayons

Independent Practice

Reason about how the numbers in each problem relate. Complete the bar diagram and write an equation to solve. Show your work.

Question 3.
enVision® STEM Andy’s class wants to test samples of river water. They want to test 47 water samples. So far, they tested 34 samples. How many more samples do they need to test?

________ _______ _________ more samples

Question 4.
93 dimes are in a box. Grant uses some to buy a game. Now, 66 dimes are in the box. How many dimes did Grant use to buy the game?

________ _______ _________ dimes

Question 5.
Maria paints 62 squares for a mural. Oscar paints 38 squares. How many more squares does Maria paint than Oscar?

________ _______ _________ more squares

Problem Solving

Planting Trees The second- and third-grade students planted these trees in Wing Park. The second-grade students planted 26 of the spruce trees. How many spruce trees did the third-grade students plant?

Question 6.
Make Sense What information can you get from the pictures?

Question 7.
Model Complete the bar diagram. Decide how the numbers in the problem relate. Then write an equation that shows how to solve the problem.

Question 8.
Reasoning How many spruce trees did the third-grade students plant? Explain how you solved the problem.
_________ spruce trees

### Topic 7 Fluency Practice Activity

Point & Tally
I can … add within 100.
Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue.
Partner I and Partner 2 each point to a black number at the same time. Both partners add those numbers.
If the answer is on your color, you get a tally mark. Work until one partner gets seven tally marks.

### Topic 7 Vocabulary Review

Understand Vocabulary
Word List

• bar diagram
• difference
• equation
• ones
• regroup
• tens

Write always, sometimes, or never.
Question 1.
A bar diagram shows subtraction. ________

Question 2.
An 8 in the ones place of a number equals 80. __________

Question 3.
A 5 in the tens place of a number equals 50. _________

Draw a line from each term to its example.

Use Vocabulary in Writing
Question 7.
Explain how you can make a model to show and help you solve the problem. Use terms from the Word List.
Molly has 64 marbles. Leslie has 29 marbles. How many fewer marbles does Leslie have?

### Topic 6 Reteaching

Set A

You can use place-value blocks to find 46 – 8. You can regroup I ten as 10 ones and then take away 8 ones.

Subtract. You can use place-value blocks to help. Draw blocks to show your work.
Question 1.
61 – 3 = _______

Question 2.
57 – 5 = _______

Set B

You can use place-value blocks to find 72 – 26. First, take away the tens. Then regroup I ten as 10 ones and take away 6 ones.

Question 3.
27 – 11 = _______

Question 4.
33 – 24 = ________

Set C

You can use place-value blocks and partial differences to find 53 – 37. First, subtract 3 tens from 5 tens. Then subtract 3 of the ones to make a 10. Then regroup I ten as a 10 ones and subtract the other 4 ones.

Subtract. Use piace-value blocks to find partial differences. Record your work.
Question 5.
22 – 14 = ________

Question 6.
73 – 38 = ________

Question 7.
45 – 25 = ________

Question 8.
84 – 46 = ________

Set D

You can mentally break apart the number you are subtracting. Find 72 – 47.
Subtract 47 in parts. You can subtract the parts in any order and record partial differences.

Subtract. Use partial differences. Break apart the number you are subtracting. Show your work.
Question 9.
47 – 29 = ________

Question 10.
55 – 36 = ________

Question 11.
55 – 37 = ________

Question 12.
77 – 53 = ________

Set E

You can draw blocks, regroup, and record partial differences. Find 52 – 33. You can regroup 1 ten as 10 ones.

Use any strategy to subtract. Show your work.
Question 13.
81 – 66 = ________

Question 14.
96 – 19 = ________

Question 15.
62 – 17 = ________

Question 16.
57 – 29 = ________

Set F

48 people are at the beach. 16 people are swimming. The rest are playing volleyball. How many people are playing volleyball?
You can use a bar diagram and partial differences to solve the problem.

Solve the problem. Show your work.
Question 17.
Mark has 33 stickers. 16 stickers are green. The rest are yellow. How many stickers are yellow?

_________ yellow stickers

Set G

Thinking Habits
Reasoning
What do the numbers and symbols in the problem mean?
How are the numbers in the problem related?
How can I show a word problem using pictures or numbers?

Complete the bar diagram and write an equation to show the problem. Then solve. Show your work.
Question 18.
94 bricks are needed to build a wall. Lindy has 65 bricks. How many more bricks does she need?

Question 19.
Explain why making a bar diagram can help you solve the problem above.

### Topic 6 Assessment Practice

Question 1.
Which is the difference of 55 – 7? You may draw place-value blocks.

A. 45
B. 46
C. 47
D. 48

Question 2.
Sam has 74 books. He puts 28 books on a shelf. How many books are NOT on the shelf? Show your work.
________ books are NOT on the shelf.

Question 3.
A ship has 68 round windows. The ship also has 16 square windows. 7 of the windows are broken. How many windows are NOT broken?
A. 45
B. 61
C. 77
D. 91

Question 4.
Ryan has 46 marbles. John has 4 fewer marbles than Ryan. John gives 9 marbles to his friend.

A. Which pair of equations should be used to find how many marbles John has now?
A. 46 – 4 = 42
42 – 9 = 33

B. 46 – 4 = 42
42 + 9 = 51

C. 46 + 4 = 50
50 – 9 = 41

D. 46 + 4 = 50
50 + 9 = 59

B. How many marbles does John have now?

Question 5.
Jason wants to find 86 – 61 using place-value blocks.
Will Jason need to regroup to find the difference? Which is correct?
A. Yes; 86 should be regrouped as 8 tens and 16 ones.
B. Yes; 61 should be regrouped as 5 tens and 11 ones.
C. Yes; 86 should be regrouped as 7 tens and 16 ones.
D. No; Regrouping is not needed.

Question 6.
A book has 72 pages. Dan reads 38 pages on Monday. He reads 26 pages on Tuesday. How many pages does Dan have left to read?
A. Which pair of equations should be used to find how many pages Dan has left to read?
A. 38 + 26 = 64
72 – 64 = 8

B. 72 – 38 = 34
34 + 26 = 60

C. 72 + 26 = 98
98 – 38 = 60

D. 72 – 26 = 46
46 + 38 = 84

B. How many pages does Dan have left to read?

Question 7.
Circle the problem that you will use regrouping of place-value blocks to solve. Then draw blocks to show how you know.
54 – 23
82 – 44

Question 8.

Show how you can break apart a number and use partial differences to solve.

Question 9.
Which numbers will complete this partial differences problem for 54 – 18? Choose all that apply.

Question 10.
Use any strategy to find 24 – 16. Show your work. Write the missing part in the bar diagram.

24 – 16 = _______

Question 11.
Peter collects 54 stamps. He gives 29 stamps to Ruth. How many stamps does Peter have now? Show the problem in the bar diagram with a ? for the unknown number. Then write an equation to solve the problem.

Question 12.
Find 53 – 27. Use partial differences to solve. Show your work.
53 – 27 = ________

Question 13.
Choose all of the problems that you will solve by regrouping if you subtract using place-value blocks. Draw blocks if needed.
☐ 45 – 0 = ?
☐ 68 – 49 = ?
☐ 84 – 37 = ?
☐ 99 – 33 = ?
☐ 78 – 18 = ?

Question 14.
Find 72 – 38. Use any strategy to solve. Then explain why your strategy works.

Stamp Collection Mary collects stamps. The table shows the number of different kinds of stamps that she has.

Question 1.
How many more stamps with butterflies does Mary have than stamps with flags? Choose a strategy to solve. Show your work.
__________ more stamps with butterflies

Question 2.
How many fewer stamps with birds does Mary have than stamps with flowers? Use a different strategy to solve. Show your work.
________ fewer stamps with birds

Question 3.
Explain why the strategy you chose in Item 2 works.

Question 4.
Luke also collects stamps. He has 57 stamps. His friend gives him 25 more stamps. Then Luke gives away some stamps. Now Luke has 44 stamps. How many stamps did Luke give away?
Part A
How many stamps does Luke have after his friend gives him more stamps?
_______ _______ = ________
_______ stamps

Part B
How many stamps did Luke give away?
_______ _______ = ________
_______ stamps

Question 5.
Mary puts 54 of her stamps in a book. The book holds 96 stamps. How many more stamps can Mary put in the book?
Part A
Complete the bar diagram to model the problem.

Explain how the bar diagram helps you understand the problem.