# Big Ideas Math Answers Grade 1 Chapter 5 Subtract Numbers within 20

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

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

Chapter 5 Subtract Numbers within 20

### 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.

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.

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______

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____

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______

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_____

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____

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_____

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_____

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_____

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_____

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______

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

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

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_____
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

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____

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____

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_____

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_______

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______

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_____

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

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

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_____

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

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_____
6 + 2 = 8

Explanation :
The addition equation is 6 + 2 = 8,
We add 2 to 6 we get 8.

Question 12.
4 + 3 = ___7_____
4 + 3 = 7

Explanation :
The addition equation is 4 + 3 = 7,
We add 3 to 4 we get 7.

Question 13.
8 + 2 = ___10____
8 + 2 = 10

Explanation :
The addition equation is 8 + 2 = 10,
We add 2 to 8 we get 10.

Question 14.
5 + 4 = ____9___
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.

____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____ .

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____ .

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____ .

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____ .

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____ .

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_____

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

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?

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

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

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____.

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____.

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_____

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

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?

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

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______
10 – 9 = 1

Explanation :
The subtraction equation is 10 – 9 = 1,
We subtract 9 from 10 we get 1.

Question 8.
9 – 9 = ____0______
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_____
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___
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_____
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____ .

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_____

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?

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_____ .

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____ .
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_____ .

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?

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

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.

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.

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______

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_______
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_____ .
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_____ .

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____ .

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?

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

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____ .
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_____ .
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____ .

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____ .

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?

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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:

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:

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.

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.

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.

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.

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.

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.

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.

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.

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?

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
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
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 + __________

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.

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.

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.
_ + 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.
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.
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.
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
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 + _______
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.

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.
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
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
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
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 – __________
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.

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.

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.

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

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

11 – 3 = 8

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,

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:

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

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?

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

Circle what you know.
Underline what you need to find.
Solve:

_________ – ________ = _________ fewer feathers

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

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:

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

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?

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

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_____
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

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
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
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.

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

Question 1.

11 – 3 = ____8______

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_____

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

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

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_____ .

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_____ .

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

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

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_____
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____
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_____ .
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____ .

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.

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.

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.

Question 15.

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_____ .

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
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

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

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

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.

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