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## Big Ideas Math Book 2nd Grade Answer Key Chapter 6 Fluently Subtract within 100

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Vocabulary

Lesson: 1 Model and Regroup to Subtract

Lesson: 2 Use Models to Subtract a One-Digit Number from a Two-Digit numbers

Lesson: 3 Use Models to Subtract Two-Digit Numbers

Lesson: 4 Use Models to Subtract Two-Digit Numbers

Lesson: 5 Use Addition to Check Subtraction

Lesson: 6 Practice Two-Digit Subtraction

Lesson: 7 More Problem Solving: Subtraction

### Fluently Subtract within 100 Vocabulary

Organize It
Use the review words to complete the graphic organizer.

Define It

Match.

### Lesson 6.1 Model and Regroup to Subtract

Explore and Grow

Model each problem. Make quick sketches to show how you found the difference.

Compare your quick sketches. What step did you use to ﬁnd 21 − 6 that you did not use to ﬁnd 19 − 6?

The step in 21 − 6 that you did not use to ﬁnd 19 − 6 is regrouping as 6 can be easily subtract from 9 but whereas 6 cannot be subtracted from 1 (21) so we need to regroup to subtract.

Show and Grow

Use models to subtract. Draw to show your work.

Question 1.

Apply and Grow: Practice

Use models to subtract. Draw to show your work.

Question 2.

Question 3.

Question 4.

Question 5.
Number Sense
Which numbers can you subtract from 44 without regrouping?

3 and 4.

Think and Grow: Modeling Real Life

You have 42 craft sticks. You use 8 of them. How many craft sticks are not used?

Subtraction equation:

Show and Grow

Question 6.
There are 74 people in a theater. 7 of them leave. How many people are left?

People left from theater are 67.

Question 7.
DIG DEEPER!
You have 50 straws. You use some of them for a project. There are 44 left. How many straws did you use?

Number of straws = 50.
Number of straws left = 44.
Number of used straws = 50 – 44. = 6 straws.

### Model and Regroup to Subtract Homework & Practice 6.1

Use models to subtract. Draw to show your work.

Question 1.

Question 2.

Question 3.
YOU BE THE TEACHER
Is Newton correct? Explain.

No, The answer is 22. after regrouping one from tens to ones . then in tens we will have 2 tens not 3 tens.

Question 4.
Modeling Real Life
You have 26 magnets. You put 9 of them on your refrigerator. How many magnets are not on the refrigerator?

Number of magnets = 26.
Number of magnets on refrigerator = 9.
Number of magnets not on refrigerator = 26 – 9 = 15.

Question 5.
DIG DEEPER!
You have 83 cotton balls. You use some of them. There are 76 left. How many cotton balls do you use?

Number of cotton balls = 83
Number of cotton balls left = 76.
Number of cotton balls used = 83 – 76 = 7.

Review & Refresh

Question 6.

Question 7.

Question 8.

### Lesson 6.2 Use Models to Subtract a One-Digit Number from a Two-Digit numbers

Explore and Grow

Make a quick sketch to ﬁnd 41 − 3.

How do you regroup 4 tens and 1 one to subtract 3?
___________________________________
___________________________________
___________________________________

We regroup one from tens to ones place then one tens will be subtracted from 4 tens so we have 3 tens remaining and in ones place we added 10 ones + 1 ones earlier .total 11 ones will be in ones place.Later we need to subtract 3 ones from 11 ones so we have 8 ones remaining after subtraction.

Show and Grow

Question 1.
31 – 4 = ?

Question 2.
7 – 5 = ?

Question 3.
88 – 9 = ?

Question 4.
63 – 2 = ?

Question 5.
90 – 8 = ?

Question 6.
Number Sense
What one-digit numbers can you subtract from 24 without regrouping? Explain.
The one digit which is less or equal to 4 can be used to subtract without regrouping are 1,2,3 and 4.

Think and Grow: Modeling Real Life

You catch 33 ﬁsh. You keep the state limit of 25. How many ﬁsh do you release?

Show and Grow

Question 7.
The temperature this morning was 72 degrees. This afternoon, it is 67 degrees. How much did the temperature drop?

Temperature in the morning= 72 degrees.
Temperature in the Afternoon= 67 degrees.
The Temperature drop= 72 – 67 =5 degrees.

Question 8.
DIG DEEPER!
You have a bowl of strawberries. You eat 7 of them. There are 19 left. How many strawberries were in the bowl to start?

Number of strawberries left =19
Number of strawberries eaten = 7.
Total Number of strawberries = 19 + 7 = 26 strawberries.

### Use Models to Subtract a One-Digit Number from a Two-Digit numbers Homework & Practice 6.2

Question 1.
\

Question 2.

Question 3.
YOU BE THE TEACHER
Is Descartes correct? Explain.

Question 4.
Modeling Real Life
Descartes scores 8 more points than Newton. How many points did Newton score?

Score of Descartes = 8 +Score of newton.
Score of Descartes = 97.
Score of newton = 97 – 8 =89.

Question 5.
DIG DEEPER!
There are some piñata toys on the ground. 6 of your friends each pick 1 up. There are17 left. How many toys were there to start?

Total pinata toys picked by friends = 6 (6 friends picked 1 so 6 x 1 = 6 toys).
Toys left =17.
Total toys = 17 + 6 =23.

Review & Refresh

Break apart an addend to ﬁnd the sum.

Question 6.

Question 7.

### Lesson 6.3 Use Models to Subtract Two-Digit Numbers

Explore and Grow

Model the problem. Make a quick sketch to ﬁnd 33 − 17.

Show and Grow

Question 1.
55 – 18 = ?

Question 2.
21 – 18 = ?

Question 3.
44 – 29 = ?

Question 4.
60 – 32 = ?

Question 5.
75 – 21 = ?

Question 6.
Number Sense
Use two of the numbers to write and solve a subtraction problem that requires regrouping

Think and Grow: Modeling Real Life

You have 68 flowers. You give 17 to Newton. Then you give 14 to Descartes. How many ﬂowers do you have left?

Subtraction problems:

Show and Grow

Question 7.
There are 32 pretzels. You eat 11 of them. Your friend eats 12 of them. How many pretzels are left?

Number of pretzels = 32.
Number of pretzels Eaten by me = 11.
Number of pretzels Eaten by my friend = 12.
Number of pretzels left = 32 – 11 – 12 = 9

Question 8.
Can you solve the problems on this page using addition and subtraction? Think: How do you know?

Yes

### Use Models to Subtract Two-Digit Numbers Homework & Practice 6.3

Question 1.
84 – 60 = ?

Question 2.
40 – 15 = ?

Question 3.
Number Sense
Which numbers can you subtract from 55 without regrouping?

Numbers that can subtract from 55 without regrouping are 15 , 33 and 24.

Question 4.
Modeling Real Life
You and your friend have 38 cups of lemonade in all. You sell 14 cups. Your friend sells 16. How many cups are left?

Total Number of Lemonade cups= 38.
Number of lemonade cups sold by me = 14.
Number of lemonade cups sold by my friend =16.
Number of cups left = 38 – 14 – 16 = 8.

Question 5.
Modeling Real Life
Your principal has 75 awards. She gives 25 to your class. Then she gives 34 to your friend’s class. How many awards are left?

Number of Total Awards = 75.
Number of Awards given to my class = 25.
Number of Awards given to my friends class = 34.
Number of Awards left = 75 – 25 – 34 = 16.

Review & Refresh

Question 6.
A bookcase has 5 shelves. There are 3 plants on each shelf. How many plants are there in all?

Each shelf has 3 plants
Total plants = 3 + 3 + 3 + 3 + 3= 15 Plants.

### Use Models to Subtract Two-Digit Numbers Homework & Practice 6.4

Make quick sketches to ﬁnd each difference.

31 – 3 =?

31 – 23 = ?

How are the problems the same? How are they different?
_______________________________________
_______________________________________
_______________________________________

The Minuend is the same for both the problems that is 31.
The Subtrahend are different for both the problems that is 3 and 23 .
Even the difference of both the problems are different that is 23 and 3 .

Show and Grow

Question 1.
52 – 19 = ?

Question 2.
46 – 9 = ?

Question 3.
60 – 21 = ?

Question 4.
66 – 8 = ?

Question 5.
84 – 2 = ?

Question 6.
65 – 38 = ?

Apply and Grow: Practice

Question 7.
58 – 22 = ?

Question 8.
33 – 4 = ?

Question 9.
22 – 15 = ?

Question 10.
70 – 60 = ?

Question 11.
43 – 26 = ?

Question 12.
95 – 4 = ?

Question 13.
Number Sense
Use the given numbers to complete the problem.

Question 14.
DIG DEEPER!
Subtract a one-digit number from a two-digit number to complete the problem.

Think and Grow: Modeling Real Life

You pick 19 yellow flowers and 24 purple flowers. You give 8 flowers away. How many flowers do you have left?

Step 1: Find the total number of flowers you picked.

Step 2: Subtract the number of ﬂowers you give away from your result in Step 1.

8 Flowers.

Show and Grow

Question 15.
You bake 36 blueberry mufﬁns and 36 banana nut mufﬁns. You sell 47 mufﬁns. How many mufﬁns do you have left?

Number of Blueberry muffins baked = 36.
Number of banana nut mufﬁns baked = 36.
Total number of muffins = 36 + 36 = 72.
Number of muffins sold = 47.
Number of muffins left = 72 – 47 = 25.

Question 16.
There are 54 ladybugs. 7 ﬂy away. Then 25 join. How many ladybugs are there now?

Number of bugs flew away = 7.
Number of bugs joined = 25.
Total number of bugs left = 54 – 7 + 25 =22.

### Use Models to Subtract Two-Digit Numbers Homework & Practice 6.4

Question 1.
25 – 7 = ?

Question 2.
65 – 35 = ?

Question 3.
33 – 29 = ?

Question 4.
80 – 53 = ?

Question 5.
92 – 47 = ?

Question 6.
56 – 4 = ?

Question 7.
Writing
Write and solve a subtraction problem using 2 two-digit numbers. Write a story to match.

From the above figure we observe that 86 is the minuend and 24 is the subtrahend.The difference is 62.
The 8 tens from minuend  have to subtract 2 tens from the subtrahend we get 6 tens in the difference . We have 6 ones in the minuend and we have to subtract 4 ones from subtrahend we get 2 ones in difference.
Therefore the difference is 6 tens and 2 ones = 62.

Question 8.
Modeling Real Life
You ﬁll up 17 large water balloons and 24 small water balloons. You break 26 balloons. How many water balloons do you have left?

Number of large water balloons = 17
Number of small water balloons = 24
Total number of balloons = 17 + 24 =41
Number of balloons broken = 26.
Number of balloons Remaining = 41 – 26 =15

Question 9.
Modeling Real Life
You have 45 rings. You throw 28 of them. You earn a bonus and get 15 more rings to throw. How many rings do you have now?

Total Number of Rings = 45.
Number of rings threw = 28.
Number of Remaining Rings = 45 – 28 = 17.
Number of rings earned as Bonus = 15.
Total Number of Rings = 17 + 15 = 32.

Review & Refresh

Question 10.
How can you make a 10 to ﬁnd 5 + 8?

10 + 3

### Lesson 6.5 Use Addition to Check Subtraction

Write the equation shown by each model.

How are the equations related?
__26 – ? =43____________________
__26 + 17 = ?____________________

Explain how you can check whether 24 – 13 = 11 is correct.
Here when we add 13 + 11 we should get 24 then the answer is correct.

Show and Grow

Question 1.

Question 2.

Apply and Grow: Practice

Question 3.
52 – 27 = ?

Question 4.
76 – 58 = ?

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.
Reasoning
Newton uses 16 + 37 to check his answer to a subtraction problem. What two subtraction problems could he have solved?

Think and Grow: Modeling Real Life

A joke book has 96 jokes. 58 are knock-knock jokes. The rest are riddles. How many riddles are there?

The rest riddles are 38.

Show and Grow

Question 10.
A museum has 71 fossils. 47 are dinosaur fossils. The rest are ﬁsh fossils. How many ﬁsh fossils are there?

Question 11.
There are 27 more countries in Europe than in North America. There are 50 countries in Europe. How many countries are there in North America?

Countries in Europe = 50.
Countries in North America = 50 – 27 ( europe has 27 more than north america).
= 23 .

### Use Addition to Check Subtraction Homework & Practice 6.5

Question 1.
44 – 21 = ?

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.
Number Sense
Descartes subtracts to ﬁnd 36 − 19. Which addition equation can he use to check his answer?

36 -19 = 17
19 + 17 = 36

Question 7.
Modeling Real Life
A theme park has 62 rides. 45 of them are in the amusement park. The rest are in the water park. How many rides are in the water park?

Number of rides in Theme park= 62
Number of rides in amusement park =45.
left over rides take place in water park
Number of rides in water park = 62 -45 = 17

Question 8.
Modeling Real Life
There are 58 more books in a library than in a classroom. There are 94 books in the library. How many books are in the classroom?

Number of books in library = 94.
Number of books in class room = 94 – 58( 58 more books are there in classroom)
Number of books in class room = 36.

Review & Refresh

Use compensation to solve.

Question 9.
18 + 44 = _____

Question 10.
63 + 27 = _____

### Lesson 6.6 Practice Two-Digit Subtraction

Work with a partner. Choose different strategies to ﬁnd 76 − 29.

I prefer Strategy – 2 as we can check the answer, which helps us to know whether the answer is correct or wrong.
Whatever the strategy may be the answer will be the same.

Show and Grow

Use any strategy to ﬁnd the difference.

Question 1.
52 – 25 = _____

Question 2.
78 – 56 = _____

Question 3.
61 – 33 = ___

Question 4.
83 – 37 = ___

Question 5.
72 – 49 = __-

Show and Grow

Question 1.
52 − 25 = __

Question 4.
83 − 37 = __

Question 5.
72 – 49 = __

Question 6.
45 – 39 = ___

Question 7.
69 – 58 = ___

Question 8.
94 – 45 = __

Question 9.
86 – 48 = __

Apply and Grow: Practice

Use any strategy to ﬁnd the difference.

Question 10.
95 – 38 = __

Question 11.
66 – 47 = ___

Question 12.
58 – 6 = __

Question 13.
81 – 35 = ___

Question 14.
43 – 17 = ___

Question 15.
37 – 8 = ___

Question 16.
28 – 19 = ___

Question 17.
72 – 30 = ___

Question 18.
82 – 4 = __

Question 19.
DIG DEEPER!
Fill in the missing digits.

Question 20.
YOU BE THE TEACHER
Is Descartes correct? Explain

18 + 23 = 41.

Think and Grow: Modeling Real Life

Is there a greater difference between the number of guests on Saturday and Sunday or on Sunday and Monday?

Show and Grow

Question 21.
Is there a greater difference between the number of bagels sold on Sunday and Monday or on Monday and Tuesday?

### Practice Two-Digit Subtraction Homework & Practice 6.6

Use any strategy to ﬁnd the difference.

Question 1.
34 – 26 = __

Question 2.
75 – 47 = ___

Question 3.
96 – 48 = __

Question 4.
51 – 21 = ___

Question 5.
23 – 16 = ___

Question 6.
47 – 8 = ___

Question 7.
25 – 3 = ___

Question 8.
87 – 69 = ___

Question 9.
48 – 29 = ___

Question 10.
Number Sense
Find each missing number.

Question 11.
Structure
Solve 31 − 14 two different ways.

Question 12.
Modeling Real Life
Is there a greater difference between the number of animals adopted in December and January or in January and February?

Review & Refresh

Question 13.

2 + 8 =10
10 – 8 = 2

Question 14.

5 + 6 = 11
11 – 6 = 5

Question 15.

9 + 8 = 17
17 – 8 = 9.

### Lesson 6.7 More Problem Solving: Subtraction

Explore and Grow

Model the story

Newton has 34 balloons. 18 ﬂy away. How many balloons does Newton have left?

Number of balloons = 34
number of balloons flew=18
Number of balloons left = 34 – 18 =16

Show and Grow

Question 1.
There are 27 more harmonicas than drums in a music room. There are 55 harmonicas. How many drums are there?

Apply and Grow: Practice

Question 2.
There are 71 ﬁsh crackers. You eat 29 of them. Your friend eats 28. How many ﬁsh crackers are left?

Number of Fish crackers = 71
Number of fish crackers eaten by me = 29
Number of fish crackers eaten by my friend = 28.
Number of fish crackers left = 71- 29 – 28 =14

Question 3.
Newton solves 16 more math problems than Descartes. Newton solves 34 math problems. How many math problems does Descartes solve?

Problems solved by Newton =34.
Problem solved by Descartes = 34 – 16( as newton solves 16 problems more)
Problem solved by Descartes = 18

Question 4.
Number Sense
You have 78 tokens. Your friend gives you 14 more. You use 35 tokens. Use the given numbers to ﬁnd how many tokens you have now.

Think and Grow: Modeling Real Life

You see 20 elephants on a safari. You see 7 fewer giraffes than elephants. Then 5 of the giraffes leave the group. How many giraffes are left?

Show and Grow

Question 5.
Your friend has 54 blocks. You have 18 fewer blocks than your friend. You use 29 blocks to make a tower. How many blocks do you have left?

Number of Blocks with my friend = 54
Number of Blocks with me = 54 – 18 = 36
Number of blocks used by me to make a tower = 29.
Number of blocks left = 36 – 29 = 7 .

Question 6.
DIG DEEPER!
You had 19 almonds. You ate some. There are 11 left. Your friend ate 3 fewer almonds than you. How many almonds did your friend eat?

Number of Almonds = 19.
Number of Almonds left = 11.
Number of Almonds eaten = 19 – 11 = 8.
Number of Almonds eaten by me = 8 – 3 = 5.
Number of Almonds eaten by my friend = 3.

### More Problem Solving: Subtraction Homework & Practice 6.7

Question 1.
Some kids are at a trampoline park. 24 leave. There are 57 left. How many kids were there to start?

Total Number of kids at a Trampoline park = X
Number of kids left the park = 24.
Number of kids remaining in the park = 57.
Total number of kids = 24 + 57 =81.

Question 2.
You have 62 dollars saved. You spend 37 dollars on a video game. Then you give 16 dollars to your friend. How many dollars do you have left?

Total Number of Dollars = 62.
Number of dollars spend on video game = 37.
Number of dollars given to my friend = 16 .
Number of dollars left = 62 – 37 – 16 =9 .

Question 3.
Structure
You have 50 toothpicks. Your friend has 30 fewer toothpicks than you. Which picture shows how many toothpicks you and your friend have in all?

Picture 2 is correct = 70 Toothpicks.
Number of tooth picks with me = 50.
Number of tooth picks with my friend = 50 – 30 = 20.
Total number of tooth picks = 50 + 20 = 70.

Question 4.
DIG DEEPER!
A museum has 12 dinosaur exhibits and some art exhibits. There are 34 exhibits in all. Then 3 more art exhibits are added. How many art exhibits are there now?

Number of Dinosaur Exhibits = 12.
Total Number of Exhibits = 34
Number of Art Exhibits = 34 – 12 = 22
Number of Art Exhibits added = 3.
Total Number of Art Exhibits =22 + 3 = 25 .

Review & Refresh

Break apart the addends to ﬁnd the sum.

Question 5.

Question 6.

### Fluently Subtract within 100 Performance Task

Question 1.
a. Your group makes 16 of them. How many snowﬂakes does the other group make?

Total Number of paper snowflakes = 53.
Number of snow flakes made by my group =16.
Number of snowflakes made by other group = 53 – 16 = 37.

b. Your teacher hangs 49 of the snowﬂakes from the ceiling in an array with 7 equal rows. How many columns of snowﬂakes are there?

Total Number snowflakes = 49.
Number of rows = 7.
Number of Columns = 49 ÷ 7 = 7.

c. Your teacher wants to hang one more equal row of snowﬂakes. Are there enough snowﬂakes? If so, how many extra snowﬂakes are there? If not, how many more snowﬂakes are needed?

Number of snowflakes = 49.
One more row means 8 th row = 7 more snowflakes = 49 + 7 =56 snowflakes.
56 snowflakes are required we have only 49 snowflakes.
Therefore , more 7 snowflakes are required

Question 2.
Another class makes 75 paper snowﬂakes. 29 are white and some are blue. They make some more blue snowﬂakes. Now they have 61 blue snowﬂakes. How many more blue snowﬂakes did they make?

Number of snowflakes = 75.
Number of white snowflakes = 29 .
Number of blue snowflakes = 75 – 29 = 46 .
Number of blue snowflakes made again = 61.
Total Number of Blue snowflakes = 61 + 46 = 107 .

### Fluently Subtract within 100 Activity

To Play: Use Solve and Cover: Subtraction Cards. Place a Difference Card face up on each box. Place the stack of Problem Cards face down. Players take turns. On your turn, ﬂip over a card from the stack. Solve the problem. Place the card on the difference. Play until all of the differences are covered.

### Fluently Subtract within 100 Chapter Practice 6

6.1 Model and Regroup to Subtract

Question 1.
Use Models to Subtract. Draw to show your work.

6.2 Use Models to Subtract a One-Digit Number from a Two-Digit Number

Question 2.
60 – 8 = ?

Question 3.
74 – 3 = ?

6.3 Use Models to Subtract Two-Digit Numbers

Question 4.
45 – 38 = ?

Question 5.
74 – 27 = ?

Question 6.
Number Sense
Use two of the numbers to write and solve a subtraction problem that requires regrouping.

The two numbers that requires regrouping for subtraction are 63 – 45 = 18

6.4 Subtract from a Two-Digit Number

Question 7.
93 – 50 = ?

Question 8.
57 – 28 = ?

Question 9.
67 – 9 = ?

6.5 Use Addition to Check Subtraction

Question 10.
64 – 27 = ?

Question 11.
86 – 36 = ?

Question 12.

Question 13.

6.6 Practice Two-Digit Subtraction

Use any strategy to find the difference.

Question 14.
55 – 37 = ___

Question 15.
60 – 20 = __

Question 16.
39 – 3 = __

6.7 More Problem Solving: Subtraction

Question 17.
Newton has some BINGO chips. He gives 25 of them away. He has 28 left. How many chips did he have to start?

Question 18.
Number Sense
You have 35 balls. You use 18 of them. You win a bonus and get 10 more balls. Use the given numbers to ﬁnd how many balls you have now.

Question 19.
Modeling Real Life
A petting zoo has 27 sheep and some goats. There are 41 animals in all. Then 16 more goats are added. How many goats are there now?