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## Big Ideas Math Book 1st Grade Answer Key Chapter 5 Subtract Numbers within 20

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**Vocabulary**

**Lesson: 1 Count Back to Subtract within 20**

**Lesson: 2 Use Addition to Subtract within 20**

**Lesson: 3 Subtract 9**

**Lesson: 4 Get to 10 to Subtract**

**Lesson: 5 More True or False Equations**

**Lesson: 6 Make True Equations**

**Lesson: 7 Problem Solving: Subtraction within 20**

- Lesson 5.7 Problem Solving: Subtraction within 20
- Problem Solving: Subtraction within 20 Practice 5.7

**Chapter 5 Subtract Numbers within 20**

- Chapter 5 Subtract Numbers within 20 Performance Task
- Chapter 5 Subtract Numbers within 20 Chapter Practice

### Chapter 5 Subtract Numbers within 20 Vocabulary

**Organize It**

Review Words:

bar model

difference

minus

part-part-whole model

subtraction equation

Use the review words to complete the graphic organizer.

Answer:

Explanation:

Given 8 – 3 = 5, Here – represents minus sign minus

represents the arithmetic operation of subtraction between

two numbers, 5 represents difference is the result of subtracting

one number from another and 8 – 3 = 5 is called subtraction equation**
**Â is a statement that shows aÂ subtractionÂ operation using the minuend,

subtrahend, difference.

**Define It**

Match the review word to its definition.

Answer:

Explanation:

In the above picture, the first one is a bar modelÂ a pictorial representation

of a problem or concept where bars or boxes are used to represent the

known and unknown quantities, the second picture is the part-part-whole model

is a simple pictorial representation of a problem that helps us

see the relationships between numbers.

### Lesson 5.1 Count Back to Subtract within 20

**Explore and Grow**

Model the story.

You are on floor number 12. You go down 4 floors. What floor are you on now?

floor number ____8______

Answer:

I am in 8 floors now.

Explanation:

Given I am on floor number 12 and go down 4 floors means

now I am on floor 12 – 4 = 8 . on the number line we start from 12

since subtracting makes numbers smaller, we move left to subtract.

So from 12 we move 4 parts back or left to 8. Therefore now I am at

8 floor now.

**Show and Grow**

Question 1.

15 – 8 = ___7____

Answer:

15 – 8 = 7

Explanation:

We subtract 15 – 8 = 7, on number line we start at 15 and

move 8 steps back or left we get 7.

Question 2.

12 – 3 = ___9______

Answer:

12- 3 = 9

Explanation:

We subtract 12 – 3 = 9, on number line we start at 12 and

move 3 steps back or left we get 9.

Question 3.

17 – 9 = ____8_____

Answer:

17 – 9 = 8

Explanation:

We subtract 17 – 9 = 8, on the number line we start at 17 and

move 9 steps back or left we get 8.

**Apply and Grow: Practice**

Question 4.

11 – 6 = ____5____

Answer:

11 – 6 = 5

Explanation:

We subtract 11 – 6 = 5, on the number line we start at 11 and

move 6 steps back or left we get 5.

Question 5.

13 – 7 = ___6_____

Answer:

13 – 7 = 6

Explanation:

We subtract 13 – 7 = 6, on the number line we start at 13 and

move 7 steps back or left we get 6.

Question 6.

18 – 9 = ___9_____

Answer:

18- 9 = 9

Explanation:

We subtract 18 – 9 = 9, on number line we start at 18 and

move 9 steps back or left we get 9.

Question 7.

20 – 10 = ____10_____

Answer:

20 – 10 = 10

Explanation:

We subtract 20 – 10 = 10, on the number line we start at 20 and

move 10 steps back or left we get 10.

Question 8.

17 – 8 = ____9_____

Answer:

17- 8 = 9

Explanation:

We subtract 17 – 8 = 9, on the number line we start at 17 and

move 8 steps back or left we get 9.

Question 9.

18 – 3 = ____15______

Answer:

18 – 3 = 15

Explanation:

We subtract 18 – 3 = 15, on the number line we start at 18 and

move 3 steps back or left we get 15.

Question 10.

___12____ = 16 – 4

Answer:

16- 4 = 12

Explanation:

We subtract 16 – 4 = 12, on the number line we start at 16 and

move 4 steps back or left we get 12.

Question 11.

___6_____ = 14 – 8

Answer:

14- 8 = 6

Explanation:

We subtract 14 – 8 = 6, on the number line we start at 14 and

move 8 steps back or left we get 6.

Question 12.

**DIG DEEPER!**

Write the equation shown by the number line.

___15_____ – __9______ = ___6_____

Answer:

The equation on the number line is 15 – 9 = 6.

Explanation:

As shown on the number line we start at 15 and move

9 steps or 9 units back or left we reached at 6 so the equation shown by the number line is 15 – 9 = 6.

**Think and Grow: Modeling Real Life**

You collect 6 gems. Your friend collects 14. How many fewer gems do you collect?

Model:

Subtraction equation:

____8____ fewer gems

Subtraction equation is 14 – 6 = 8,

I have 8 fewer gems.

Explanation:

Given I have collected 6 gems and friend collects 14 gems

now how many less or fewer gems I have than my friend are

14 – 6 = 8 gems, On number line we start at 14 and

move 6 steps or 6 units back or left we reach at 8.

So the Subtraction equation is 14 – 6 = 8,

I have 8 fewer gems.

**Show and Grow**

Question 13.

Your friend finds 16 gold bars. You find 9. How many fewer gold bars do you find?

Model:

Subtraction equation:

_____7_____ gold bars

Answer:

Subtraction equation is 16 – 9 = 7,

I have 7 fewer gold bars.

Explanation:

Given friend finds 16 gold bars and I found 9,

now how many less or fewer gold bars I have than my friend are

16 – 9 = 7 gold bars, On number line we start at 16 and

move 9 steps or 9 units back or left we reach at 7.

So the Subtraction equation is 16 – 9 = 7,

I have 7 fewer gold bars.

### Count Back to Subtract within 20 Practice 5.1

Question 1.

12 – 5 = __7____

Answer:

12 – 5 = 7

Explanation:

We subtract 12 – 5 = 7, on number line we start at 12 and

move 5 steps back or left we get 7.

Question 2.

15 – 7 = ____8____

Answer:

15 – 7 = 8

Explanation:

We subtract 15 – 7 = 8, on number line we start at 15 and

move 7 steps back or left we get 8.

Question 3.

13 – 6 = ___7_____

Answer:

13 – 6 = 7

Explanation:

We subtract 13 – 6 = 7, on number line we start at 13 and

move 6 steps back or left we get 7.

Question 4.

14 – 5 = ___9_______

Answer:

14 – 5 = 9

Explanation:

We subtract 14 – 5 = 9, on number line we start at 14 and

move 5 steps back or left we get 9.

Question 5.

11 – 5 = ____6______

Answer:

11- 5 = 6

Explanation:

We subtract 11 – 5 = 6, on number line we start at 11 and

move 5 steps back or left we get 6.

Question 6.

15 – 4 = ___11_____

Answer:

15- 4 = 11

Explanation:

We subtract 15 – 4 = 11, on number line we start at 15 and

move 4 steps back or left we get 11.

Question 7.

__10____ = 18 – 8

Answer:

18 – 8 = 10

Explanation:

We subtract 18 – 8 = 10, on number line we start at 18 and

move 8 steps back or left we get 10.

Question 8.

____4_____ = 12 – 8

Answer:

12 – 8 = 4

Explanation:

We subtract 12 – 8 = 4, on number line we start at 12 and

move 8 steps back or left we get 4.

Question 9.

**DIG DEEPER**

Write the equation shown by the number line.

___14_____ – ___9_____ = ___5_____

Answer:

The equation on the number line is 14 – 9 = 5.

Explanation:

As shown on the number line we start at 14 and move

9 steps or 9 units back or left we reach at 5, so the

equation shown by the number line is 14 – 9 = 5.

Question 10.

**Modeling Real Life**

You play soccer. The visiting team scores 12 goals. Your team scores 4 fewer. How many goals does your team score?

_____8_____ goals

Answer:

Subtraction equation is 12 – 4 = 8,

My team scored 8 goals

Explanation:

Given visiting team scores 12 goals, My team scores 4 fewer goals

My team have scored 12 – 4 = 8 goals, On number line we start at

12 and move 4 steps or 4 units back or left we reach at 8.

So the Subtraction equation is 12 – 4 = 8,

therefore my team score 8 goals.

**Review & Refresh**

Question 11.

6 + 2 = ___8_____

Answer:

6 + 2 = 8

Explanation :

The addition equation is 6 + 2 = 8,

We add 2 to 6 we get 8.

Question 12.

4 + 3 = ___7_____

Answer:

4 + 3 = 7

Explanation :

The addition equation is 4 + 3 = 7,

We add 3 to 4 we get 7.

Question 13.

8 + 2 = ___10____

Answer:

8 + 2 = 10

Explanation :

The addition equation is 8 + 2 = 10,

We add 2 to 8 we get 10.

Question 14.

5 + 4 = ____9___

Answer:

5 + 4 = 9

Explanation :

The addition equation is 5 + 4 = 9,

We add 4 to 5 we get 9.

### Lesson 5.2 Use Addition to Subtract within 20

**Explore and Grow**

Model the story.

Your class needs to make 15 scrapbook pages. 8 are already made. How many more pages does your class need to make?

____7_____ more pages

15 – 8 = 7,

We need 7 more pages to make.

Explanation:

Given my class needs to make 15 scrapbook pages,

8 are already made ,We need 15 – 8 = 7 more pages

are neededÂ to make scrapbook.

**Show and Grow**

Question 1.

11 – 7 = ?

Think 7 + ___4____ = 11.

So, 11 – 7 = ___4____ .

Answer:

7 + 4 = 11

11 – 7 = 4

Explanation:

Explanation:

First we move from 7 on number line and start moving till

11 we count how many units right we have moved we get

4 units so 7 + 4 = 11 or we start at 11 on number line and

move 7 steps back or left we get 4, 11 – 7 = 4.

Question 2.

16 – 8 = ?

Think 8 + ___8____ = 16.

So, 16 – 8 = ___8____ .

Answer:

8 + 8 = 16

16 – 8 = 8

Explanation:

First we move from 8 on number line and start moving till

16 we count how many units right we have moved we get

8 units so 8 + 8 = 16 or we start at 16 on number line and

move 8 steps back or left we get 8, 16 – 8 = 8.

Question 3.

13 – 10 = ?

Think 10 + __3_____ = 13.

So, 13 – 10 = ___3____ .

Answer:

10 + 3 = 13

13 – 10 = 3

Explanation:

First we move from 10 on number line and start moving till

13 we count how many units right we have moved we get

3 units so 10 + 3 = 13 or we start at 13 on number line and

move 10 steps back or left we get 3, 13 – 10 = 3.

**Apply and Grow: Practice**

Question 4.

12 – 7 = ?

Think 7 + ___5____ = 12.

So, 12 – 7 = ___5____ .

Answer:

7 + 5 = 12

12 – 7 = 5

Explanation:

First we move from 7 on number line and start moving till

12 we count how many units right we have moved we get

5 units so 7 + 5 = 12 or we start at 12 on number line and

move 7 steps back or left we get 5, 12 – 7 = 5.

Question 5.

17 – 8 = ?

Think 8 + ___9____ = 17.

So, 17 – 8 = __9____ .

Answer:

8 + 9 = 17

17 – 8 = 9

Explanation:

First we move from 8 on number line and start moving till

17 we count how many units right we have moved we get

9 units so 8 + 9 = 17 or we start at 17 on number line and

move 8 steps back or left we get 9, 17 – 8 = 9.

Question 6.

11 – 2 = ___9_____

Answer:

11 – 2 = 9

Explanation:

We subtract 11 – 2 = 9, on number line we start at 11 and

move 2 steps back or left we get 9.

Question 7.

_____14____ = 19 – 5

Answer:

19 – 5 = 14 or 14 = 19 – 5

Explanation:

We subtract 19 – 5 = 14, on number line we start at 19 and

move 5 steps back or left we get 14.

Question 8.

**DIG DEEPER!**

Tell what subtraction problem Newton and Descartes solved. Think: What strategies did they use?

Answer:

Newton and Descartes solved the subtraction equation as

FirstÂ by 5 + 8Â = 13

Second by 13 – 5 =_8Â

Explanation :

Newton and Descartes solved the subtraction equation on the number line

first they solved equation 5 + _______ = 13 as started from 5 and moved

8 units right reached till 13 so the missing number is 8, 5 + 8 = 13.

In second method they solved by starting from 13 and moved 5 units

left till they reached 8 on the number line so they solved

the subtraction equation as 13 – 5 = 8.

**Think and Grow: Modeling Real Life**

There are 15 people in an elevator. Some of them exit. There are 7 left. How many people exit?

Model:

Subtraction equation:

15 – 7 = 8

____8_____ people

Answer:

15 – 7 = 8,

8 people exit.

Explanation:

Given 15 people are there in elevator, some of them exit,

There are 7 left, So people exit are 15 – 7 = 8,

So 8 people exit from elevator.

**Show and Grow**

Question 9.

There are 18 people in a subway car. Some of them exit. There are 9 left. How many people exit?

Model:

Subtraction equation:

18 -9 = 9

_____9_____ people

Answer:

18 – 9 = 9,

9 people exit.

Explanation:

Given there are 18 people in a subway car , some of them exit,

There are 9 left, So people exit are 18 – 9 = 9,

So 9 people exit from subway car.

### Use Addition to Subtract within 20 Practice 5.2

Question 1.

13 – 9 = ?

Think 9 + __4____ = 13

So, 13 – 9 = ___4____.

Answer:

9 + 4 = 13

13 – 9 = 4

Explanation:

First we move from 9 on number line and start moving till

13 we count how many units right we have moved we get

4 units so 9 + 4 = 13 or we start at 13 on number line and

move 9 steps back or left we get 4, 13 – 9 = 4.

Question 2.

17 – 8 = ?

Think 8 + __9____ = 17

So, 17 – 8 = ___9____.

Answer:

8 + 9 = 17

17 – 8 = 9

Explanation:

First we move from 8 on number line and start moving till

17 we count how many units right we have moved we get

9 units so 8 + 9 = 17 or we start at 17 on number line and

move 8 steps back or left we get 9, 17 – 8 = 9.

Question 3.

14 – 7 = ____7_____

Answer:

14 – 7 = 7

Explanation:

We subtract 14 – 7 = 7, on number line we start at 14 and

move 7 steps back or left we get 7.

Question 4.

____13_____ = 17 – 4

Answer:

17 – 4 = 13

Explanation:

We subtract 17 – 4 = 13, on number line we start at 17 and

move 4 steps back or left we get 13.

Question 5.

**DIG DEEPER!**

Tell what subtraction problem Newton and Descartes solved. Think: What strategies did they use?

Answer:

Newton and Descartes solved the subtraction equation as

First by 11 – 7 =_4Â

SecondÂ by 7 + Â 4Â =Â 11

Explanation :

Newton and Descartes solved the subtraction equation on the number line

first method they solved by starting from 11 and moved 7 units

left till they reached 4 on the number line so they solved

the subtraction equation as 11 – 7 = 4.

Second they solved equation 7 + ______ = 11 as started from 7 and moved

4 units right reached till 11 so the missing number is 4, 7 + 4 = 11.

Question 6.

**Modeling Real Life**

There are 13 people on a train. Some of them exit. There are 6 left. How many people exit?

_____7_______ people

Answer:

13 – 6 = 7,

So, 7 people exit.

Explanation:

Given there are 13 people on a train , some of them exit,

There are 7 left, So people exit are 13 – 6 = 7,

So 7 people exit from the train.

**Review & Refresh**

Question 7.

10 – 9 = ____1______

Answer:

10 – 9 = 1

Explanation :

The subtraction equation is 10 – 9 = 1,

We subtract 9 from 10 we get 1.

Question 8.

9 – 9 = ____0______

Answer:

9 – 9 = 0

Explanation :

The subtraction equation is 9 – 9 = 0,

We subtractÂ 9 from 9 we get 0.

### Lesson 5.3 Subtract 9

**Explore and Grow**

Use counters to find each difference.

Explanation:

To find 15 -10 =Â here we use two countersÂ first

we take total 15 circles in that we strike 10 numbers

the left number of circles are 5, So 15 – 10 = 5.

To find 15 – 9 = here we use two counters and we take

15 circles in that we will strike out 9 numbers the left are

6, So 15 – 9 = 6.

**Show and Grow**

Get to 10 to subtract.

Question 1.

17 – 9 = ?

17 – __7____ = 10

10 – ___2____ = ___8___

So, 17 – 9 = ___8_____

Answer:

17 – 7 = 10 we get 10

10 – 2 = 8,

So 17 – 9 = 8

Explanation:

We have 2 counters in counter one we have 10 circles

and in next counter we have 7 circles so in total we have 17,

First we see out of 17 if we consider counter-2 we have 7 strike outs

means 17 – 7 = 10 we got 10 in counter-1 and if we see first counter

we have 2 strike outs 10 – 2 = 8, So total number of circles strike out

from 2-counters are 7 + 2 = 9, So making equation as 17 – 9 = 8.

Question 2.

14- 9 = ?

14 – __4____ = 10

10 – ___5____ = ___5___

So, 14 – 9 = _____5___

Answer:

14 – 4Â = 10 we get 10

10 – 5 = 5

So 14 – 9 = 5

Explanation:

We haveÂ 2 counters in counter one we have 10 circles

and in next counter we have 4 circles so in total we have 14,

First we see out of 14 if we consider counter-2 we have 4 strike outs

means 14 – 4 = 10 we got 10 in counter-1 and if we see first counter

we have 5 strike outs 10 – 5 = 5,So total number of circles strike out

from 2-counters are 4 + 5 = 9, So making equation as 14 – 9 = 5.

**Apply and Grow: Practice**

Question 3.

16 – 9 = ?

16 – ___6___ = 10

10 – ____3___ = __7____

So, 16 – 9 = ___7_____

Answer:

16 – 6 = 10 we get 10

10 – 3 = 7

So 16 – 9 = 7

Explanation:

We haveÂ 2 counters in counter one we have 10 circles

and in next counter we have 6 circles so in total we have 16,

First we see out of 16 if we consider counter-2 we have 6 strike outs

means 16 – 6 = 10 we got 10 in counter-1 and if we see first counter

we have 3 strike outs 10 – 3 = 7, So total number of circles strike out

from 2-counters are 6 + 3 = 9, So making equation as 16 – 9 = 7.

Question 4.

11 – 9 = ?

11 – ___1____ = 10

10 – ___8____ = ___2____

S0, 11 – 9 = ____2____ .

Answer:

11 – 1 = 10 we get 10

10 – 8 = 2

So 11 – 9 = 2

Explanation:

To solve 11 – 9Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter we have 1 circle so in total we have 11,

Now in all we will strike 9 circles, 1 circle from counter-2 making equation

as 11 – 1 = 10 we got 10 in counter-1 and we strike outÂ 8 circles from counter-1

we are left with 2 making it as 10 – 8 = 2, So in total we have taken 8 + 1 = 9

from 11 in 2-counters, making equation as 11 -9 = 2 as shown in the picture.

Question 5.

15 – 9 = ?

15 – __5_____ = 10

10 – __4______ = __6______

So, 15 – 9 = ___6_____

Answer:

15- 5 = 10 we get 10

10 – 4 = 6

So 15 – 9 = 6

Explanation:

To solve 15 – 9Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter we have 5 circles so in total we have 15,

Now in all we will strike 9 circles, 5 circles from counter-2 making equation

as 15 – 5 = 10 we got 10 in counter-1 and we strike 4 circles from counter-1

we are left with 6 making it as 10 – 4 = 6, So in total we have taken 5 + 4 = 9

from 15 in 2-counters, making equation as 15 -9 = 6 as shown in the picture.

Question 6.

MP Structure

Which models show 12 – 9?

Answer:

First model and third model shows 12 – 9.

Explanation:

If we see all models are having 12 now we will see which model is subtracting 9,

For this we consider both counters and count total strike outs

Model 1 have 9 strike outs , Model 2 have 10 strike outs,

Model 3 have 9 strike outs, So first model and third model shows 12 – 9.

**Think and Grow: Modeling Real Life**

You have 12 eggs. You use 9 of them. How many eggs are left?

Model:

Subtraction equation:

___3_______ eggs

12 – 9 = 3,

So 3 eggs are left.

Explanation:

Given I have 12 eggs and use 9 eggs,

By using counters first I take total 12 circles then I strike out 9,

So left are 3 so the subtraction equation is 12 – 9 = 3,

So 3 eggs are left.

**Show and Grow**

Question 7.

An egg carton has 18 eggs. You crack 9 of them. How many eggs are not cracked?

Model:

Subtraction equation:

_____9_______ eggs

18 – 9 = 9,

So 9 eggs are not cracked.

Explanation:

Given egg carton has 18 eggs and crack 9 of them,

By using counters first I take total 18 circles then I strike out 9,

So left are 9 so the subtraction equation is 18 – 9 = 9,

So 9 eggs are not cracked.

### Subtract 9 Practice 5.3

Get to 10 to subtract.

Question 1.

18 – 9 = ?

18 – ___8_____ = 10

10 – __1_____ = __9_____

So, 18 – 9 = ____9_____ .

Answer:

18- 8 = 10 we get 10

10 – 1 = 9

So 18 – 9 = 9

Explanation:

To solve 18 – 9Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter we have 8 circles so in total we have 18,

Now in all we will strike 9 circles, 8 circles from counter-2 making equation

as 18 – 8 = 10 we got 10 in counter-1 and we strike 1 circle from counter-1

we are left with 9 making it as 10 – 1 = 9, So in total we have taken 8 + 1 = 9

from 18 in 2-counters, making equation as 18 – 9 = 9 as shown in the picture.

Question 2.

12 – 9 = ?

12 – ___2_____ = 10

10 – ___7____ = ___3____

So, 12 – 9 = _____3____ .

Answer:

12 – 2 = 10 we get 10

10 – 7 = 3

12 – 9 = 3

Explanation:

To solve 12 – 9Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter we have 2 circles so in total we have 12,

Now in all we will strike 9 circles, 2 circles from counter-2 making equation

as 12 – 2 = 10 we got 10 in counter-1 and we strike 7 circles from counter-1

we are left with 3 making it as 10 – 7 = 3, So in total we have taken 2 + 7 = 9

from 12 in 2-counters, making equation as 12 – 9 = 3 as shown in the picture.

Question 3.

19 – 9 = ?

19 – ____9____ = 10

10 – ___0____ = ___10____

So, 19 – 9 = ____10_____ .

Answer:

19 – 9 = 10,

10 – 0 = 10

So, 19 -9 = 10

Explanation:

To solve 19 – 9Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter we have 9 circles so in total we have 19,

Now in all we will strike 9 circles, 9 circles from counter-2 making equation

as 19 – 9 = 10 we got 10 in counter-1, we will not strike in counter-1 as we have

already taken 9 ,So 10 – 0 = 10, We are left with 10 and the equation is 19 – 9 = 10.

Question 4.

**MP Structure**

Which models show 16 – 9?

Answer:

Second model and third model shows 16 – 9.

Explanation:

If we see all models are having 16 now we will see which model is subtracting 9,

For this we consider both counters and count total strike outs

Model 1 have 10 strike outs , Model 2 have 9 strike outs,

Model 3 have 9 strike outs, So Second model and third model shows 16 – 9.

Question 5.

**Modeling Real Life**

You have 14 water balloons. You break 9 of them. How many water balloons are left?

____5______ Water balloons

Answer:

14 – 9 = 5

5 water balloons are left.

Explanation:

Given I have 14 water balloons. I break 9 of them,

So I will take 2 counters counter-1 has 10 circles and counter-2 has

4 circles in all I have 14 number of circles, now over all I will

strike out 9 from the 2-counters. As counter-2 has only 4 I will take 5 from

counter-1 so that in total 4 + 5 = 9 circles are strike out so we are left with 5,

So the subtraction equation is 14Â – 9 = 5, So 5 water balloons are left.

**Review & Refresh**

Question 6.

Use the picture to complete the number bond.

Answer:

Explanation:

Number bonds are pictures that show the bond between parts and whole.

So here we know that 10 is the whole number

and 8 is one of the numbers from the pair of number bonds.

The other number that combines with 8 to give 10 is 2.

### Lesson 5.4 Get to 10 to Subtract

**Explore and Grow**

Use counters to find the difference. Show how you can make a 10 to solve.

Answer:

14 – 4 = 10

10 – 2 = 8

14 – 6 = 8

Explanation:

To solve 14 – 6Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter we have 4 circles so in total we have 14,

Now in all we will strike 6 circles, 4 circles from counter-2 making equation

as 14 – 4 = 10 we got 10 in counter-1 and we strike 2 circles from counter-1

we are left with 8 making it as 10 – 2 = 8, So in total we have taken 4 + 2 = 6

from 14 in 2-counters, making equation as 14 – 6 = 8 as shown in the picture.

**Show and Grow**

Get to 10 to subtract.

Question 1.

12 – 5 = ?

12 – __2____ = 10

10 – __3___ = ___7_____

So, 12 – 5 = ____7______

Answer:

12 – 2 = 10 we get 10

10 – 3 = 7

12 – 5 = 7

Explanation:

To solve 12 – 2Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 2 circles so in total we have 12,

Now in all we will strike 5 circles, 2 circles from counter-2 making equation

as 12 – 2 = 10 we got 10 in counter-1 and we strike 3 circles from counter-1

we are left with 7 making it as 10 – 3 = 7, So in total we have taken 2 + 3 = 5

from 12 in 2-counters, making equation as 12 – 5 = 7 as shown in the picture.

Question 2.

17 – 8 = ?

17 – ___7___ = 10

10 – __1___ = ___9_____

So, 17 – 8 = ___9_______

Answer:

17 – 7 = 10

10 – 1 = 8

So 17 – 8 = 9

Explanation:

To solve 17 -8Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 7 circles so in total we have 17,

Now in all we will strike 8 circles, 7 circles from counter-2 making equation

as 17 – 7 = 10 we got 10 in counter-1 and we strike 1 circle from counter-1

we are left with 9 making it as 10 – 1 = 9, So in total we have taken 7 + 1 = 8

from 17 in 2-counters, making equation as 17 – 8 = 9 as shown in the picture.

**Apply and Grow: Practice**

Get to 10 to subtract

Question 3.

16 – 7 = ?

I6 – __6______ = 10

10 – ___1_____ = ____9____

So, 16 – 7 = _____9_____ .

Answer:

16 – 6 = 10

10 – 1 = 9

So 16 – 7 = 9

Explanation:

To solve 16 -7Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 6 circles so in total we have 16,

Now in all we will strike 7 circles, 6 circles from counter-2 making equation

as 16 – 6 = 10 we got 10 in counter-1 and we strike 1 circle from counter-1

we are left with 9 making it as 10 – 1 = 9, So in total we have taken 6 + 1 = 7

from 16 in 2-counters, making equation as 16 – 7 = 9 as shown in the picture.

Question 4.

11 – 4 = ?

11 – ____1___ = 10

10 – ___3____ = ___7_____

So, 11 – 4 = ___7_____ .

Answer:

Answer:

11 – 1 = 10

10 – 3 = 7

So 11 – 4 = 7

Explanation:

To solve 11 -4Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 1 circles so in total we have 11,

Now in all we will strike 4 circles, 1 circles from counter-2 making equation

as 11 – 1 = 10 we got 10 in counter-1 and we strike 3 circles from counter-1

we are left with 9 making it as 10 – 3 = 7, So in total we have taken 1 + 3 = 4

from 11 in 2-counters, making equation as 11 – 4 = 7 as shown in the picture.

Question 5.

13 – 5 = ?

13 – ____3_____ = 10

10 – ____2_____ = ____8______

So, 13 – 5 = ____8____ .

Answer:

13 – 3 = 10

10 – 2 = 8

So 13 – 5 = 8

Explanation:

To solve 13 -5Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 3 circles so in total we have 13,

Now in all we will strike 5 circles, 3 circles from counter-2 making equation

as 13 – 3 = 10 we got 10 in counter-1 and we strike 3 circles from counter-1

we are left with 8 making it as 10 – 2 = 8, So in total we have taken 3 + 2 = 5

from 13 in 2-counters, making equation as 13 – 5 = 8 as shown in the picture.

Question 6.

**MP Number Sense**

Which equations did Newton use to solve the problem?

Answer:

Newton uses Equation 3 : 12 – 2 =10 , 10 – 4 = 6 so we get 12 – 6 = 6

Explanation:

If we see picture we have two counters in total we have total 12 circles,

In counter-2 we have 2 strike out means 12 – 2 = 10 and from counter-1

we have 4 strike out so 10 – 4 = 6 so in total out of 12 we strike 6 making

the equation as 12 – 6 = 6.

Out of three equations Newton uses equation 12 – 2 = 10 , 10 – 4 = 6,

other equations have 17 count in total and only 3rd equation is having

12 count as per the given picture, So newton use Equation 3.

**Think and Grow: Modeling Real Life**

Your friend checks out 13 books. You check out 4 fewer. How many books do you check out?

Model:

Subtraction equation:

____9___ books

Answer:

I have checked 9 books.

Explanation:

Given my friend checks out 13 books and I check out 4 fewer,

Means I will take 2 counters in counter-1 I will have 10 books and counter-2

3 books in total 13 books, now I have 4 fewer means I will strike out 4,

3 from counter-2 and 1 from counter-1 in total 4 from both the counters,

So 13 – 4 = 9, I checked 9 books.

**Show and Grow**

Question 7.

Your friend skips 16 stones. You skip 8 fewer. How many stones do you skip?

Model:

Subtraction equation:

_____8_______ stones

16 – 8 = 8

So I skip 8 stones.

Explanation:

Given my friend skips 16 stones and I skip 8 fewer,

Means I will take 2 counters in counter-1 I will have 10 stones and counter-2

6 stones in total 16 stones, now I have 8 fewer means I will strike out 8 ,

6 from counter-2 and 2 from counter-1 in total 8 from both the counters,

So 16 – 8 = 8, I skip 8 stones.

### Get to 10 to Subtract Practice 5.4

Get to 10 to Subtract

Question 1.

15 – 6 = ?

15 – __5_____ = 10

10 – ___1____ = __9______

So, 15 – 6 = ____9____ .

Answer:

15 – 5 = 10

10 -1 = 9

So, 15 – 6 = 9.

Explanation:

To solve 15 -6Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 5 circles so in total we have 15,

Now in all we will strike 6 circles, 5 circles from counter-2 making equation

as 15 – 5 = 10 we got 10 in counter-1 and we strike 1 circle from counter-1

we are left with 9 making it as 10 – 1 = 9, So in total we have taken 5 + 1 = 6

from 15 in 2-counters, making equation as 15 – 6 = 9 as shown in the picture.

Question 2.

12 – 4 = ?

12 – ___2____ = 10

10 – ___2____ = ___8_____

So, 12 – 4 = ___8_____ .

Answer:

12 – 2 = 10

10 -2 = 8

So, 12 – 4 = 8.

Explanation:

To solve 12 -4Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 2 circles so in total we have 12,

Now in all we will strike 4 circles, 2 circles from counter-2 making equation

as 12 – 2 = 10 we got 10 in counter-1 and we strike 2 circles from counter-1

we are left with 8 making it as 10 – 2 = 8, So in total we have taken 2 + 2 = 4

from 12 in 2-counters, making equation as 12 – 4 = 8 as shown in the picture.

Question 3.

13 – 7 = ?

13 – ___3____ = 10

10 – ___4____ = ___6_____

So, 13 – 7 = ____6____ .

Answer:

13 – 3 = 10

10 – 4 = 6

13 – 7 = 6

Explanation:

To solve 13 -7Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 3 circles so in total we have 13,

Now in all we will strike 7 circles, 3 circles from counter-2 making equation

as 13 – 3 = 10 we got 10 in counter-1 and we strike 4 circles from counter-1

we are left with 6 making it as 10 – 4 = 6, So in total we have taken 3 + 4 = 7

from 13 in 2-counters, making equation as 13 – 7 = 6 as shown in the picture.

Question 4.

14 – 8 = ?

14 – ___4____ = 10

10 – ___4____ = ___6_____

So, 14 – 8 = ____6____ .

Answer:

14 – 4 = 10

10 – 4 = 6

14 – 8 = 6

Explanation:

To solve 14 -8Â and to get 10,

We solve by using 2 counters in counter one we have 10 circles

and in next counter two we have 4 circles so in total we have 14,

Now in all we will strike 8 circles, 4 circles from counter-2 making equation

as 14 – 4 = 10 we got 10 in counter-1 and we strike 4 circles from counter-1

we are left with 6 making it as 10 – 4 = 6, So in total we have taken 4 + 4 = 8

from 14 in 2-counters, making equation as 14 – 8 = 6 as shown in the picture.

Question 5.

**MP Number Sense**

Which equations did Descartes use to solve the problem?

Answer:

Descartes uses Equation 1 : 15 – 5 =10 , 10 – 4 = 6 so we get 15 – 9 = 6

Explanation:

If we see picture we have two counters in total we have total 15 circles,

In counter-2 we have 5 strike out means 15 – 5 = 10 and from counter-1

we have 4 strike out so 10 – 4 = 6 so in total out of 15 we strike 9 making

the equation as 15 – 9 = 6.

Out of three equations Newton uses equation 15 – 5 = 10 , 10 – 4 = 6,

other equations have 20 count in total and only 1st equation is having

15 count as per the given picture, So newton use 1 Equation.

Question 6.

**Modeling Real Life**

Your friend recycles 14 cans. You recycle 7 fewer. How many cans do you recycle?

____7_____ cans

Answer:

I recycle 7 cans.

Explanation:

Given my friend recycle 14 cans and I recycle 7 fewer,

Means I will take 2 counters in counter-1 I will have 10 cans and counter-2

4 cans in total 14 cans, now I have 7 fewer means I will strike out 7,

4 from the counter-2 and 3 from counter-1 in total 7 from both the counters,

So 14 – 7 = 7, I recycle 7 cans.

**Review & Refresh**

Is the equation true or false?

Question 7.

Answer:

3 + 2 = 5 + 0

5 = 5 ,

So True.

Explanation:

We take 3 + 2 means adding 3 and 2 we get 3 + 2 = 5

and 5 + 0 is 5 so both sides are equal therefore

3 + 2 = 5 + 0 is True.

Question 8.

Answer:

8 – 2 = 6 â‰ 5 + 5 = 10

6 â‰ 10

So False

Explanation:

We take 8 – 2 means subtracting 2 from 8 we get 8 – 2 = 6

and 5 + 5 means adding 5 and 5 we get 5 + 5Â =10,

If we see both sides they are not equal as 6 â‰ 10,

So 8 – 2 =Â 5 + 5 is False.

### Lesson 5.5 More True or False Equations

**Explore and Grow**

Color the stars that have a sum or difference equal to 19 – 5.

Answer:

Explanation:

We color the stars that have a sum or difference equal to 19 – 5,

meansÂ 19 – 5 = 14, We check each star if equal to 14 we will color.

a. The sum is 9 + 5 = 14, so color it with green,

b. The difference is 20 – 6 = 14, we color it with blue

c. The sum is 12 + 1 + 1 = 14, we color it with green

d. The difference is 16 – 2 = 14, we color it with blue

e. The difference is 13 – 1 = 12 , we will not color it

as this is not equal to 14.

f. The sum is 14 + 0 = 14 , we will color it with green

**Show and Grow**

Is the equation true or false ?

Question 1.

Answer:

As 17 – 9 = 8 Â â‰ 14 -5 = 9

So False

Explanation:

We take 17 – 9 means subtracting 9 from 17 we get 17 – 9 = 8

and 14 – 5 means subtracting 5 from 14 we get 14 – 5 = 9,

If we see both sides they are not equal as 8 â‰ 9,

So 17 – 9 =Â 14 – 5 is False.

Question 2.

Answer:

As 6 + 5 = 11 = 18 – 7 = 11

So True.

Explanation:

We take 6 + 5 means adding 6 and 5 we get 6 + 5 = 11,

and 18 – 7 means subtracting 7 from 18 we get 18 – 7 = 11,

As both sides are equal therefore

6 + 5 = 11 = 18 – 7 = 11 is True

**Apply and Grow: Practice**

Is the equation true or false?

Question 3.

Answer:

As 5 + 7 = 12Â â‰ Â 3 + 8 = 11

So False

Explanation:

We take 5 + 7 means adding 5 and 7 we get 5 + 7 = 12,

and 3 + 8 means adding 3 and 8 we get 3 + 8 = 11,

As both sides are not equal therefore

5 + 7 = 12 â‰ 3 + 8 = 11 is False.

Question 4.

Answer:

As 4 + 9 = 13 = 5 + 3 + 5 = 13

Is True.

Explanation:

We take 4 + 9 means adding 4 and 9 we get 4 + 9 = 13,

and 5 + 3 + 5Â means adding 5 , 3 and 5 we get 5 + 3 + 5 = 13,

As both sides are equal therefore

4 + 9 = 13 = 5 + 3 + 5 = 13 is True.

Question 5.

Answer:

As 12 – 7 = 5 â‰ 13 – 5 = 8

So False.

Explanation:

We take 12 – 7 means subtracting 7 from 12 we get 12 – 7 = 5,

and 13 – 5 means subtracting 5 from 13 we get 13 – 5 = 8,

As both sides are not equal therefore

12 – 7Â = 5 â‰ 13 – 5 = 8 is False.

Question 6.

Answer:

As 14 – 8 = 6 = 12 – 6 = 6

So True.

Explanation:

We take 14 – 8 means subtracting 8 from 14 we get 14 – 8 = 6,

and 12 – 6 means subtracting 6 from 12 we get 12 – 6 = 6,

As both sides are equal therefore

14 – 8Â = 6 = 12 – 6 = 6 is True.

Question 7.

Answer:

1 + 8 = 9 = 16 -7 = 9

So True.

Explanation:

We take 1 + 8Â means adding 1 and 8 we get 1 + 8Â = 9,

and 16 – 7 means subtracting 7 from 16 we get 16 – 7 = 9,

As both sides are equal therefore

1 + 8Â = 9 = 16 – 7 = 9 is True.

Question 8.

Answer:

18 – 9 = 9 â‰ Â 5 + 1 + 4 = 10

So False.

Explanation:

We take 18 – 9Â means subtracting 9 from 18 we get 18 – 9Â = 9,

and 5 + 1 + 4 means adding 5,1 and 4 we get 5 + 1 + 4 = 10,

As both sides are not equal therefore

18 – 9Â = 9 â‰ 5 + 1 + 4 = 10 is False.

Question 9.

**MP Number Sense**

Circle all of the equations that are true.

Answer:

Explanation:

Given equations are a. 20 = 2 as 20 is not equal to 2,false so we will not circle,

b. 19 – 7 = 12 as 19 – 7 is 12 this is true we will circle it.

c. 6 + 6 + 3 = 7 + 8 as 6 + 6 + 3 = 15 and 7 + 8 = 15, Both are same

and true we will circle the equation.

**Think and Grow: Modeling Real Life**

You hove 12 lemons. You use 4 of them. Your friend has 3 lemons and buys 4 more.

Do you each have the same number of lemons?

Equation:

Answer:

No each do not have the same number of lemons as 8 â‰ 7 .

Explanation:

Given I have 12 lemons and use 4 of them means 12 – 4

My friend have 3 lemons and buys 4 more means 3 + 4

now checking both of them 12 – 4 = 8 and 3 + 4 = 7 as 8 â‰ 7

both are not equal each do not have the same number of lemons.

**Show and Grow**

Question 10.

You have 14 grapes. You eat 7 of them. Your friend has 10 grapes and eats 3 of them.

Do you each have the same number of grapes?

Equation:

Answer:

Yes each have the same number of grapes as 7 = 7.

Explanation:

Given I have 14 grapes and I eat 7 of them means 14 -7

My friend has 10 grapes and eats 3 of them means 10 – 3,

Now checking both we have 14 – 7 = 7 and 10 – 3 = 7,

Both are equal, So, Yes each of them have the same number of grapes 7= 7.

### More True or False Equations Practice 5.5

Is the equation true or false?

Question 1.

Answer:

13 – 9 = 4 = 11 – 7 = 4

So True.

Explanation:

Checking 13 – 9 and 11 – 7 , subtracting 9 from 13 we get 4

and subtracting 7 from 11 we get 4

as both equations values are equal, true.

Question 2.

Answer:

9 + 8 = 17 = 17 + 0 = 17

So True.

Explanation:

Checking 9 + 8 and 17 + 0, as 9 + 8 = 17 and

17 + 0 = 17 as both equations values are equal to 17 so true.

Question 3.

Answer:

12 – 4 = 8 â‰ 15 – 6 = 9,

So False.

Explanation:

Checking 12 – 4 and 15 – 6, We get 12 – 4 = 8 and

15 – 6 = 9 as both equations values are not equal 8 â‰ 9,

So false.

Question 4.

Answer:

4 + 5 = 9 â‰ 11 – 3 = 8

Is False

Explanation:

Checking 4 + 5 and 11 – 3, We get 4 + 5 = 9 and

11 – 3 = 8 as both equations values are not equal 9 â‰ 8,

So false.

Question 5.

Answer:

15 – 7 = 8 = 4 + 4 = 8

So True.

Explanation:

Checking 15 – 7 andÂ 4 + 4Â we get 15 – 7 = 8

andÂ 4 + 4 = 8 as both equations values are same 8 = 8

so true.

Question 6.

Answer:

0 + 5 + 2 = 7 = 12 – 5 =Â 7

So True.

Explanation:

Checking 0 + 5 + 2 = 12 – 5, We get 0 + 5 + 2 = 7

and 12 – 5 = 7 as both equations values are same 7 = 7

so true.

Question 7.

Answer:

16 – 8 = 8Â â‰ Â 2 + 3 + 2 = 7

So False

Explanation:

Checking 16 – 8 and 2 + 3 + 2 we see 16 – 8 = 8

andÂ 2 + 3 + 2 = 7 as both equations are not equal

8 â‰ 7 so false.

Question 8.

**MP Number Sense**

Circle all of the equations that are false.

Answer:

Explanation:

Checking equations

a. 7 + 2 = 9 and 11 -2 = 9 both are equal so true we will not circle.

b. 3 , 12 – 8 = 4 as 3 â‰ Â 4, So false we will circle it.

c. 4 + 1 + 4 = 9 and 14 -6 = 12 as 9 â‰ 12 , So false we will circle it.

Question 9.

**Modeling Real Life**

You have 9 badges. You earn 3 more. Your friend has 5 badges and earns 7 more. Do you each have the same number of badges?

Answer:

Yes , each have the same number of badges.

Explanation:

Given I have 9 badges andÂ earn 3 more means 9 + 3 = 12,

My friend has 5 badges and earns 7 more means 5 + 7 = 12,

as both are having 12 badges Yes, I and my friend each

have same number of badges .

**Review & Refresh**

Question 10.

_____4____ + 2 = 6

Answer:

4 + 2 = 6

Explanation:

Given _______ + 2 = 6, Let us take missing number as X,

X + 2 = 6 means X = 6 – 2 = 4, X = 4 So missing number is 4,

the equation is 4 + 2 = 6.

Question 11.

____6____ + 3 = 9

Answer:

6 + 3 = 9

Explanation:

Given _______ + 3 = 9, Let us take missing number as X,

X + 3 = 9 means X = 9 – 3 = 6, X = 6 So missing number is 6,

the equation is 6 + 3 = 9.

### Lesson 5.6 Make True Equations

**Explore and Grow**

Complete the equation.

14 – 5 = 3 + __________

Answer:

14 – 5 = 3 + 6

Explanation:

Given 14 – 5 = 3 + ________ Let us take missing number as X,

First we see 14 – 5 on number line we move

5 steps left from 14 we get 9, means 3 + X = 9

so to get X we move on number line from 3 till 9

we got 6 units means X = 6,

therefore the true equation is 14 – 5 = 3 + 6.

**Show and Grow**

Question 1.

? + 6 = 10 – 3

? + 6 = __7______

___1_____ + 6 = ___7____

So, ____1____ + 6 = 10 – 3.

Answer:

1 + 6 = 10 – 3

Explanation:

Given _____ + 6 = 10 – 3

Now first we start from 10 and move 3 units back on the

number line we get 7, 10 – 3 = 7 now from 6 we will move

right till we get 7 we moved 1 unit means 6 + 1Â = 7,

So the true equation is 1 + 6 = 10 – 3.

Question 2.

12 – 9 = ? – 5

____3____ = ? – 5

____3____ = __8_____ – 5

So, 12 – 9 = ____8____ – 5.

Answer:

12 – 9 = 8 – 5

Explanation:

First we find 12 – 9 we start from 12 on number line

and move 9 units back we get 3 means 12 – 9 = 3 and ____ – 5 = 3,

Let us take missing number as X and X – 5 = 3 , therefore X = 3 + 5

on number line we move 3 units right from 5 we get 8,

making the true equation as 12 – 9 = 8 – 5.

**Apply and Grow: Practice**

Question 3.

? + 8 = 9 + 6

? + 8 = __15______

____7____ + 8 = _15___

So, ___7_____ + 8 = 9 + 6.

Answer:

_ + 8 = 9 + 6

_ + 8 = 15

7 + 8 = 15

So 7 + 8 = 9 + 6

Explanation :

Given ___ +Â 8 = 9 + 6, First we see 9 + 6 = 15 means

____ + 8 = 15 So let us take missing number as X ,

X + 8 = 15 therefore X = 15 – 8 = 7 making true equation as

7 + 8 = 9 + 6.

Question 4.

13 – 8 = ? – 6

___5_____ = ? – 6

____5____ = __11_ – 6

So, 13 – 8 = __11_ – 6.

Answer:

13 – 8 = _______ – 6

5 = ______ – 6

5 = 11 – 6

So 13 – 8 = 11 – 6

Explanation:

Given 13 – 8 = ____ – 6 means first we see 13 – 8 we get 5

means _____ – 6 = 5 let us take missing number as X

So X – 6 = 5, X = 5 + 6 = 11 making the true equation as

13 – 8Â = 11 – 6.

Question 5.

14 – 6 = ? + 2

___8_____ = ? + 2

____8____ = ___6____ + 2

So, 14 – 6 = ____6____ + 2.

Answer:

14 – 6 = _____ + 2

8 = ________ + 2

8 = 6 + 2

So 14 – 6 = 6 + 2

Explanation:

Given 14 – 6 is equal to ________ + 2 , first we see 14 – 6 we get

8 means _______ + 2 = 8 , let us take missing number as X

so 8 = X + 2 means X = 8 – 2 = 6 making the true equation as

14 – 6 = 6 + 2.

Question 6.

15 – ? = 3 + 3

15 – ? = __6______

15 – ___9_____ = ___6____

So, 15 – ____9____ = 3 + 3.

Answer:

15 – ___ = 3 + 3

15 – ___ =Â 6

15 – 9 = 6

15 – 9 = 3 + 3

Explanation:

Given 15 – ___ = 3 + 3 means first we see 3 + 3 = 6,

means 15 – __ = 6 , Let us take X as missing number means

15 – X = 6 we get X = 15 – 6 = 9Â therefore 15- 9 = 6,

making true equation as 15 – 9 = 3 + 3.

Question 7.

_____12_____ – 6 = 3 + 2 + 1

Answer:

12 – 6 = 3 + 2 + 1

Explanation:

Given __________ – 6 = 3 + 2 + 1 we see first

3 + 2 + 1 = 6 means ________ – 6 = 6,

let us take missing number as X , X – 6 = 6,

X = 6 + 6 = 12 making the true equation as 12 – 6 = 3 + 2 + 1.

Question 8.

6 + 4 + 4 = 6 + _______

Answer:

6 + 4 + 4 = 6 + 8

Explanation:

Given 6 + 4 + 4 = 6 + _______, First we add 6 + 4 + 4 we get 14

means 14 = 6 + ____, we will take missing number as X So that

6 + X = 14 , X = 14 – 6 = 8 making the true equation as 6 + 4 + 4 = 6 + 8.

Question 9.

**YOU BE THE TEACHER**

Newton says 2 makes the equation true. Is Newton correct? Show how you know.

Answer:

Yes, Newton is correct, as 7 + 2 = 9 = 11 – 2.

Explanation:

Given the equation as 7 + 2 = 11 -____ and newton says 2

makes the equation true, First we see 7 + 2 = 9

on number line we move 2 steps from 7 we get 9 so

now on number line we need to reach 9Â from 11

so we will move 2 steps back or left we reach 9 so 11 – 2 = 9,

Both equations are equal so Newton is true.

**Think and Grow: Modeling Real Life**

You catch 11 butterflies. 4 fly away. Your friend catches 3 butterflies.

How many more butterflies must your friend catch to have the same number as you?

Equation:

___11____ – ___4_____ = ____3___ + ?

____4______ butterflies

11 – 4Â = 3 + 4

My friend should catch 4 butterflies to have same number as me.

Explanation :

Given I catch 11 butterflies. 4 fly away means I have

11 – 4 = 7 butterflies now and my friend catches 3 butterflies

to have same number of butterflies let my friend should catch

X butterflies as 3 + X = 7 so X = 7 – 3 = 4 making equation as

11 – 4 = 3 + 4. Therefore my friend should catch 4 butterflies

to have same number as me.

**Show and Grow**

Question 10.

You catch 15 leaves. 6 of them blow away. Your friend catches 12 leaves and some of them blow away. Now you each have the same number of leaves. How many of your friendâ€™s leaves blow away?

Equation:

___15____ – ___6_____ = ___12____ – ?

______3____ leaves

15 – 6 = 12 – 3,

3 leaves of my friendâ€™s blow away.

Explanation:

Given I catch 15 leaves and 6 of them blow away means I have

15 – 6 = 9, Your friend catches 12 leaves and some of them blow away

lets take it as X numberÂ and given IÂ & my friend have same number of leaves now

12 – X = 9 , X = 12 – 9 = 3. So 3 leaves of my friendâ€™s blow away.

### Make True Equations Practice 5.6

Question 1.

12 – ? = 8 – 4

12 – ? = __4______

12 – ___8_____ = ___4____

So, 12 – ___4_____ = 8 – 4.

Answer:

12 – ____ = 8 – 4

12 – ___ = 4

12 – 8 = 4

So, 12 – 8 =Â 8 – 4

Explanation:

Given equation as 12 – ___ = 8 – 4, first we see 8 – 4

we get as 4, 8-4 = 4 So 12 – ___ = 4,

Let us take missing number as X so 12 – X = 4,

X = 12 – 4= 8, Now the true equation is 12 – 8 = 8 – 4.

Question 2.

7 + 9 = 8 + ?

____16____ = 8 + ?

_____16___ = 8 + ___8____

So, 7 + 9 = 8 + ___8_____ .

7 + 9 = 8 + ___

16 = 8 + ___

16 = 8 + 8

So, 7 + 9 = 8 + 8

Explanation:

Given equation as 7 + 9 = 8 + __,Â So first we see

7 + 9 = 16 means 8 + ___ = 16 ,Let us take X as missing number

8 + X = 16, X = 16 – 8Â = 8, Now the true equation is 7 + 9 = 8 + 8

Question 3.

4 + 3 = __________ – 7

Answer:

4 + 3 = 14 – 7

Explanation:

Given 4 + 3 = ___ – 7, first we see 4 + 3 we get 7,

means 7Â = ____ – 7, Let us take X as missing number

so 7 = X – 7, X = 7 + 7 = 14 making true equation as

4 + 3 = 14 – 7.

Question 4.

7 + _________ = 17 – 0

Answer:

7 + 10 = 17 – 0

Explanation:

Given as 7 + ___ = 17 – 0 first we see 17 – 0 we get 17

means 7 + ___ = 17, Now we take missing number as X,

7 + X = 17, X = 17 – 7 = 10 therefore the true equation is

7 + 10 = 17 – 0.

Question 5.

__________ + 20 = 8 + 10 + 2

Answer:

0 + 20 = 8 + 10 + 2

Explanation:

Given ____ + 20 = 8 + 10 + 2, We solve first 8 + 10 + 2

we get 20 soÂ ____ + 20 = 20, Let us take missing number as X,

X + 20 = 20 therefore X = 20 -20 = 0 , Making true equation as

0 + 20 = 8 + 10 + 2.

Question 6.

3 + 1 + 1 = 14 – __________

Answer:

3 + 1 + 1 = 14 – 9

Explanation:

Given 3 + 1 + 1 = 14 – ____, first we see 3 + 1 + 1 we get

5 and 14 – ___ = 5 , Let us take missing number as X, 14 – X = 5,

X = 14 – 5 = 9, making true equation as 3 + 1 + 1 = 14 – 9.

Question 7.

**YOU BE THE TEACHER**

Descartes says 5 makes the equation true. Is Descartes correct? Show how you know.

Answer:

17 – 9 â‰ 5 – 2 ,So Descartes is in correct.

Explanation:

Given equation is 17 – 9 = ___ – 2 and 5 makes the equation true ,

we see first 17 – 9 on number line we start from 17 and move 9 units back

we get 8 means 17 – 9 = 8, Now we take as per Descartes 5 – 2 on number line

we start from 5 and move 2 units back we get 3 which is not equal to 8,

So 17 – 9 â‰ 5 – 2 ,So Descartes is in correct.

Question 8.

Modeling Real Life

You catch 14 fireflies. You lose 8 of them. Your friend catches 11 fireflies and loses some of them.

Now you each have the same number of fireflies. How many fireflies does your friend lose?

___14_____ – ___8____ = ___11____ – ?

__5_____ fireflies

14 – 8 = 11 – 5, My friend loses 5 fireflies.

Explanation:

Given I catch 14 fireflies and lose 8 of them, means I have

14 – 8 = 6 with me, My friend catches 11 fireflies and

loses some of them let us take my friend loses X fireflies and

each have the same number of fireflies means 11 – X = 6, So

X = 11 – 6 = 5, making the equation as 14 – 8 = 11 – 5,

therefore my friend loses 5 fireflies.

**Review & Refresh**

Question 9.

color the rectangles.

Answer:

Explanation:

Given in the picture we have four shapes and we color the third shape

which is rectangle means a quadrilateral with four right angles,Â or a parallelogram

containing a right angle, so colored it with purple color.

Question 10.

color the squares.

Answer:

Explanation:

Given in the picture we have four shapes and we color the first shape

which is rectangle means a quadrilateral with four right angles,Â or a parallelogram

containing a right angle, so colored it with orange color.

### Lesson 5.7 Problem Solving: Subtraction within 20

**Explore and Grow**

Model the story.

There are 18 seagulls. Some of them fly away. There are 9 left. How many seagulls flew away?

_____9___ seagulls

Answer:

18 – 9 = 9

9 seagulls flew away.

Explanation:

Given there are 18 seagulls. Some of them fly away.

There are 9 left means out of 18 we are left with 9,

Let us take X number of them fly away means

18 – XÂ = 9, X = 18 – 9 = 9, We show in bar model as

total we have 18, 9 left and 9 seagulls flew away.

**show and Grow**

Question 1.

You have some stuffed animals. You give 3 away. You have 8 left. How many stuffed animals did you have to start?

Circle what you know.

Underline what you need to find.

Solve:

____11____ â—‹ ___3______ = ____8______

_____11_____ stuffed animals

Answer:

11 – 3 = 8

I have to start with 11 stuffed animals.

Explanation:

Given I have some stuffed animals and I give 3 away so have 8 left,

let I have X number of stuffed animals so From XÂ gave 3 so

X – 3 = 8 , X = 8 + 3 = 11 I know I gave 3 and left with 8 so I circled them,

I need to know how many stuffed animals I had so underlined it

as shown above in the picture. making equation as 11 – 3 = 8,

therefore I have to start with 11 stuffed animals.

**Apply and Grow: Practice**

Question 2.

A group of students are at an arcade. 8 of them leave. There are 3 left. How many students were at the arcade to start?

Circle what you know.

Underline what you need to find.

Solve:

Answer:

11 – 8 = 3,

11 students were at the arcade to start.

Explanation:

Given a group of students are at an arcade let us take as X,

8 of them leave and there are 3 left means X – 8 = 3,

X = 3 + 8 = 11 as shown in bar modelÂ 8 leave and 3 left total 11.

the equation is 11 – 8 = 3, I circled 8 and 3 I know, underlined 11

to find. So there are 11 students at the arcade to start.

Question 3.

You have 15 trucks. Your friend has 7. How many more trucks do you have?

_____8____ more trucks

Answer:

15 – 7 = 8

I have 8 more trucks.

Explanation:

Given I have 15 trucks and friend have 7, So more trucks I have than my

friend are 15 – 7 = 8, as shown in bar model I have 15 and friend have

7 and 8 more trucks I have than my friend.

Question 4.

**DIG DEEPER**

You have 16 stickers. Your friend has 7 fewer than you. Which bar model shows how many stickers your friend has?

Answer:

16 – 7 = 9

circled the equation shown in bar model which

shows how many stickers my friend has.

Explanation:

Given I have 16 stickers and my friend has 7 fewer than me

means my friend have 16 – 7 = 9 stickers ,So I have circled the

equation shown in bar model which shows how many stickers my friend has.

**Think and Grow: Modeling Real Life**

Your friends mask has 13 feathers. Your mask has 7 feathers. How many fewer feathers does your mask have?

Circle what you know.

Underline what you need to find.

Solve:

_________ – ________ = _________ fewer feathers

Answer:

Explanation:

Given friends mask has 13 feathers and my mask has 7 feathers,

So I have 13 – 7 = 6 feathers fewer in my mask as shown in the bar model

I have circled 13, 7 in the equation as I know how many my friend

and I have and underlined 6 so that how many fewer feathers my mask have.

**Show and Grow**

Question 5.

There are 12 party hats. There are 5 fewer noisemakers than party hats. How many noisemakers are there?

Circle what you know.

Underline what you need to find.

Solve:

____12_____ – ____5____ = ____7_____ noisemakers

Answer:

12 – 5 = 7

So there are 7 noisemakers.

Explanation:

Given there are 12 party hats and there are 5 fewer

noisemakers than party hats means 12 – 5 = 7 noisemakers

are available, as I know how many party hats and how many fewer

noisemakers are there so I circled them 12, 5 and I need to find how

many noisemakers are there so I underlined 7 in the equation.

### Problem Solving: Subtraction within 20 Practice 5.7

Question 1.

You have 12 erasers. Your friend takes some of them. You have 5 left. How many erasers does your friend take?

Circle what you know.

Underline what you need to find.

Solve:

Answer:

12 – 7 = 5

My friend have taken 7 erasers.

Explanation:

Given I have 12 erasers and my friend takes some of them

and I have 5 left. Let my friend takes X number so

12 – X = 5, X = 12 – 5 = 7 , So 12 – 7 = 5 as shown in bar model,

As I know 12 and 5 I have circled it and I need to find

how many my friend have taken so I have underlined 7 in the

equation.

Question 2.

You have 17 glitter pens. Your friend has 9 fewer than you. How many does your friend have?

_____8______ glitter pens

Answer:

17 – 9 = 8,

My friend have 8 glitter pens.

Explanation:

Given I have 17 glitter pens and my friend has 9 fewer than me,

Now let us take my friend have X number of glitter pens so

X = 17 – 9, X = 8 therefore my friend have 8 glitter pens.

Question 3.

**DIG DEEPER!**

A group of students are at a library. 6 of them leave. There are 7 left. Which part-part whole model shows how many students were at the library to start?

Answer:

Second One shows

13 number students were there at the library to start.

Explanation:

Given a group of students are at a library 6 of them leave and

there are 7 left. So a number of students were there at the library

to start are 6 + 7 = 13, so the second one part-part whole model shows

how many students were there at the library to start.

Question 4.

**Modeling Real Life**

Your friendâ€™s shirt has 14 buttons. Your shirt has 7 fewer. How many buttons does your shirt have?

___________ buttons

Answer:

14 – 7 = 7

My shirt have 7 buttons.

Explanation:

Given my friendâ€™s shirt has 14 buttons and my shirt has 7 fewer,

So my shirt have 14 – 7 = 7 buttons as shown in the bar model

therefore my shirt has 7 buttons.

**Review & Refresh**

Question 5.

There are 8 .

3 swim away.

How many are left?

____8____ – ___3____ = ___5_____

Answer:

8 – 3 = 5,

There are 5 seals left.

Explanation:

Given there are 8 seals and 3 of them swim away means

from 8 we will take 3 making equation as 8 – 3 = 5,

So there are 5 seal left.

### Chapter 5 Subtract Numbers within 20 Performance Task

Question 1.

You keep track of the number of honeybees and bumblebees you see.

a. How many more honeybees did you see on Monday than on Tuesday?

_____6_____ more honeybees

Answer:

12 – 6 = 6,

I have 6 more honeybees seen on Monday than on Tuesday.

Explanation:

Given track of the number of honeybees seen

in that on Monday it is 12 and on Tuesday it is 6,

more number of honeybees seen are 12 – 6 = 6 on Monday than on Tuesday.

b. How many fewer bees did you see on Monday than on Tuesday?

_____9_____ fewer bees

Answer:

14 – 5 = 9

9 fewer bees I have seen on Monday than on Tuesday.

Explanation:

Given track of the number of beesÂ seen

in that on Monday it is 5 and on Tuesday it is 14, now on Monday

it is less than TuesdayÂ so out of 14 we have seen 5 means

we have 14 – 5Â = 9Â fewer bees seen on Monday than on Tuesday.

c. How many bumblebees must you see on Wednesday so that the numbers of bees you see on

Tuesday and Wednesday are the same?

____14______ bumblebees

Answer:

14 number of bumblebees I must see on Wednesday so that the numbers

of bees I see on Tuesday and Wednesday are the same.

Explanation:

Given track of the number of bumblebees seen on Tuesday are 14, So

bumblebees I mustÂ see on Wednesday so that the numbers of bees I see on

Tuesday and Wednesday are the same are 14 only as both days is should be the same.

### Chapter 5 Subtract Numbers within 20 Chapter Practice

### Count Back to Subtract within 20 Homework & Practice 5.1

Question 1.

11 – 3 = ____8______

Answer:

11 – 3 = 8

Explanation:

We subtract 11 – 3 = 9, on number line we start at 11 and

move 3 steps back or left we get 8.

Question 2.

13 – 4 = _____9_____

Answer:

13 – 4 = 9

Explanation:

We subtract 13 – 4 = 9, on number line we start at 13 and

move 4 steps back or left we get 9.

Question 3.

____12______ = 15 – 3

Answer:

12 = 15 – 3

Explanation:

We subtract 15 – 3 = 12, on number line we start at 15 and

move 3 steps back or left we get 12.

Question 4.

____8______ = 16 – 8

Answer:

8 = 16 – 8

Explanation:

We subtract 16 – 8 = 8, on number line we start at 16 and

move 8 steps back or left we get 8.

### Use Addition to Subtract within 20 Homework & Practice 5.2

Question 5.

11 – 9 = ?

Think 9 + ___2____ = 11

So, 11 – 9 = ____2_____ .

Answer:

9 + 2 = 11

11 – 9 = 2

Explanation:

First we move from 9 on number line and start moving till

11 we count how many units right we have moved we get

2 units, so 9 + 2 = 11 or we start at 11 on number line and

move 9 steps back or left we get 2, 11 – 9 = 2.

Question 6.

13 – 8 = ?

Think 8 + __5_____ = 13

So, 13 – 8 = ____5_____ .

Answer:

8 + 5 = 13

13 – 8 = 5

Explanation:

First we move from 8 on number line and start moving till

13 we count how many units right we have moved we get

5 units, so 8 + 5 = 13 or we start at 13 on number line and

move 8 steps back or left we get 5 so 13 – 8 = 5.

Question 7.

____13_____ = 20 – 7

Answer:

13 + 7 = 20

20 – 7 = 13

Explanation:

First we move from 13 on number line and start moving till

20 we count how many units right we have moved we get

7 units, so 13 + 7 = 20 or we start at 20 on number line and

move 7 steps back or left we get 13 so 20 – 7 = 13.

Question 8.

____9____ = 12 – 3

Answer:

9 + 3 = 12

9 = 12 – 3

Explanation:

First we move from 9 on number line and start moving till

12 we count how many units right we have moved we get

3 units so 9 + 3 = 12 or we start at 12 on number line and

move 3 steps back or left we get 9 so 12 – 3 = 9.

### Subtract 9 Homework & Practice 5.3

Get to 10 to subtract

Question 9.

15 – 9 = ?

15 – ____5____ = 10

10 – _____4_____ = ____6_____

So, 15 – 9 = ___6_____

Answer:

15 – 5 = 10

10 – 4 = 6

So, 15 – 9 = 6

Explanation:

We have 2 counters in counter one we have 10 circles

and in the next counter we have 5 circles so in total we have 15,

First we see out of 15 if we consider counter-2 we have 5 strike outs

means 15 – 5 = 10 we got 10 in counter-1 and if we see first counter

we have 4 strike outs 10 – 4 = 6, So total number of circles strike out

from 2-counters are 5 + 4 = 9, So making equation as 15 – 9 = 6.

Question 10.

17 – 9 =?

17 – ___7_____ = 10

10 – _____2_____ = ____8_____

So, 17 – 9 = ____8____

Answer:

17 – 7 = 10

10 – 2 = 8

So, 17 – 9 = 8

Explanation:

We have 2 counters in counter one we have 10 circles

and in next counter we have 7 circles so in total we have 17,

First we see out of 17 if we consider counter-2 we have 7 strike outs

means 17 – 7 = 10 we got 10 in counter-1 and if we see first counter

we have 2 strike outs 10 – 2 = 8, So total number of circles strike out

from 2-counters are 7 + 2 = 9, So making equation as 17 – 9 = 8.

### Get to 10 to subtract Homework & Practice 5.4

Get to 10 to subtract

Question 11.

12 – 7 = ?

12 – ____2_____ = 10

10 – ____5______ = ____5_____

So, 12 – 7 = _____5_____ .

Answer:

12 – 2 = 10

10 – 5 = 5

So, 12 – 7 = 5.

Explanation:

We have 2 counters in counter one we have 10 circles

and in the next counter, we have 2 circles so in total we have 12,

First, we see out of 12 if we consider counter-2 we have 2 strike outs

means 12 – 2 = 10 we got 10 in counter-1 and if we see first counter

we have 5 strike outs 10 – 5 = 5, So the total number of circles strike out

from 2-counters are 5 + 2 = 7, So making equation as 12 – 7 = 5.

Question 12.

17 – 8 = ?

17 – ____7____ = 10

10 – ____1_____ = ___9_____

So, 17 – 8 = ___9____ .

Answer:

17 – 7 = 10

10 – 1 = 9

So, 17 – 8 = 9

Explanation:

We have 2 counters in counter one we have 10 circles

and in the next counter, we have 7 circles so in total we have 17,

First, we see out of 17 if we consider counter-2 we have 7 strike outs

means 17 – 7 = 10 we got 10 in counter-1 and if we see the first counter

we have 1 strike outs 10 – 1 = 9, So the total number of circles strike out

from 2-counters are 7+ 1 = 8, So making equation as 17 – 8 = 9.

### More True or False Equations Homework & Practice 5.5

Is the equation true or false?

Question 13.

Answer:

8 + 3 + 8Â = 13 + 6

19 = 19 ,

So True.

Explanation:

We take 8 + 3 + 8 means adding 8 to 3 and

again adding 8 we get 8 + 3 + 8 = 19

Now 13 + 6 is 19 so both sides are equal therefore

8 + 3 +8 = 13 + 6 is True.

Question 14.

Answer:

16 – 8 = 6 + 2

8 = 8

So True.

Explanation:

We take 16 – 8 means subtracting 8 from 16

we get 16 – 8 = 8,

Now 6 + 2 is 8 so both sides are equal therefore

16 – 6Â = 6 + 2Â is True.

14 – 7 = 7 â‰ 12 – 9 = 3

7 â‰ 3

So False

Explanation:

We take 14 – 7 means subtracting 7 from 14 we get 14 – 7 = 7

and 12 -9 means subtractingÂ 9 from 12 we get 12 – 9 = 3,

If we see both sides they are not equal as 7 â‰ 3,

So 14 – 7 = 12 -9 is False.

### Make True Equations Homework & Practice 5.6

Question 16.

11 – 7 = 10 – ?

___4____ = 10 – ?

___4____ = 10 – ___6_____

So, 11 – 7 = 10 – ___6_____ .

Answer:

11 – 7 = 10 – ____

___4____ = 10 – ___

___4____ = 10 – ___6_____

So, 11 – 7 = 10 – ___6_____ .

Explanation :

Given 11 – 7 = 10 –Â ___, First we see 11 – 7 = 4 means

10 – ___ = 4 So let us take missing number as X ,

10 – X = 4 therefore X = 10 – 4 = 6 making true equation as

11 – 7 = 10 – 6.

Question 17.

2 + 0 + 6 = ? – 5

____8____ = ? – 5

____8____ = ___13___ – 5

So, 2 + 0 + 6 = ____13____ – 5

Answer:

2 + 0 + 6 = ____ – 5

____8____ = ___ – 5

____8____ = ___13___ – 5

So, 2 + 0 + 6 = ____13____ – 5

Explanation :

Given 2 + 0 + 6 = ___- 5 , First we see 2 + 0 + 6 = 8 means

___ – 5 = 8 So let us take missing number as X ,

X – 5 = 8 therefore X = 8 + 5 = 13 making true equation as

2 + 0 + 6 = 13 – 5.

### Problem Solving: Subtraction within 20 Homework & Practice 5.7

Question 18.

There are 13 people on a train. Some of them exit. There are 5 left. How many people exit the train?

Circle what you know.

Underline what you need to find.

Solve:

_____13_____ â—‹- ____8______ = _____5______, ____8_____ people

Answer:

13 – 8 = 5

8 people exit the train.

Explanation:

Given there are 13 people on a train, some of them exit and

there are 5 left. On number line we start at 13 and move 5 units

left or back so we reach at 8 means 8 people exit the train,

As we know 13 people are on the train and 5 left we circle

in the equation and we need to know how many exit the train,

so we underline 8 in the equationÂ 13 – 8 =5 above.

Question 19.

A group of students are at a museum. 8 of them leave. There are 7 left. How many students were there to start ?

_____15_______ Students

Answer:

8 + 7 = 15 or 15 – 8 = 7

There were 15 students at the start.

Explanation:

Given a group of students are at a museum, 8 of them leave,

There are 7 left. We start from 8 and move 7 units rights we get 15,

8 + 7 = 15, So there are 15 students at the start.

Question 20.

You and a friend play basketball. Your friend scores 17 points. You score 8 fewer. How many points do you score?

_____9_______ points

Answer:

17 – 8 = 9

I scored 9 points.

Explanation:

Given I and a friend play basketball my friend scores 17 points

and I score 8 fewer. On the number line, I start from 17 and move

8 steps left I reach at 9 means 17 – 8 = 9, so I scored 9 points.

*Conclusion:*

Students can find Big Ideas Math Solution Keys for all the chapters at one place. All the Concepts in the Big Ideas Math Answer are prepared by the subject experts. Resolve all your queries and assess your preparation standard using the Common Core Big Ideas Math Grade 1 Answer Key.