Go through the enVision Math Common Core Grade 1 Answer Key Topic 3 Addition Facts to 20: Use Strategies regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 3 Addition Facts to 20: Use Strategies

Envision STEM Project: What Do They Eat?
Find Out Talk to friends and relatives about the things different animals eat. Ask how their teeth help them survive and meet their needs.

Journal: Make a Book Show what you found out. In your book, also:

• Draw pictures of animals and what they eat.
• Make up and solve addition problems about animals and what they eat.

Answer :
Carnivores are animals that eat meat. They have canines, which are sharp teeth used to tear meat.
Herbivores are animals that only eat plants. They have molars that are strong, flat, and perfect for grinding up plant matter.
Animals which eat plants are :

Animals which eat meat are :

Number of herbivore animals in the above figure = 9
Number of Carnivore animals in the above figure = 14
Total Number of Animals = 14 + 9 = 23 animals .

Review What You Know

Vocabulary

Question 1.
Circle the problem that
shows a double.
5 + 5 = 10
5 + 4 = 9
5 + 3 = 8
Answer:

Explanation :
When both the addends are equal then sum is double the addend .

Question 2.
Circle the word that tells which strategy can be used to add the numbers.
7 + 8 = ?
doubles
near doubles
count back
Answer:
7 + 8 = 15 .

Explanation :
Doubles plus 1 is a strategy used to add two consecutive numbers that is, when they are next to each other. We simply add the smaller number twice or double it and then, add 1 to it, to get the final result. Here consecutive numbers 7 and 8 have been added using the doubles plus one strategy
7 + 7 + 1 = 14 + 1  = 15 which is near to doubles .

Question 3.
Circle the sum in the problem below.
7 + 4 = 11
Answer:

Explanation :
11 is the sum
7 and 4 are addends .

Addition and Subtraction

Question 4.
Robin has 3 stamps. Joe gives her 4 stamps. How many stamps does Robin have now?
___ stamps
Answer:
Number of Stamps with Robin = 3 Stamps
Number of Stamps Joe gave to Robin = 4 Stamps
Total Number of Stamps Robin have now = 3 + 4 = 7 Stamps .

Question 5.
Jen has 8 cat treats. She feeds some treats to her cat. Jen has 4 treats left. How many treats did Jen feed her cat?
___ treats
Number of Cat treats with Jen = 8 treats
Number of treats left with Jen now = 4 treats
Total Number of treats fed to her cats = 8 – 4 = 4 treats .

Doubles Facts

Question 6.
Solve this doubles fact.
3 + 3 = ___
Answer:
3 + 3 = 6
Explanation :
When both the addends are equal then sum is double the addend .

Pick a Project

PROJECT 3A
Can you see the gecko? Project: Create an Animal Model

Answer :

Explanation :
The above image contains the Animal Model of Dinosaur and Cat .
Cut the paper into given shapes and fold them we get the given shapes .

PROJECT 3B
Would you like to live on a boat? Project: Make a Sailboat Model

Answer :

This are the different models of sail boats .

PROJECT 3C
What is your favorite ride? Project: Make a Poster about Roller Coasters

Answer :

3-ACT MATH PREVIEW

Math Modeling
Go for a Spin

Before watching the video, think: What was the last game you played? What kind of game was it? Video games, board games, and card games all have something in common. They need someone to test that the game is fun to play, and that it is fair.

Answer :
The last game which I played was Block puzzle . it is a puzzle game helps in building the blocks and clearing them . It is a mobile Game.

Lesson 3.1 Count On to Add

Solve & Share

Abby has 5 cubes. Salina gives her 7 more cubes. How many cubes does Abby have now? Show your thinking.

Visual Learning Bridge

Convince Me!
How do you know where to start counting on? How do you know how many to count on?
Answer:
Whatever may be the order of the addends but the sum does not change .
in the below figure we notice 5 + 7 = 12 and 7 + 5 = 12
The order of the addends 5 and 7 is interchanged and but the sum is the same .
that means order of addends doesn’t change the sum .

Explanation :
Order property of addition refers to two sets of addition in which numbers interchange or switch their places the answer remain the same. That means if the numbers are same and if you add any number first answer remains the same. For addition you can change the places of numbers.

Guided Practice

Use the number line to count on. Write each sum.

Question 1.

Answer:

Explanation :
Find 9 on number line. Then count on 7 more to add 9 + 7 = 16
Start at 9 and make 7 jumps . You land on 16 .

Question 2.
9 + 9 = ____

Answer:

Explanation :
Find 9 on number line. Then count on 9 more to add 9 + 9 = 18
Start at 9 and make 9 jumps . You land on 18 .

Independent Practice

Use a number line. Count on to find each sum.

Question 3.
7 + 4 = ___
Answer:
7 + 4 = 11

Explanation :
Find 7 on number line. Then count on 4 more to add 7 + 4 = 11
Start at 7 and make 4 jumps . You land on 11 .

Question 4.
6 + 8 =
Answer:
6 + 8 = 14

Explanation :
Find 6 on number line. Then count on 8 more to add 6 + 8 = 14
Start at 6 and make 8 jumps . You land on 14 .

Question 5.
9 + 4 = ____
Answer:

Explanation :
Find 9 on number line. Then count on 94more to add 9 + 4 = 13
Start at 9 and make 4 jumps . You land on 13.

Question 6.
9 + 6 = ___
Answer:
9 + 6 = 15

Explanation :
Find 9 on number line. Then count on 9 more to add 9 + 6 = 15
Start at 9 and make 6 jumps . You land on 15 .

Question 7.
7 + 7 = ___
Answer:
7 + 7 = 14

Explanation :
Find 7 on number line. Then count on 4 more to add 7 + 7 = 14
Start at 7 and make 7 jumps . You land on 14 .

Question 8.
9 + 8 = ___
Answer:
9 + 8 = 17

Explanation :
Find 9 on number line. Then count on 8 more to add 9 + 8 = 17
Start at 9 and make 8 jumps . You land on 17 .

Question 9.
6 + 4 = ___
Answer :
6 + 4 = 10

Explanation :
Find 6 on number line. Then count on 4 more to add 6 + 4 = 10
Start at 6 and make 4 jumps . You land on 10 .

Question 10.
8 + 5 = ___
Answer:
8 + 5 = 13

Explanation :
Find 8 on number line. Then count on 5 more to add 8 + 5 = 13
Start at 8 and make 5 jumps . You land on 13 .

Question 11.
3 + 9 = ___
Answer :
3 + 9 = 12

Explanation :
Find 3 on number line. Then count on 9 more to add 3 + 9 = 12
Start at 3 and make 9 jumps . You land on 12 .

Solve. Use a number line to count on.

Question 12.
envision® STEM
Kim works at a zoo. She feeds the big cats 9 pounds of meat. She feeds the tortoises 7 pounds of leaves and berries.
How many pounds of food does Kim feed the animals?
___ pounds of food
Answer:
Quantity of food fed to big cats = 9 pounds
Quantity of food fed to tortoises = 7 pounds
Total Quantity of food fed to Animals = 9 + 7 = 16 pounds .
Explanation :

Explanation :
Find 9 on number line. Then count on 7 more to add 9 + 7 = 16
Start at 9 and make 7 jumps . You land on 16 .

Problem Solving

Solve the problems below. Use a number line.

Question 13.
Reasoning
Scott walks 6 blocks. Then he walks 3 more blocks. Write the numbers that will help find out how many blocks Scott walked in all.
Start at ___. Count on ___ more.
6 + 3 = ___
Answer:
Number of Blocks Scott walk = 6
Number of more blocks he walk = 3
Total Number of blocks Scott walk = 6 + 3 = 9 blocks .
Explanation :

Find 6 on number line. Then count on 4 more to add 6 + 3 = 9
Start at 6 and make 3 jumps . You land on 9 .

Question 14.
Reasoning
Ramona mails 3 letters. Then she mails 8 more letters. Write the numbers that will help find out how many letters Ramona mailed in all.
Start at ____. Count on ___ more.
3 + 8 = ___
Answer :
Number of mails Ramona mails = 3
Number of more mails Ramona mails = 8
Total Number of mails Ramona mails = 3 + 8 = 11 letters
Explanation :

Find 3 on number line. Then count on 8 more to add 3 + 8 = 11
Start at 3 and make 8 jumps . You land on 11 .

Question 15.
Higher Order Thinking
Write and solve an addition story problem.

Answer:
Samy has 3 balls . His Brother Gaurish gave 9 more balls to him . How many balls Samy have now ?
Explanation :
Number of balls with Samy = 3
Number of Balls gaurish give to samy = 9
Total Number of balls samy have now = 3 + 9 = 12 balls .

Find 3 on number line. Then count on 9 more to add 3 + 9 = 12
Start at 3 and make 9 jumps . You land on 12 .

Question 16.
Assessment Practice
Solve 5 + 9 = ? on the number line. Show your work.

Answer:

Find 5 on number line. Then count on 9 more to add 5 + 9 = 14
Start at 5 and make 9 jumps . You land on 14 .

Lesson 3.2 Count On to Add Using an Open Number Line

Solve & Share

Arnie runs 6 miles on Thursday. He runs 5 more miles on Friday. How many miles did Arnie run in all? Use the number line to show how you know.

Visual Learning Bridge

Convince Me!
What number is always included on an open number line when you add?
Answer:
The number which is included always on the number line is the addend 6 .
Number of miles Arnie ran on Thursday = 6 miles .
Number of miles miles ran on Friday = 5 miles .
Total Number of Miles ran by Arnie = 6 + 5 = 11 miles

Guided Practice
Use the open number line to solve. Practice Show your work.

Question 1.

Answer:

Explanation :
You can also break apart adding 3 and 2 is one way to add 5 more .

Question 2.
6 + 2 = ___

Answer:

Explanation :
Counting on by 1 is one way to add 2 more .
Start at 6 and Then count on 2 more .You land on 8 which is the sum .

Independent Practice

Find each sum. Use the open number line to show your work.

Question 3.
4 + 7 = ___

Answer:
4 + 7 = 11
4 + 4 + 3 = 11

Explanation :
You can also break apart adding 4 and 3 is one way to add 11 more .

Question 4.
8 + 8 = ___

Answer:
8 + 8 = 16

Explanation :
You can also break apart adding 4 and 4 is one way to add 8 more .

Question 5.
6 + 6 = ___

Answer:
6 + 6 = 12

Explanation :
You can also break apart adding 3 and 3 is one way to add 6 more .

Question 6.
9 + 7 = ___

Answer:
9 + 7 = 16

Explanation :
You can also break apart adding 4 and 3 is one way to add 7 more .

Question 7.
Vocabulary
Solve the problem.
Show your work on the open number line below.
8 + 6 = ___

Answer:
8 + 6 = 14

Explanation :
You can also break apart adding 2 and 4 is one way to add 6 more .
The sums after adding the addends are included on the number line .

Problem Solving

Solve each problem. Choose a tool to help. Solving Write an equation to match.

Question 8.
Use Tools
Marco rides his bike 7 miles. Then he rides 9 more miles. How many miles did Marco ride in all?

__ miles
Answer:
Number of miles Marco rides = 7 miles .
Number of more miles he rides = 9 miles .
Total Number of miles Marco rides = 7 + 9 = 16 miles .
Therefore, Macro rides 16 miles in all .

Question 9.
Use Tools
Ana reads 10 books in January. She reads 10 books in February. How many books did Ana read in all?
___ books
Answer:
Number of Books Read by Ana in January = 10 books
Number of Books Read by Ana in February = 10 books
Total Number of Books read in all by Anna = 10 + 10 = 20 books .
Therefore, Anna reads 20 books in all .

Question 10.
Higher Order Thinking
Kate has 8 roses. She picks some more roses. Now Kate has 17 roses. How many roses did Kate pick? Use words or pictures to explain how you know.
Answer:
Number of roses with Kate =  8
Number of Roses picked = x
Number of Roses with Kate now = 17
Number of Roses picked = 8 + x = 17 .

Here number of jumps represent number of roses picked.
Here it starts at 8 and  lands at 17 that means 9 jumps are required to land at 17 so 9 roses are picked .

Question 11.
Assessment Practice
Find the sum. Show your work on the open number line below.
9 + 6 = ___

Answer:
9 + 6 = 15

Explanation :
You can also break apart adding 3 and 3 is one way to add 6 more .

Lesson 3.3 Doubles

Solve & Share

Carlos and Alisa each have the same number of books. They each have more than 5 books. How many books do they have in all? Show your thinking below.

Visual Learning Bridge

Convince Me!
Becca shows 6 + 7 with cubes and says it is not a doubles fact. Is she correct? How do you know?

Guided Practice

Decide if the cubes show a doubles fact. Circle your answer. Then write an equation to match the cubes.

Question 1.

Answer:

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. but here 5 and 6 are two different numbers . So, it is not a Double Fact .

Question 2.

Answer:

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. Here 4 is added to itself so, it is a double fact .

Independent Practice

Decide if each set of cubes shows a doubles fact. Circle your answer. Write an equation to match the cubes.

Question 3.

Answer:

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. Here 6 is added to itself so, it is a double fact .

Question 4.

Answer:

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. but here 8 and 9 are two different numbers . So, it is not a Double Fact .

Question 5.

Answer:

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. Here 7 is added to itself so, it is a double fact .

Question 6.

Answer:

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. Here 10 is added to itself so, it is a double fact .

Question 7.
0 + 0 =
Answer:

Explanation :
Any number added to 0 gives the number itself .

Question 8.
= 9 + 9
Answer:
18 = 9 + 9

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. Here 9 is added to itself so, it is a double fact .

Question 9.
8 + 8 =
Answer:
8 + 8 = 16

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. Here 8 is added to itself so, it is a double fact .

Question 10.
5 + 5 =
Answer:
5 + 5 = 10

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. Here 5 is added to itself so, it is a double fact .

Problem Solving
Draw cubes to help you solve each number story. Then write an equation to match the problem.

Question 11.
Make Sense
Andrew and his sister each pick 10 flowers. How many flowers did they pick in all?

____ flowers
Answer:
Number of Flowers picked by Andrew = 10 flowers
Number of Flowers picked by Andrew sister = 10 flowers
Total Number of flowers picked = 10 + 10 = 20 flowers

Question 12.
Make Sense
Pearl and Charlie each buy 5 books. How many books did they buy in all?

___ books
Answer:
Number of Books Pearl bought = 5 books
Number of Books Charlie bought = 5 books
Total Number of books bought in all = 5 + 5 = 10 books .

Question 13.
Higher Order Thinking
A hockey team plays 2 games. The team scores the same number of goals in each game. The team scores 12 goals in all. How many goals did the team score in each game?

___ goals in each game
Answer:
Total Score in 2 games = 12 .
Number of games = 2
Score of two games is same so Team score = 12 = 6 + 6

Question 14.
Assessment Practice
Which equations show a doubles fact? Choose two that apply.

Answer:

Explanation :
Double Fact means To get a double of a number, we add the same number to itself.

Lesson 3.4 Doubles Plus

Solve & Share

Carlos and I each pick 5 strawberries. What doubles fact shows how many strawberries we have in all? If I pick I more strawberry, how could you find how many strawberries in all?

Visual Learning Bridge

Convince Me!
How does knowing 7 + 7 help you find 7 + 8?
Answer :

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 8 is one more than 7. So, we can write 8 as 7 + 1.
We already know the double of 7 is 14.
So, the required sum is one more than double. That is 15. Therefore, 7 + 8 = 15.

Guided Practice
Add the doubles. Then use the doubles facts to help you solve the doubles-plus facts.

Question 1.

Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 7 is two more than 5. So, we can write 7 as 5 + 2.
We already know the double of 5 is 10.
So, the required sum is two more than double. That is 12. Therefore, 5 + 7 = 12.

Question 2.

___ + ____ = ___
So, 8 + 9 = ___.
Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 9 is one more than 8. So, we can write 9 as 8 + 1.
We already know the double of 8 is 16.
So, the required sum is one more than double. That is 17. Therefore, 8 + 9 = 17.

Independent Practice

Add the doubles. Then use the double facts to help you solve the doubles-plus facts.

Question 3.

Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 8 is one more than 7. So, we can write 8 as 7 + 1.
We already know the double of 7 is 14.
So, the required sum is one more than double. That is 15. Therefore, 8 + 7 = 15.

Question 4.

Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 6 is two more than 4. So, we can write 6 as 4 + 2.
We already know the double of 4 is 8.
So, the required sum is two more than double. That is 10. Therefore, 4 + 6 = 10.

Question 5.

Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 6 is one more than 5. So, we can write 6 as 5 + 1.
We already know the double of 5 is 10
So, the required sum is one more than double. That is 11. Therefore, 5 + 6 = 11

Question 6.

Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 10 is one more than 9. So, we can write 10 as 9 + 1.
We already know the double of 9 is 18.
So, the required sum is one more than double. That is 19. Therefore, 9 + 10 = 19.

Question 7.

Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 7 is one more than 6. So, we can write 7 as 6 + 1.
We already know the double of 6 is 12.
So, the required sum is one more than double. That is 13. Therefore, 6 + 7 = 13

Question 8.

Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 9 is two more than 7. So, we can write 9 as 7 + 2.
We already know the double of 7 is 14.
So, the required sum is two more than double. That is 16. Therefore, 9 + 7 = 16.

Use a doubles-plus fact to write an equation for the problem. Then draw a picture to match the equation.

Question 9.
Higher Order Thinking
Max has some blue marbles. Tom has some red marbles. Tom has 2 more marbles than Max. How many marbles do they have in all?

Answer:
Number of blue marbles with Max = 5 ( taken )
Tom has 2 more marbles than Max So,
Number of Red marbles with tom = 5 + 2 = 7
Total Marble in all = 5 + 7 = 12 .

Problem Solving

Solve each problem below. Then write an equation to match the problem.

Question 10.
Reasoning
Carrie and Pete each pick 7 cherries. Then Pete picks more. How many cherries do they have in all?

Answer:
Number of cherries Carrie pick = 7 cherries
Number of Cherries Pete pick = 7 cherries .
Pete picks more that means more than 7 Pete picks the cherries so, take Pete picks 2 more .
Number of cherries Pete picks = 7 + 2 = 9 cherries.
Total Number of cherries in all = 7 + 9 = 16 cherries .
Therefore, Total Number of cherries in all = 16 cherries .

Question 11.
Reasoning
Manny and Pam each buy 5 apples. Then Pam buys 2 more. How many apples do they have in all?

Answer:
Number of Apples bought by Manny = 5 apples
Number of apples Pam bought = 5 apples
Number of apples bought by pam later = 2 apples .
Total Number of apples with pam = 5 + 2 = 7 apples .
Total Number of apples in all = 5  + 7 = 5 + 5 + 2 = 10 + 2 = 12 apples .
Therefore, Total Number of apples in all = 12 apples .

Question 12.
Higher Order Thinking
Laura has to solve 9 + 8. Explain how she could use 8 + 8 to find the sum.
Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 9 is one more than 8. So, we can write 9 as 8 + 1.
We already know the double of 8 is 16.
So, the required sum is one more than double. That is 17. Therefore, 9 + 8 = 17.

Question 13.
Assessment Practice
Use a doubles fact to help you find the missing addend.
8 + __ = 17
A. 8
B. 9
C. 7
D. 1

Answer:
The Missing Addend is 9 option – B

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 9 is one more than 8. So, we can write 9 as 8 + 1.
We already know the double of 8 is 16.
So, the required sum is one more than double. That is 17. Therefore, 8 + 9 = 17.

Lesson 3.5 Make 10 to Add

Solve & Share

Andy says that he can find 9 + 5 by starting with 9 + 1 = 10. What do you think about Andy’s way? Show your work and explain.

Visual Learning Bridge

Convince Me!
How would you make 10 to find the sum of 9 + 4?
Answer :

Guided Practice
Draw counters to make 10. Then write the sums.

Question 1.

Answer:

Explanation :
Make 10 to add
we have 7 counters in 7 so 3 counters are left to make it 10 .
So, move 3 counters from 6 to join 7.
now, we have 10 and 3 .
Therefore 10 + 3 = 13 and 7 + 6 = 13 both are same .

Question 2.

Answer:

Explanation :
Make 10 to add
we have 8 counters in 8 so 2 counters are left to make it 10 .
So, move 2 counters from 6 to join 8 .
now, we have 10 and 4 .
Therefore 10 + 4 = 14 and 8 + 6 = 14 both are same .

Independent Practice

Draw counters to make 10. Then write the sums.

Question 3.

Answer:

Explanation :
Make 10 to add
we have 7 counters in 7 so 3 counters are left to make it 10 .
So, move 3 counters from 8 to join 7 .
now, we have 10 and 5 .
Therefore 10 + 5 = 15 and 7 + 8 = 15 both are same .

Question 4.

Answer:

Explanation :
Make 10 to add
we have 9 counters in 9 so 1 counter is left to make it 10 .
So, move 1 counters from 6 to join 9 .
now, we have 10 and 5 .
Therefore 10 + 5 = 15 and 9 + 6 = 15 both are same .

Question 5.

Answer:

Explanation :
Make 10 to add
we have 7 counters in 7 so 3 counters are left to make it 10 .
So, move 3 counters from 7 to join 7 .
now, we have 10 and 4 .
Therefore 10 + 4 = 14 and 7 + 7 = 14 both are same .

Question 6.

Answer:

Explanation :
Make 10 to add
we have 6 counters in 6 so 4 counters are left to make it 10 .
So, move 4 counters from 5 to join 6 .
now, we have 10 and 1 .
Therefore 10 + 1 = 11 and 6 + 5 = 11 both are same .

Question 7.

Answer:

Explanation :
Make 10 to add
we have 4 counters in 4 so 6 counters are left to make it 10 .
So, move 6 counters from 8 to join 4 .
now, we have 10 and 2 .
Therefore 10 + 2 = 12 and 4 + 8 = 12 both are same .

Question 8.

Answer:

Explanation :
Make 10 to add
we have 9 counters in 9 so 1 counter is left to make it 10 .
So, move 1 counters from 5 to join 9 .
now, we have 10 and 4 .
Therefore 10 + 4 = 14 and 9 + 5 = 14 both are same .

Problem Solving
Draw counters to help you solve each problem below. Use 2 different colors.

Question 9.
Model
Carlos sees 7 yellow birds in a tree. Then he sees 6 white birds. How many birds does Carlos see in all?

__ birds
Answer:
Number of Yellow Birds seen by Carlos = 7
Number of White birds seen by Carlos = 6
Total Number of Birds seen by Carlos = 7 + 6 = 10 + 3 = 13 .

Question 10.
Model
Emily picks 8 red flowers. Then she picks 8 yellow flowers. How many flowers does Emily pick in all?

___ flowers
Answer:
Number of red flowers Emily have = 8
Number of yellow flowers Emily have = 8
Total number of flowers Emily have in all = 8 + 8 = 10 + 6 = 16 flowers .

Question 11.
Higher Order Thinking
Look at the model. Complete the equations to match what the model shows.

Answer:

Explanation :
we have 9 counters in 9 and one counter is moved from 6 to join 9 to make it 10 ,
so we have 10 and 5 = 15 is the sum.
so, 9+ 6 = 15 .

Question 12.
Assessment Practice
Which number belongs in the ?

Answer:

Explanation :
10 + 1 = 11
a. 6 + 16 = 22
b. 6 + 11 = 17
c. 6 + 6 = 12
d. 6 + 5 = 11 .
so, to get 11 we have to add 5 to 6 .
Therefore, option d is right .

Lesson 3.6 Continue to Make 10 to Add

Solve & Share

How can you make 10 to solve 8 + 5? Show your work and explain.

Answer :

Explanation :
Make 10 to add
we have 8 counters in 8 so 2 counters are left to make it 10 .
So, move 2 counters from 5 to join 8 .
now, we have 10 and 3 .
Therefore 10 + 3 = 13 and 8 + 5 = 13 both are same .

Visual Learning Bridge

Convince Me!
How can you make 10 to find the sum of 7 + 6?
Answer :

Guided Practice

Make 10 find the sum. Use the number line to help you.

Question 1.

Answer:

Explanation :
Make 10 to add
You can think 8 + 6  as 8 + 2 + 4 , because 6 = 2 + 4
mark an arrow from 8 to 10 and from 10 to 14 on the number line is marked.

Independent Practice

Make 10 to find each sum. Use a number line to help you.

Question 2.

Answer:

Explanation :
Make 10 to add
You can think 7 + 8  as 7 + 3 + 5 , because 8 = 3 + 5
To make 7 as 10 add 3 and then add 5 to the 10
and the same is represented on number line as shown in above figure .

Question 3.

Answer:
Explanation :
Make 10 to add
You can think 4 + 9  as 4 + 6 + 3 , because 9 = 6 + 3
To make 4 as 10 add 6 and then add 3 to the 10
and the same is represented on number line as shown in above figure .

Question 4.

Answer:

Explanation :
Make 10 to add
You can think 8 + 4  as 8 + 2 + 2 , because 4 = 2 + 2
To make 8 as 10 add 2 and then add 2 to the 10
and the same is represented on number line as shown in above figure .

Question 5.

Answer:

Explanation :
Make 10 to add
You can think 9 + 7  as 9 + 1 + 6 , because 7 = 1 + 6
To make 9 as 10 add 1 and then add 6 to the 10
and the same is represented on number line as shown in above figure .

Question 6.

Answer:

Explanation :
Make 10 to add
You can think 6 + 7  as 6 + 4 + 3 , because 7 = 4 + 3
To make 6 as 10 add 4 and then add 3 to the 10
and the same is represented on number line as shown in above figure .

Question 7.
Number Sense
Jon adds 8 + 5. First, he adds 8 + 2 to make 10. What should he do next?
Answer:
8 + 5 = 8 + 2 + 3 = 10 + 3 = 13.
Explanation :
5 is written as 2 + 3 because to make 8 we need 2 so in it divided in such a way that 8 can be made 10 nad then next divided part is added to 10 .
8 + 2 + 3 = 10 + 3 = 13.

Problem Solving

Make 10 to help you solve each number story.

Question 8.
Look for Patterns
Conrad has 8 apples. Sam gives him 4 more. How many apples does Conrad have now? Use the open number line to show your work.


Conrad has ___ apples.
Answer:
Number of apples with Conrad = 8 apples .
Number of apples Sam gave to Conrad = 4 apples
Total Apples with Conrad = 8 + 4 = 12 apples .

Explanation :
Make 10 to add
You can think 8 + 4  as 8 + 2 + 2 , because 4 = 2 + 2
To make 8 as 10 add 2 and then add 2 to the 10
and the same is represented on number line as shown in above figure .

Question 9.
Higher Order Thinking
Pat makes 10 to solve 7 + 5 by changing the problem to 7 + 3 + 2. How does Pat make 10?
Answer:
7+ 5 = 7 + 3 + 2 = 10 + 2 = 12 .
Explanation :
5 is written as 3+ 2
then add 7 + 3+ 2 = first add 7 + 3 we get 10 then later add 2 to 10 we get 12 as sum .

Question 10.
Assessment Practice
Which shows how to make 10 to add 9 + 6?
A. 9 + 4 + 2
B. 9 + 3 + 3
C. 9 + 1 + 5
D. 9 + 0 + 6
Answer:
Option C.
Explanation :
9 + 6
9 needs only 1 to make 10 so 6 is written as 1 + 5
9 + 1 + 5 = 10 + 5 = 15 .

Lesson 3.7 Explain Addition Strategies

Solve & Share

8 + 6 = ?
Choose a strategy to solve the problem. Use words, objects, or pictures to explain your work.

Answer :

Explanation :
Make 10 to add
we have 8 counters in 8 so 2 counters are left to make it 10 .
So, move 2 counters from 6 to join 8 .
now, we have 10 and 4 .
Therefore 10 + 4 = 14 and 8 + 6 = 14 both are same .

Visual Learning Bridge

Convince Me!
What strategy could you use to solve 7 + 8? Why is it a good strategy?
Answer :
Near Doubles .

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 8 is one more than 7. So, we can write 8 as 7 + 1.
We already know the double of 7 is 14.
So, the required sum is one more than double. That is 15. Therefore, 7 + 8 = 15.

Guided Practice
Find each sum. Choose a strategy to use.

Question 1.

Answer:
Doubles Fact Strategy

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. Here 6 is added to itself so, it is a double fact .

Question 2.

Answer:
Make 10 Strategy

Explanation :
Make 10 to add
You can think 9 + 7  as 9 + 1 + 6 , because 7 = 1 + 6
To make 9 as 10 add 1 and then add 6 to the 10
and the same is represented on number line as shown in above figure .

Question 3.

Answer:
Near Doubles or Double Plus and Make 10 strategy Both Strategies can be used .

Explanation :
Double Plus:
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 7 is one more than 6. So, we can write 7 as 6
Make 10:
Make 10 to add
You can think 6 + 7  as 6 + 4 + 3 , because 7 = 4 + 3
To make 6 as 10 add 4 and then add 3 to the 10
and the same is represented on number line as shown in above figure .

Question 4.

Answer:
8 + 9 = 17 .

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 9 is one more than 8. So, we can write 9 as 8 + 1.
We already know the double of 8 is 16.
So, the required sum is one more than double. That is 17. Therefore, 8 + 9 = 17.

Independent Practice

Find each sum.

Question 5.

Answer:

Explanation :
Make 10 to add
You can think 6 + 8  as 6 + 4 + 4 , because 8 = 4 + 4
To make 6 as 10 add 4 and then add 4 to the 10
and the same is represented on number line as shown in above figure .

Question 6.

Answer:

Explanation :
Make 10 to add
You can think 4 + 9  as 4 + 6 + 3 , because 9 = 6 + 3
To make 4 as 10 add 6 and then add 3 to the 10
and the same is represented on number line as shown in above figure .

Question 7.

Answer:

Explanation :
Make 10 to add
we have 7 counters in 7 so 3 counters are left to make it 10 .
So, move 3 counters from 6 to join 7.
now, we have 10 and 3 .
Therefore 10 + 3 = 13 and 7 + 6 = 13 both are same .

Question 8.

Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 9 is one more than 8. So, we can write 9 as 8 + 1.
We already know the double of 8 is 16.
So, the required sum is one more than double. That is 17. Therefore, 9 + 8 = 17.

Question 9.

Answer:

Explanation :
Make 10 to add
we have 8 counters in 8 so 2 counters are left to make it 10 .
So, move 2 counters from 5 to join 8 .
now, we have 10 and 3 .
Therefore 10 + 3 = 13 and 8 + 5 = 13 both are same .

Question 10.

Answer:

Explanation :
Make 10 to add
we have 7 counters in 7 so 3 counters are left to make it 10 .
So, move 3 counters from 4 to join 7.
now, we have 10 and 1 .
Therefore 10 + 1 = 11 and 7 + 4 = 11 both are same .

Question 11.
Algebra
Jan has 9 green marbles and some red marbles. She has 11 marbles in all.
9 + ___ = 11
Jan has ___ red marbles.
Answer :
Number of Green Marbles = 9
Number of Red marbles = x
Total Number of Marbles = 11
Number of Red marbles = Total Marbles – Number of Green Marbles = 11 – 9 = 2 Marbles .

Problem Solving

Solve each problem below.

Question 12.
Make Sense
Brett has 8 shirts in his closet. He puts more shirts in the dresser. Brett has 16 shirts in all. How many shirts did Brett put in the dresser?
___ shirts in the dresser
Answer:
Total  umber of Shirts = 16 .
Number of Shirts in Closet = 8
Number of more shirts added in the dresser = 16 – 8 = 8 Shirts .

Question 13.
Higher Order Thinking
Manuel and Jake have 13 pencils in all. How many pencils could each boy have?

Answer:
Total Number of Pencils = 13
Number of Pencils Manuel have = 7 ( taken )
Number of Pencils Jake have = total Pencils – Number of pencils with Manuel .

Explanation :
Make 10 to add
we have 7 counters in 7 so 3 counters are left to make it 10 .
So, move 3 counters from 6 to join 7.
now, we have 10 and 3 .
Therefore 10 + 3 = 13 and 7 + 6 = 13 both are same .

Question 14.
Assessment Practice
Which strategies could help you find 7 + 8?
Choose three that apply.

Answer:

Lesson 3.8 Solve Addition Word Problems with Facts to 20

Solve & Share

Caleb has 4 more stickers than Zoe. Zoe has 5 stickers. How many stickers does Caleb have? Use objects, drawings, or an equation to show your thinking.

Answer :

Number of stickers with Zoe = 5
Number of stickers with Celeb = 4 more than Zoe = 4 + 5 = 9 stickers .

Visual Learning Bridge

Convince Me!
Could you find out how many books Seth read by drawing a picture? Explain.
Answer :
Yes , number of books read by Seth = 12 books.
Explanation :
Number of books read by Tanya = 5
comparison between Tanya and Seth is given unknown term can be calculated .
Number of books Seth read = Seth reads 7 books more than Tanya so, 5 + 7 = 12 books .
Therefore, Total Number of books read by Seth = 12 books .

Guided Practice
Solve each problem. Use counters or draw a picture. Then write an equation.

Question 1.
Tim writes 9 stories. He writes 3 fewer stories than Daisy. How many stories did Daisy write?

Answer:
Number of Stories Tim writes = 9
Number of stories Daisy write = 3 more than Tim = 9 + 3 = 12 stories .
Therefore, Number of stories Daisy write = 12 stories .

Question 2.
Sherry reads 6 comic books. Dally reads 5 more comic books than Sherry. How many comic books did Dally read?

Answer:
Number of comic books Sherry reads = 6 books
Number of comic books Dally read = 5 more comic books than Sherry = 6 + 5 = 11 books .
Therefore, Number of comic books Dally read = 11 books .

Independent Practice

Solve the problems with objects, drawings, or an equation. Show your work.

Question 3.
Tracy buys 10 buttons on Monday. She buys more buttons on Tuesday. Now she has 19 buttons. How many buttons did Tracy buy on Tuesday?
______ buttons
Answer:
Number of buttons bought on Monday = 10 buttons
Total Number of buttons = 19
Number of buttons bought on Tuesday = total buttons – buttons bought on Monday = 19 – 10 = 9 buttons .

Question 4.
Jen has 9 coins. Jen has 6 fewer coins than Owen. How many coins does Owen have?
___ coins
Answer:
Number of coins with Jen = 9
Jen has 6 fewer coins than Owen that means Owen has 6 coins more than Jen .
Number of coins with Own = 9 + 6 = 15 coins .

Question 5.
14 cans are on the table. 5 cans are big and the rest are small. How many small cans are on the table?
___ small cans
Answer:
Number of cans on the table = 14
Number of big cans = 5
Number of small cans = Total Cans – Big cans = 14 – 5 = 9 .

Problem Solving
Solve each problem below.

Question 6.
Model
Leland cuts out 12 flowers. How many can he color red and how many can he color yellow? Draw a picture and write an equation to help solve the problem.
___ red flowers ____ yellow flowers

Answer:
Total Number of flowers = 12
Number of red flowers taken = 6
Then
Number of yellow flowers = 12 – 6 = 6 flowers .

Question 7.
Higher Order Thinking
Nicole scored 8 goals this season. She scored 9 fewer goals than Julien. How many goals did Julien score? Write this problem using the word more.
Nicole scored 8 goals this season. Julien scored ________
Answer:
Number of goals scored by Nicole = 8 goals
Nicole scored 9 fewer goals than Julien that means Julien scored 9 goals than Nicole
Number of goals by Julien = 8 + 9 = 17 goals .

Question 8.
Assessment Practice
Dan drinks 6 more glasses of water than Becky. Becky drinks 5 glasses of water. How many glasses of water did Dan drink?
A. 6 – 5 = 1 glass of water
B. 6 + 5 = 11 glasses of water
C. 11 + 6 = 17 glasses of water
D. 11 – 6 = 5 glasses of water
Answer:
Option B .
Explanation :
Number of glasses of water drank by Becky = 5
Dan drinks 6 more glasses of water than Becky
Number of glasses of water drank by Dan = 6 + 5 = 11 glasses .

Lesson 3.9 Critique Reasoning

Solve & Share

A pet store has 9 frogs. 5 of the frogs are green and the rest are brown. Lidia adds 5 + 9 and says that the store has 14 brown frogs.
Circle if you agree or do not agree with Lidia. Use pictures, words, or equations to explain.

Answer :

Explanation:
Lidia should subtract green frogs from the total number of frogs then only number of brown frogs can be known but Lidia did addition which is wrong so, i disagree with Lidia .
Therefore, Number of brown frogs = total frogs – green frogs = 9 – 5 = 4 brown frogs .

Visual Learning Bridge

Convince Me!
What question would you ask Joe to have him explain his thinking?
Answer :
Visualize thinking helps to understand the concept clearly .

Guided Practice
Circle your answer. Use pictures, Practice words, or equations to explain.

Question 1.
9 cats chase a ball. Some cats stop to eat. Now 4 cats are chasing the ball. Stan says 13 cats stop to eat because 9 + 4 = 13. Do you agree or not agree with Stan?

Answer:
Total Number of cats chase a ball = 9
Number of cats chase a ball now = 4
Number of cats stop to eat = 9 = 5 + 4
Therefore, Number of cats stop to eat = 5 cats .

Independent Practice

Circle your answer. Use pictures, words, or equations to explain.

Question 2.
14 grapes sit in a bowl. 9 are green. The rest are purple. How many are purple? Steve says 6 grapes are purple because 9 + 6 = 14. Do you agree or not agree with Steve?

Answer:

Explanation :
Total Grapes = 14
Number of green grapes = 9
Number of purple grapes = 9 + 5 = 14 .
So, Purple grapes are 5 .
But Steve said 9 + 6 = 14 it is wrong as 9 + 6 = 15 .
Therefore I disagree what Steve said .

Question 3.
11 oranges are in a bag. 8 oranges fall out. How many oranges are left in the bag? Maria says 3 oranges are left because 11 – 8 = 3. Do you agree or not agree with Maria?

Answer:

Explanation :
Number of Oranges in bag = 11
Number of Oranges out off bag = 8
8 + 3 = 11 so, Number of oranges in bag = 3
Therefore, Number of oranges in bag = 3 oranges .

Problem Solving

Performance Task

Flower Vases Jill has 15 roses. She wants to put some in a red vase and some in a blue vase.
Help Jill solve the problem. Answer the items below to check Jill’s thinking. Use pictures, words, or equations to explain.

Question 4.
Explain Jill says she can put an equal number of roses in each vase. She says she can write a doubles fact to match the flowers in the blue and red vases. Do you agree? Explain.
Answer:
I Disagree

Explanation :
Total Number of Flowers = 15
Put the flowers in blue vase and red vase equally
Number of Flowers in blue vase = 7
Number of Flowers in red vase = 7
Total Flowers in blue vase and red vase = 7 + 7 = 14
1 Flower is left .
So, i disagree flowers cant be divided equally to put in both vases as 1 lower is left .

Question 5.
Model How could Jill use words or drawings to show the problem?
Answer:
It is explained in the above sum image .

Topic 3 Fluency Practice Activity

Find a partner . Get paper and a pencil. Each partner chooses a different color: light blue or dark blue. Partner 1 and Partner 2 each point to a black number at the same time. Both partners add those numbers. If the answer is on your color, draw a tally mark. Work until one partner draws twelve tally marks.

Answer:

Topic 3 Vocabulary Review

Understand Vocabulary

Question 1.
Circle True or False.
10 + 5 = 15 is a doubles-plus fact.

Answer:

False
Explanation :
Double Plus:
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 10 is five more than 5.

Question 2.
Circle True or False.
In the equation below, 8 is the whole.

Answer:

Explanation :
10 and 8 are the addends and 18 is the sum of the equation .

Question 3.
Show how to make 10 to add 8 + 6.
Answer:

Explanation :
Make 10 to add
we have 8 counters in 8 so 2 counters are left to make it 10 .
So, move 2 counters from 6 to join 8 .
now, we have 10 and 4 .
Therefore 10 + 4 = 14 and 8 + 6 = 14 both are same .

Question 4.
Write a doubles-plus fact.
Answer:
8 + 9 = 17 .

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 9 is one more than 8. So, we can write 9 as 8 + 1.
We already know the double of 8 is 16.
So, the required sum is one more than double. That is 17. Therefore, 8 + 9 = 17.

Question 5.
Show 15 on the open number line.

Answer:

Use Vocabulary in Writing

Question 6.
What strategy could help you solve 7 + 8 = ? Use at least one term from the Word List.
Answer:

Explanation :
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 8 is one more than 7. So, we can write 8 as 7 + 1.
We already know the double of 7 is 14.
So, the required sum is one more than double. That is 15. Therefore, 7 + 8 = 15.

Topic 3 Reteaching

Set A

You can use a number line to add. Start counting at one addend. Count on the number of the other addend.

Answer:
10 + 8 = 18 .

Use a number line. Count on to find the sum.

Question 1.
7 + 6 = ___

Answer:

Explanation :
Find 7 on number line. Then count on 4 more to add 7 + 6 = 13
Start at 7 and make 6 jumps . You land on 13 .

Set B

An open number line can help you add.
7 + 5 = ?
Start with the first addend.

You can count on by 1s to add 5 more.

Answer:
7 + 5 = 12
Explanation :
From 7 on number line. count on 5 more 1s to add 7 + 5 = 12
Started at 7 and  5 jumps are made and lands on 12 .
12 is the sum ..

Use an open number line to solve the problem. Show your work.

Question 2.
4 + 9 = ___

Answer:

Explanation :
Start at 4 .
Count on by 1s to add 9 more and lands on 13 which is the sum .

Set C

A doubles-plus fact is a doubles fact and 1 or 2 more.

7 + 7 = 14
14 and 1 more is 15.

Add the doubles. Then use the doubles facts to help you solve the double-plus facts.

Question 3.

Answer:

Explanation :
Double Plus:
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 6 is one more than 5. So, we can write 6 as 5 + 1

Question 4.

Answer:

Explanation :
Double Plus:
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 9 is one more than 8. So, we can write 9 as 8 + 1

Question 5
.

Answer:

Explanation :
Double Plus:
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 8 is two more than 6. So, we can write 8 as 6 + 2

Question 6.

Answer:

Explanation :
Double Plus:
The addition of any two consecutive numbers can be done by using doubles plus 1 or doubles minus 1 strategy.
The number 7 is two more than 5. So, we can write 7 as 5 + 2

Set D

You can make 10 to add.

Make 10 to add. Draw counters in the ten-frame to help you.

Question 7.

Answer:

Explanation :
Make 10 to add
we have 7 counters in 7 so 3 counters are left to make it 10 .
So, move 3 counters from 8 to join 7 .
now, we have 10 and 5 .
Therefore 10 + 5 = 15 and 7 + 8 = 15 both are same .

Topic 3 Reteaching

Set E

You can choose different ways to add.

Find each sum. Circle the strategy that you used.

Question 8.

Answer:

Explanation :
Make 10 to add
You can think 8 + 4  as 8 + 2 + 2 , because 4 = 2 + 2
To make 8 as 10 add 2 and then add 2 to the 10
and the same is represented on number line as shown in above figure .

Question 9.

Answer:

Explanation :
Make 10 to add
we have 7 counters in 7 so 3 counters are left to make it 10 .
So, move 3 counters from 8 to join 7 .
now, we have 10 and 5 .
Therefore 10 + 5 = 15 and 7 + 8 = 15 both are same .

Set F

You can write an equation to help you solve addition problems. Sean plays in 8 soccer matches. Karla plays in 3 more matches than Sean. In how many matches does Karla play?

Answer:
Number of soccer matches played by Sean = 8 matches .
Number of soccer matches played by Karla = 3 more matches than Sean = 3 + 8 = 11 matches .
Therefore, Number of soccer matches played by Karla = 11 matches .

Write an equation to solve the problem.

Question 10.
Leslie has 8 pencils. She has 9 fewer pencils than Grace. How many pencils does Grace have?

Grace has ___ pencils.
Answer :
Number of Pencils with Leslie = 8 pencils
Leslie have 9 fewer pencils than Grace that means grace have 9 more pencils than Leslie .
Number of pencils with Grace = 8 + 9 = 17 pencils .
Therefore , Grace has 17 pencils.

Set G

What questions can I ask to understand other people’s thinking? Are there mistakes in other people’s thinking? Can I improve on other people’s thinking?

Circle your answer. Use pictures, words, or equations to explain.

Question 11.
6 books are on a shelf. Maya puts more books on the shelf. Now 15 books are on the shelf. How many books did Maya put on the shelf?
Kyle says that Maya put 9 books put on the shelf because 6 + 9 = 15. Do you agree or not agree with Kyle?

Answer:

Explanation :
Total Number of books = 15
Number of books on shelf = 6
Number of boos kept on shelf by Maya = ?
6 + ? = 15 .
6 + 9 = 15 .
Adding 9 to 6 we get 15 so, Number of books kept on shelf by Maya = 9 books .

Topic 3 Assessment Practice

Question 1.
Frank has 7 paper airplanes. He makes 9 more. How many paper airplanes does Frank make in all?
A. 18
B. 17
C. 16
D. 15
Answer:
Option D .
Explanation :
Number of paper airplanes made By Frank = 7
Number of more paper airplanes are made = 9
Total Number of airplanes = 7 + 9 = 16 airplanes .

Question 2.
Mark has 7 red marbles. He has 8 blue marbles. Which shows two ways to find how many marbles Mark has in all?
A. 7 + 8 = 14 and 8 + 7 = 14
B. 7 + 8 = 15 and 8 + 7 = 15
C. 7 + 7 = 14 and 8 + 8 = 14
D. 7 + 7 = 16 and 8 + 8 = 16
Answer:
Option B 7 + 8 = 15 and 8 + 7 = 15
Explanation :
Number of Red marbles = 7
Number of blue marbles = 8
Total Number of marbles with Mark = 7 + 8 or 8 + 7 = 15

Question 3.
Use the open number line. Show how to count on to find 7 + 9. Then write the sum.

7 + 9 = ____
Answer :

Explanation :
Find 7 on number line. Then count on 9 more to add 7 + 9 = 16
Start at 7 and make 9 jumps . You land on 16 .

Question 4.
Which are doubles facts? Choose two that apply.

Answer:

Explanation :
Double Fact means To get a double of a number, we add the same number to itself. but here option 3 and 4 are Double facts numbers . where 7 is added to itself in option 3 and in option 4 10 is added to itself .

Question 5.
8 birds are in a tree. 9 more birds join them. How many birds are in the tree now? Write an equation to solve the problem.

Answer:
Number of birds on tree = 8
Number of more birds joined = 9
Total Number of birds on tree now = 8 + 9 = 17 birds .

Question 6.
Gloria has 7 yellow pencils. She has 9 red pencils. How many pencils does Gloria have in all? Explain.

A. 15 pencils; Doubling 7 gives 14, and I more is 15.
B. 19 pencils; Doubling 9 gives 18, and I more is 19.
C. 16 pencils; 7 + 3 = 10, and 6 more is 16.
D. 17 pencils; 7 + 2 = 10, and 7 more is 17.
Answer:
Option C. 16 pencils; 7 + 3 = 10, and 6 more is 16.
Explanation :
Number of Yellow pencils = 7
Number of Red pencils = 9
Total Number of pencils = 7 + 9 = 7 + 3 + 6 = 10 + 6 = 16 pencils .

Make 10 to add
You can think 7 + 9  as  7 + 3 + 6 , because 9 = 3 + 6

Question 7.
Nina bakes 8 corn muffins on Tuesday. She bakes 8 corn muffins on Wednesday. How many corn muffins does Nina bake in all? Which number line shows the problem?

Answer:
Option C
Explanation :
Number of corn muffins baked on Tuesday = 8
Number of corn muffins baked on Wednesday = 8
Total Number of corn muffins baked = 8 + 8 = 16 muffins .

Find 8 on number line. Then count on 8 more to add 8 + 8 = 16
Start at 8 and make 8 jumps . You land on 16 .

Question 8.
Sandy makes 9 bracelets. Then she makes 5 more bracelets. How many bracelets does Sandy have now?
Use words or pictures to explain.
Answer:

Explanation :
Number of Bracelets made by sandy = 9
Number of more bracelets done = 5
Total Number of Bracelets = 9 + 5 = 14 bracelets .

Question 9.
Find 8 + 5. Make a 10 to add.

A. 11
B. 13
C. 15
D. 17
Answer:

Explanation :
Make 10 to add
we have 8 counters in 8 so 2 counters are left to make it 10 .
So, move 2 counters from 5 to join 8 .
now, we have 10 and 3 .
Therefore 10 + 3 = 13 and 8 + 5 = 13 both are same .

Question 10.
Maria has 8 more scarves than Lucy. Lucy has 8 scarves. How many scarves does Maria have? Write an equation to solve.
___ + ___ = ___
___ scarves
Answer:
Number of Scarves Lucy have = 8
Number of Scarves Maria have = 8 more scarves than Lucy = 8 + 8 = 16 Scarves .
Therefore, Number of Scarves Maria have = 16 Scarves .

Question 11.
There are 19 limes on the table. 10 fall to the floor. Nicky says there are 9 limes left on the table.
Do you agree or not agree with Nicky’s thinking? Use pictures, words, or an equation to explain.

Answer:

Explanation :
Total Number of limes = 19
Number of limes fall on floor = 10
Number of Limes left on table = 9 as 19 = 10 + 9
I agree with the Nicky thinking as, there are 9 limes on the table .

Topic 3 Performance Task

Roger’s Reading Record
Roger loves to read!
The chart shows how many books he read for six months.

Question 1.
How many books did Roger read in all in April and June? Write an equation to solve.
___ + ___ = ___
___ books
Answer:
Number of Books read in April = 8
Number of Books read in June = 8
Total number of books read in April and June = 8 + 8 = 16 books .

Question 2.
Roger read 4 more books in July than he did in January. How many books did he read in July? Draw a picture to solve. Then write an equation to match.
___ +__ = ___
He read ____ books in July.
Answer:
Number of books read in January = 9
Number of books read in July = 4 more books than January = 9 + 4 = 13 books .

Question 3.
In February, Tracy and Roger read 15 books in all. How many books did Tracy read in February? Explain the strategy that you used to solve the problem.
Answer:
Number of books read by Tracy and Roger = 15 books
Number of books read by Roger in February = 7 books .
Number of books read by Tracy in February = 7 + ? = 15
if we add 8 to 7 then only we get 15
Therefore , Number of books read by Tracy in February = 8 books .

Question 4.
Sharon read 8 books in March. She said that she read 2 fewer books than Roger in March. Do you agree or not agree with Sharon? Circle your answer. Use pictures, words, or equations to explain.

Answer:
Number of books read by Roger in March = 6 books .
Number of books read by Sharon in March = 8 books .
Sharon have more books than Roger
therefore, I disagree what Sharon said .

Go through the enVision Math Common Core Grade 2 Answer Key Topic 3 Add Within 100 Using Strategies regularly and improve your accuracy in solving questions.

enVision Math Common Core 2nd Grade Answers Key Topic 3 Add Within 100 Using Strategies

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

enVision STEM Project: Earth Changes and Addition Strategies
Find Out Find and share books about how the Earth changes. Talk about changes that people can see, hear, and feel. Talk about changes that people cannot see happening.
Journal: Make a Book Show what you learn in a book. In your book, also:

• Write new science words you learn. Draw pictures that help show what the words mean.
• Write new math words you learn. Draw pictures that help show what the words mean.

Review What You Know

Vocabulary
Question 1.
Draw a circle around each even number. Use cubes to help.
15
7
14
2
19
18
Answer:

In the given numbers 14, 2 and 18 are the even numbers.know draw a circle around the 14, 2 and 18.

Question 2.
Draw a square around each odd number. Use cubes to help.
12
3
6
17
11
4
Answer:

In the given numbers 3,17 and 11 are the odd numbers. Know draw the square around the 3, 17 and 11.

Question 3.
Complete the bar diagram to show the sum of 3 + 5.

Answer:

In the above diagram they have given a 3 dots on the left side. Know we want to draw 5 dots on the right side. By adding both sides of the dots wet get 3 + 5 = 8

Arrays

Write an equation to show the number of circles in each array.
Question 4.

By rows
_______ + _______ = _______
Answer:

Given,
Total number of rows = 2
Each row contains 4 circles.
4 + 4 = 8

Question 5.

By columns
_______ + _______ = _______
Answer:
Given that,
Total number of columns = 3
Each column contains 3 circles.
3 + 3 + 3 = 9

Math Story
Question 6.
Joe has 5 apples. He picks 3 more apples. How many apples does Joe have now?
_______ apples
Does Joe have an even or an odd number of apples?
_________ number
Answer:
Given that
Total number of apples at Joe = 5
Joe picks more apples = 3
Total number of apples near Joe = 5 + 3 =8
Joe has an even number of apples.

Pick a Project

PROJECT ЗА
How far would you travel to cheer for your team?
Project: Make a Map to the Game

PROJECT ЗB
What are some important things to do at the airport?
Project: Write a List of Air Travel Tasks

PROJECT 3C
How many Olympic Games have there been?
Project: Create an Olympics Poster

3-ACT MATH PREVIEW

Math Modeling
Piled Up

Lesson 3.1 Add Tens and Ones on a Hundred Chart

Solve & Share
How can you use the hundred chart to help you find 32 + 43? Explain.
Write an equation to show the sum.

I can … add within 100 using place-value strategies and properties of operations.

______ + _______ = ________

Visual Learning Bridge

Convince Me! Max says that to find 54 + 18 on a hundred chart, you can start at 54, move down 2 rows, and move back 2 spaces. Do you agree? Explain.

Guided Practice

Add using the hundred chart. Draw arrows on the chart if needed.

Question 1.
17 + 32 = ________
Answer:
We are using the hundred chart to find the sum of 17 + 32
In the hundred charts we start at 17 moves down to 3 rows and move front to 2 spaces then we get 49
17 + 32 = 49
Question 2.
28 + 21 = ________
Answer:
We are using the hundred chart to find the sum of 28 + 21
In the hundred charts we start at 28 move down to 2 rows and move front to 1 space then we get 49.
28 + 21 = 49
Question 3.
________ = 19 + 20
Answer: we are using a hundred charts to find the sum of 19 + 20
In the hundred charts we start at 19 moves down to 2 rows then we get 39.
39 = 19 + 20
Question 4.
18 + 8 = ________
Answer:
We are using the hundred chart to find the sum of 18 + 8
In the hundred charts, we start at 18 moves down to 1 row and back to 2 space then we get 26
18 + 8 = 26

Independent Practice

Add using the hundred chart.

Question 5.
33 + 9 = ________
Answer:
We are using the hundred chart to find the sum of 33 + 9
In the hundred charts we start at 33 down to 1 row and move back to 1 space then we get 42
33 + 9 = 42

Question 6.
________ = 12 + 73
Answer:
We are using the hundred chart to find the sum of 12 + 73
In the hundred charts we start at 12 down to 7 rows and move front to 3 Space we get 85
85 = 12 + 73
Question 7.
38 + 21 = ________
Answer:
We are using the hundred chart to find the sum of 38 + 21
In the hundred charts we start at 38 down to 2 rows and front to 1 space then we get 59
38 + 21 = 59
Question 8.
56 + 42 = ________
Answer:
We are using the hundred chart to find the sum of 56 + 42
In the hundred charts we start at 56 down to 4 rows and front to 2 spaces then we get 98
56 + 42 = 98
Question 9.
________ = 47 + 28
Answer:
We are using the hundred chart to find the sum of 47 + 28
In the hundred charts, we start at 47 down to 3 rows and back to  2 spaces then we get 75
75 = 47 + 28
Question 10.
39 + 17 = ________
Answer:
We are using the hundred chart to find the sum of 39 + 17
In the hundred charts, we start at 39 down to 2 rows and back to 3 spaces then we get 56
39 + 17 =56
Question 11.
________ = 61 + 19
Answer:
We are using the hundred chart to find the sum of 61 + 19
In the hundred charts, we start at 61 and down to 2 rows and back to 8 space then we get 89
89 = 61 + 19

Question 12.
Higher Order Thinking Write the digit that makes each equation true.

Answer:
7 + 83 = 90
The number 7 makes the equation true.
34 + 25 = 57
The digit 5 makes the equation true.
16 + 52 = 67
The digit 1 makes the equation true.
62 + 21 = 83
The digit 2 makes the equation true.
Problem Solving

Use Tools Use the hundred chart to solve the problems.

Question 13.
Sara has 48 buttons. Luis has 32 buttons. How many buttons do they have in all?
________ buttons
Answer:
Given that,
Total number of buttons at Sara = 48
Total number  buttons at Luis = 32
The total number of buttons at both of them have = 48 + 32
By using a hundred charts the sum of 48 + 32 is
In the hundred charts Start at 48 and down to 3 rows and front to 2 spaces then we get 80.
48 + 32 = 80
Question 14.
Mika had 70 buttons. Then she found 19 more buttons. How many buttons does Mika have now?
_______ buttons
Answer:
Given that,
Total number of buttons at Mika  = 70
She found more buttons = 19
Total number of buttons with Mike = 70 + 19
By using the hundred chart we find the sum of 70 + 19
In the hundred chart, we start at 70 then down to 2 rows and back to 1 space then we get
Question 15.
Higher Order Thinking Write the steps you take to add 43 and 39 on a hundred chart.
Answer:
We are using the hundred chart to find the sum of 43 and 39
In the hundred charts, we start at 43 and down to 4 rows and back to 1 space then we get 82
43 + 39 = 82
Question 16.
Assessment Practice which has a sum of 35? Choose all that apply.
☐ 15 + 20
☐ 16 + 19
☐ 20 + 15
☐ 30 + 15
Answer:
15 + 20 has a sum of 35.
16 + 19 has a sum of 35
20 + 15 has a sum 0f 35

Lesson 3.2 Add Tens and Ones on an Open Number Line

Solve & Share
How can you use the open number line to find 35 + 24?
Write an equation to show the sum. Explain your work.

I can … use an open number line to add tens and ones within 100.

Visual Learning Bridge

Convince Me! Explain how you can use an open number line to find 56 + 35.

Guided Practice

Use an open number line to find each sum.
Question 1.
59 + 24 = _________

Answer: 59 + 24 = 83
Question 2.
47 + 25 = _________

Answer:
First, draw a line.
Represent the numbers on the line.
The first number is 47 and counts by 20 then it gets 67 and hump 5 then we get 72.
Count the numbers and draw an arrow
47 + 25 = 72

Independent Practice

Use an open number line to find each sum.
Question 3.
34 + 15 = ________

Answer:
First, draw the line.
Represent the numbers on the line.
The first number is 34 and counts by 10 then it gets 44 and 5 then we get 49.
Count the numbers and draw an arrow.
34 + 15 = 49

Question 4.
34 + 46 = ________

Answer:
34 + 46 = 80
First, draw the Line.
Represent the number on the line.
The first number is 34 and counts by 20 then it gets 54 and counts again 20 then it gets 74 and jump to 6 then it gets 80.
Count the numbers and draw an arrow

Question 5.
16 + 28 = _________

Answer:
16 + 28 =44
First, draw the Line.
Represent the number on the line.
The first number is 16and counts by 10 then it gets 26 and jumps to 2 then it gets 28.

Count the numbers and draw an arrow.
Question 6.
59 + 26 = ________

Answer: 59 + 26 = 85
First draw the Line.
Represent the number on the line.
The first number is 59 and counts by 20 then it gets 79 and jumps to 6 then it gets 85.
Count the numbers and draw an arrow.

Question 7.
Number Sense Matt found 55 + 28 using the open number line below. Is his work correct? Explain.

Answer: 55 + 28 = 83

Problem Solving

Use the open number line to solve each problem below.
Question 8.
Reason There are 24 apples in a basket. There are 19 apples on a tray. How many apples are there in all?

_________ apples
Answer: Apples in a basket = 24
Apples in a tray = 19
Total number of apples = 24 + 19 = 43
Using the number line.
First, draw the Line.
Represent the number on the line.
The first number is 24 and counts by 10 then it gets 34 and jumps to 9 then it gets 43.
Count the numbers and draw an arrow.

Question 19.
Reason Jamie has 27 more berries than Lisa. Lisa has 37 berries. How many berries does Jamie have?

_________ berries
Answer:
Lisa has berries = 37
Jamie has berries = 27 berries more than Lisa
Jamie has berries = 37 + 27 =64
First draw the Line.
Represent the number on the line.
The first number is 37 and counts by 20 then it gets 54  and jumps to 9 then it gets 80.
Count the numbers and draw an arrow.

Question 10.

Higher Order Thinking Use two different number lines to show that 34 + 23 has the same value as 23 + 34.


Answer:
34 + 23 = 57
First, draw the Line.
Represent the number on the line.
The first number is 34 and counts by 20 then it gets 54 and jumps to 3 then it gets 57.
Count the numbers and draw an arrow.

23 + 34 = 57
First, draw the Line.
Represent the number on the line.
The first number is 23 and counts by 30 then it gets 53 jumps to 3 then it gets 57.
Count the numbers and draw an arrow.

Question 11.
Assessment Practice Use the numbers on the cards. Write the missing numbers under the number line to show how to find the sum.

43 + 25 = _________
Answer:
43 + 25 = 68

Lesson 3.3 Break Apart Numbers to Add

Solve & Share
Josh has 34 cans to recycle. Jill has 27 cans. How many cans do they have in all? Solve any way you choose. Use drawings and equations to explain your work.
I can … break apart numbers into tens and ones to find their sum.

Visual Learning Bridge

Convince Me! Explain how you can break apart 28 to find 33 + 28.

Guided Practice

Break apart the second addend to find the sum. Show your work. Use an open number line to help.
Question 1.

Independent Practice

Break apart the second addend to find the sum. Show your work. Draw an open number line to help.
Question 2.
42 + 16 = ________
Answer:
42 + 16 =
42 + 10 + 6
52 + 6 = 58
First draw the Line.
Represent the number on the line.
The first number is 42 and counts by 10 then it gets 52 and jumps to 6 then it gets 58.
Count the numbers and draw an arrow.

Question 3.
36 + 44 = ________
Answer:
36 + 44
36 + 40 + 4
76 + 4 = 80
First draw the Line.
Represent the number on the line.
The first number is 36 and counts by 20 then it gets 56 and counts again by 20 ten we get 76 and jump to 4 then it gets 80.
Count the numbers and draw an arrow.

Question 4.
41 + 37 = ________
Answer:
41 + 37
41 + 30 + 7
71 + 7 = 78
First draw the Line.
Represent the number on the line.
The first number is 41 and counts by 30 then it gets 71 and jumps to 7 then it gets 78.
Count the numbers and draw an arrow.

Question 5.
35 + 47 = ________
Answer:
35 + 47
35 + 40 + 7
75 + 7 = 82
First draw the Line.
Represent the number on the line.
The first number is 35 and counts by 40 then it gets 75 and jumps to 7 then it gets 82.
Count the numbers and draw an arrow.

Question 6.
32 + 28 = ________
Answer:
32 + 28
32 + 20 + 8
52 + 8 = 60
First draw the Line.
Represent the number on the line.
The first number is 32 and counts by 20 then it gets 52 and jumps to 8 then it gets 60.
Count the numbers and draw an arrow.

Question 17.
48 + 27 = ________
Answer:
48 + 27
48 + 20 + 7
68 + 7 = 75
First draw the Line.
Represent the number on the line.
The first number is 48 and counts by 20 then it gets 68 and jumps to 7 then it gets 75.
Count the numbers and draw an arrow

Question 8.
Number Sense Write the digit that makes each equation true.

Answer:
36 + 52 = 88
Here the digit 2 makes the equation true.
28 + 47 = 75
Here the digit 7 makes the equation true.
14 + 43 = 57
Here the digit 3 makes the equation true.
53 + 29 = 82
Here the digit 9 makes the equation true.
Problem Solving

Solve each problem. Show your work.
Question 9.
Amir planted 35 trees. Juan planted 27 trees. How many trees did they plant in all?
________ trees
Answer:
Given that,
Total number of trees planted by Amir  = 35
Total number of trees planted by Juan = 27
Total number of  plants planted by Amir and Juan = 35 + 27 = 62
Question 10.
Carmen has 18 pennies. Patrick has 12 more pennies than Carmen. How many pennies does Patrick have?
________ pennies
Answer:
Given that,
Total number of pennies at Carmen  = 18
Total number of pennies at Patrick  more than Carmen = 12
Total number of pennies at Patrick = 18 + 12 = 30
Question 11.
Higher Order Thinking Use the numbers on the cards. Use each number once to write a true equation.

Answer:
The numbers on the card are 3, 2, 8
First, write the 2 in the first empty box then we get 52, and write the 3 in the second empty box then we get 34
By adding 52 and 34 we get 86. Write the 8 in the third box.
The true equation is
52 + 34 = 86

Question 12.
Assessment Practice which has a sum of 67? Choose all that apply.

Answer:
15 + 52 = 67

Lesson 3.4 Add Using Compensation

Solve & Share
27 + 16 = ________
Draw counters on the ten frames to show each addend. Then show how you can move some counters to make it easier to find the sum. Explain your work.
I can … break apart addends and combine them in different ways to make numbers that are easy to add mentally.

Visual Learning Bridge

Convince Me! Solve.
19 + 26 = ☐
Explain how you can change the addends to make them easier to add.

Guided Practice

Use compensation to make numbers that are easier to add. Then solve. Show your work.
Question 1.
17 + 9 = ________

Question 2.
16 + 14 = __________

Answer:

Independent Practice

Use compensation to make numbers that are easier to add. Then solve. Show your work.
Question 3.
33 + 19 = __________
Answer:
33 + (10 + 9)
(33 + 10) + 9
43 + 9 = 52
Question 4.
28 + 8 = __________
Answer:
28 + (2 + 6)
(28 + 2) + 6
30 + 6 = 36
Question 5.
27 + 36 = __________
Answer:
27  + ( 30 + 6)
(27 + 30) + 6
57 + 6 = 63
Question 6.
Number Sense Explain how you can use compensation to make numbers that are easy to add. Solve. Show your work.
28 + 37 =
______ + ______ =
Answer:
28 + 37 =
28 + ( 30 + 7)
(28 + 30) + 7
58 + 7 = 65
Question 7.
Higher Order Thinking Show two different ways you could use compensation to make numbers that are easy to add. Solve. Show your work.
17 + 26 =
Answer:
17 + 26
17 + (20 + 6)
(17 + 20) + 6
37 + 6 = 43

Problem Solving

Use compensation to make numbers that are easier to add. Then solve. Show your work.
Question 8.
Explain Bella said there is only one way to rewrite this problem to make the numbers easier to add. Is she correct? Explain. Then solve.
42 + 29 =
Answer:
42 + 29
42 + (20 + 9)
(42 + 20) + 9
62 + 9 = 71
Question 9.
Vocabulary Show two different ways to use compensation to find the sum. Then solve.
58 + 35 =
What number is close to 58 or 35?
Answer:
58 + 35
58 + (30 + 5)
(58 + 30) + 5
88 + 5 = 92
Question 10.
Higher Order Thinking Show two different ways to use compensation to find the sum. Then solve.
37 + 16 + 5 =
Answer:
37 + (10 + 6) + 5
(37 + 10) + 6 + 5
47 + 6 + 5
47 + 11
47 +(10 + 1)
(47 + 10) + 1
57 + 1= 58
Question 11.
Assessment Practice which is equal to 42 + 18? Choose all that apply.
☐ 58
☐ 40 + 20
☐ 40 + 10 + 8
☐ 50 + 10
Answer:
The equation 40 + 20 and 50 + 10 are equal to 42 + 18

Lesson 3.5 Practice Adding Using Strategies

Solve & Share
Tameka has 39 blocks. Kim has 43 blocks. How many blocks do they have in all? Choose any strategy. Solve. Show and explain your work.

I can … choose a strategy to help me add two-digit numbers.

_________ bolcks

Visual Learning Bridge

Convince Me! In 66 + 25 above, why was 4 added to 66 and then subtracted from 95?

Guided Practice

Find each sum. Use any strategy. Show your work.
Question 1.

Question 2.
67 + 26 = ___________
Answer:
67 + 26 =
67 + 20 + 6
87 + 6 = 93

Independent Practice

Find each sum. Use any strategy. Show your work.
Question 3.
33 + 52 = ___________
Answer:
33 + 52 =
33 + 50 + 2
73 + 2 = 75
Question 4.
27 + 6 = ___________
Answer:
27 + 6 = 33
Question 5.
___________ = 49 + 45
Answer:
49 + 45
49 + 40 + 5
89 + 5 = 94
Question 6.
57 + 12 = ___________
Answer:
57 + 12
57 + 10 + 2
67 + 2 = 69
Question 7.
___________ = 63 + 20
Answer:
66 + 20 = 86
Question 18.
14 + 58 = ___________
Answer:
14 + 58
14 + 50 + 8
64 + 8 = 72
Question 9.
45 + 55 = ___________
Answer:
45 + 55
45 + 50 + 5
95 + 5 = 100
Question 10.
87 + 9 = ___________
Answer:
87 + 9 = 96
Question 11.
19 + 61 = ___________
Answer:
19 + 61
19 + 60 + 1
79 + 1 = 80

Number Sense Write the digit that makes each equation true.
Question 12.
45 + 1☐ = 61
Answer:
45 + 16 = 61
The digit 6 makes the equation true.
Question 13.
84 = ☐8 + 56
Answer:
84 = 28 + 56
The digit 2 makes the equation true.
Question 14.
3☐ + 19 + 56
Answer:
30 + 19 + 56 = 105
The digit 0 makes the equation true

Problem Solving

Use the hundred chart to solve each problem. Be prepared to explain your work.

Question 15.
Reasoning Martin has 44 marbles. Carol has 39 marbles. Steve has 90 marbles. How many marbles do Martin and Carol have in all? Do they have more or fewer marbles than Steve?

_______ marbles
Circle:
more
fewer
Answer:
Given that,
Total number of marbles at Martin = 44
Total number of marbles at Carol = 39
Total number of marbles at Steve = 90
Total  number of marbles at Martin and Carol  = 44 + 39
Using a hundred charts find the sum of 44 + 39
In the hundred charts we start at 44 then down to 3 rows we get 74 and front to 4 space then we get 78
44 + 39 = 78
They both them have fewer marbles than Steve.
Question 16.
Higher Order Thinking José collected 32 leaves on Saturday. On Sunday, he collected 14 more leaves than he did on Saturday.
How many leaves did José collect in all?

________ leaves
Answer:
Given that
Total number of leaves Jose collected  on Saturday = 32
Total number of leaves Jose collected on Sunday = 14
Total number of leaves they collected = 32 + 14 = 46
Question 17.
Lucita wants to use an open number line to find 53 + 18. Show how Lucita can use an open number line to find 53 + 18.

Answer:
53 + 18 = 71
First, draw the Line.
Represent the number on the line.
The first number is 53 and counts by 10 then it gets 63 and jumps to 8 then it gets 71.
Count the numbers and draw an arrow.

Question 18.
Assessment Practice Maria used a hundred chart to find a sum. She started at 68. Then she moved down 3 rows and back I space. Which number did she land on?
A. 88
B. 97
C. 98
D. 99
Answer:
Maria started at 68
She moved down to three rows is 98
And she back to 1 space then his number is 97

Lesson 3.6 Solve One-Step and Two-Step Problems

Solve & Share
The red team has 15 more points than the blue team. The blue team has 36 points. How many points does the red team have?
Choose any strategy. Solve. Explain your work.

I can … use drawings and equations to solve one-step and two-step problems.

Visual Learning Bridge

Convince Me! What steps did you take to find the number of tickets Amy sold? Explain.

Guided Practice

Solve the two-step problem. Show your work.
Question 1.
Steve read 15 books. Sam read 9 fewer books than Steve. Dixon read 8 more books than Sam. How many books did Sam read?

Sam read _______ books.

sam read 6 books.

How many books did Dixon read?

Dixon read _______ books.

Dixon read 14 books.

Independent Practice

Solve the problems below. Show your work.
Question 2.
Brian has 17 fewer marbles than Kyle. Brian has 21 marbles. How many marbles does Kyle have?
________ marbles
Answer:
Given that,
Total number of marbles at Brain = 21
The total number of marbles at Brain has  fewer than Kyle  = 17
Total number of marbles marbles at Kyle = 21 + 17 = 38
Question 3.
Clint catches 7 frogs. 3 frogs hop away. Then Clint catches 6 more frogs. How many frogs does Clint have now?
_________ frogs
Answer:
Given that,
Total number of frogs the Clint catches = 7
Total number of Frogs hop away = 3
Clint catches another more frogs = 6
Total number of frogs at Clint = 7 – 3 + 6 = 10
Question 4.
Erwin sees 23 birds in a tree. Then 18 more birds come. How many birds does Erwin see now?
_________ birds
Answer:
Given that,
Erwin sees the total number of birds in a tree = 23
More birds come on the tree = 18
Total number of birds that seen bye the Erwin  = 23 + 18 = 41
Question 5.
There are 31 bluefish in a pond. There are also 8 goldfish and 3 redfish in the pond. How many fish are in the pond?
________ fish
Answer:
Given that
Total number of Blue fishes in a pound = 31
Total number of Goldfishes in a pound = 8
Total number of Red fishes in a pound = 3
Total number of fishes in a pound = 31 + 8 + 3 = 42
Question 6.
Higher Order Thinking Mr. Leu buys 6 bananas. Then he buys 8 more bananas. He gives some bananas to Mr. Shen. Now Mr. Leu has 5 bananas. How many bananas did Mr. Leu give to Mr. Shen?
_________ bananas
Answer:
Given that,
Mr. Leu buys bananas = 6
He buys more bananas = 8
Total bananas at Mr. Leu = 6 + 8 = 14
Mr. Leu gave some bananas to the Mr. Shen
Mr. Leu left only 5 bananas
Mr. Leu gave to Mr. Shen = 14 – 5 = 9

Problem Solving

Solve the problems below. Show your work.
Question 7.
There are 21 more green crayons than blue crayons. There are 14 blue crayons. How many green crayons are there?
__________ green crayons
Answer:
Given that,
Total number of Blue crayons = 14
Green crayons are 21 more than blue crayons.
Total number of Green crayons = 14 + 21 = 35

Question 8.
Make Sense Dan swims 4 laps on Monday. He swims 5 laps on Tuesday. Then he swims 9 laps on Wednesday. How many laps does Dan swim in all?
_________ laps
Answer:
Given that,
Dan swims on Monday = 4 laps
Dan swims on Tuesday = 5 laps
Dan swims on Wednesday = 9 laps
Total number of laps that Don swim = 4 + 5 + 9 = 18

Question 9.
Higher Order Thinking Robert has 20 blueberries. He has 10 more blueberries than Janessa. He has 14 fewer blueberries than Amari. How many blueberries does Janessa have? How many blueberries does Amari have?
Janessa has ________ blueberries.
Amari has __________ blueberries.
Answer:
Given that,
A robot has 20 blueberries
He has 10 more blueberries than Janessa
Janessa has blueberries = 20 – 10 = 10
The robot has 14 blueberries fewer than Amari
Amari has total number of blueberries = 20 + 14 = 34

Question 10.
Assessment Practice Billy saw 19 animals at Grayson Zoo in the morning. He saw 17 more animals after lunch. How many animals did Billy see in all?
__________ animals
Answer:
Given that,
Billy saw animals at Grayson Zoo in the morning = 19
Billy saw animals at Grayson Zoo in the afternoon = 17
Total number of animals that Billy saw = 19 + 17

Lesson 3.7 Problem Solving

Construct Arguments
Solve & Share
Carrie has 16 more red apples than green apples. She has 24 green apples. How many red apples are there?
Use any strategy to solve. Use pictures, numbers, or words to explain your thinking and work.

I can … use pictures, numbers, and words to explain why my thinking and work are correct.

Thinking Habits
Construct Arguments
How can I use math to explain why my work is correct?
Am I using numbers and symbols correctly?
Is my explanation clear?

Visual Learning Bridge

Convince Me! Are both math arguments above clear and complete? Explain.

Guided Practice

Solve. Use pictures, words, or numbers to make a math argument. Show your work.
Question 1.
There are 16 chickens in the yard. There are 19 chickens in the barn. There are 30 nesting boxes. Will all of the chickens have a nest? Explain.

Answer:
Given that,
Total number of Chickens in a yard = 16
Total number of Chickens in a barn = 19
Total number of Chickens in a nesting  = 30
Total number of chickens = 16 + 19 = 35
5 chickens have no nest

Independent Practice

Solve each problem. Use pictures, words, or numbers to make a math argument. Show your work.
Question 2.
Greg had 45 sports cards. Jamal gives him 26 more cards. How many sports cards does Greg have now?

_________ sports cards
Answer:
Given that,
Total number of sports cards at Grah  = 45
Jamal gives more cards to Grah = 26
Total number of sports cards at Grah = 45 + 26 = 71

Question 3.
Denise drew 8 stars with crayons. Then she drew 6 more stars. Trina drew 5 stars. How many fewer stars did Trina draw than Denise?
________ fewer stars
Answer:
Given that,
Denise draw stars with crayons = 8
She draws more stars = 6
Total number of stars drawn by Denise = 8 + 6 = 14
Trina draw a star = 5
14 – 5 = 9
Trina draw 9 fewer stars than Denise

Problem Solving

Performance Task
Bean Bag Toss Evan and Pam each throw two bean bags. Points are added for a score. Pam’s total score is 100. Which two numbers did Pam’s bean bags land on?

Question 4.
Make Sense What information is given? What do you need to find?
Answer:
In the above task, Pam and Evan play a bean bag toss game.
The score Pam’s is 100
The numbers that Pam’s bean bag lands on are 56 and 44.
By adding 56 and 44 we get 100.so, the beam bag lands on 56 and 44.
Question 5.
Explain Which numbers did Pam’s bags land on? Explain how you know.
Answer:
Given that,
Pam’s bags land on 56 and 44
The total score Pam’s is 100
By adding 56 and 44 we get 100
So, Pam’s bags are landed on 56 and 44.

Question 6.
Explain How could you use a hundred charts to solve the problem? Explain.

Answer:
using a hundred charts for example you went to find the sum of 10  + 15.
first, mark the 10 in the hundred charts and down to 1 row and back to 5 places then we get 15 has the answer.
This is the way to solve the problem using a hundred charts.

Topic 3 Fluency Practice Activity

Find & Match
Find a partner. Point to a clue. Read the clue.
Look below the clues to find a match. Write the clue letter in the box next to the match.
Find a match for every clue.
I can … subtract within 20.

Clues
A. Every difference equals 3.
B. Every difference is less than 2.
C. Every difference equals 11 – 5.
D. Exactly two differences are equal.
E. Every difference is greater than 8.
F. Exactly three differences are odd.
G. Every difference equals 16 – 8.
H. Exactly three differences are even.

Topic 3 Vocabulary Review

Understand Vocabulary
Word List

• bar diagram
• break apart
• compensation
• mental math
• ones
• open number line
• tens

Question 1.
Circle the numbers that have a 3 in the one’s place.
33
45
13
38
Answer:
In the above-given numbers, 33 and 13 has 3 in the one’s place then circle the 33 and 13.
Question 2.
Cross out the numbers that do NOT have an 8 in the tens place.
80
18
78
89
Answer:
In the above-given numbers, 18 and 78 do not have 8 in the ten’s place. Then cross out the 18 and 78.

Question 3.
Write an equation to show how to break apart 54 by place value.
Answer: 50 + 4
Question 4.
Use the open number line to find 38 + 23. Add the tens and then add the ones.

Answer:
38 + 23
38 + (20 + 3)
58 + 3 = 61
First draw the Line.
Represent the number on the line.
The first number is 38 and counts by 20 then it gets 54 and jumps to 3 then it gets 61.
Count the numbers and draw an arrow.

Use Vocabulary in Writing
Question 5.
Describe a way to find 47 + 18. Use terms from the Word List.
Answer:
47 + (10 + 8)
(47 + 10) + 8
57 + 8 = 65

Topic 3 Reteaching

Set A

You can use a hundred charts to help you add. Find 62 + 12.
Start at 62. Move down 1 row to add the 1 ten in 12.
Then move over 2 columns to add the 2 ones in 12.

Use a hundred charts to find each sum.
Question 1.
85 + 15 = _______
Answer:
Using the hundred chart the sum of 85 + 15 is
In the hundred charts, we start at the 85 then down to 1 row then we get 95, and move front to 5 space then we get 100.
85 + 15 = 100
Question 2.
60 + 23 = _________
Answer:
Using the hundred chart the sum of 60 + 23 is
In the hundred charts, we start at 60 and then move down to 2 rows then we get 80 and move front to 3 space then we get 83
60 + 23 = 83

Set B

You can use an open number line to find 49 + 32.

Place 49 on the number line. There are 3 tens in 32. So, count on by 10 three times. There are 2 ones in 32. So, count on 2 from 79.
So, 49 + 32 = 81

Use an open number line to find each sum.
Question 3.
35 + 13 = ________

Answer:
35 + 13 = 48
First, draw the Line.
Represent the number on the line.
The first number is 35 and counts by 10 then it gets 45  and jumps to 3 then it gets 48.
Count the numbers and draw an arrow.

Question 4.
47 + 26 = _________

Answer:
47 + 26 = 73
First, draw the Line.
Represent the number on the line.
The first number is 47 and counts by 20 then it gets 67 and jumps to 6 then it gets 73.
Count the numbers and draw an arrow.

Set C

Find 55 + 17.
Break apart 17 into 10+ 7.

Break apart the second addend to find the sum. Show your work.
Question 5.
53 + 28 = _________
Answer:
53 + 28
53 + 20 + 8
73 + 8 = 81Question 6.
78 + 19 = _________
Answer:
78 + 19
78 + 10 + 9
88 + 9 = 97

Set D

Find 48 + 27.
48 is close to 50. So, take 2 from 27 and give it to 48 to make 50.
48 + 27 = ?

Use compensation to make numbers that are easier to add. Then solve. Show your work.
Question 7.
17 + 46 = ________
Answer:
17 + 46
17 + 40 + 6
57 + 6 = 63

Question 8.
29 + 57 = ________
Answer:
29 + 57
29 + 50 + 7
79 + 7 = 86

Set E

You can use different strategies and tools to find a sum.
You can:

• Use a hundred chart
• Use an open number line
• Break apart one addend
• Use compensation

Solve. Show your work.
Question 9.
Ted’s puzzle has 37 more pieces than his brother’s puzzle. His brother’s puzzle has 48 pieces. How many pieces does Ted’s puzzle have?
________ pieces
Answer:

Given that,
Ted’s puzzle has more pieces than her brother = 37
His brother puzzle has pieces = 48
Total number of pieces does Ted’s have = 48 + 37 = 85

Set F

Marla walks 12 blocks on Monday. On Tuesday, she walks 4 fewer blocks. How many blocks does Marla walk in all?
Blocks Marla walks on Tuesday:

Solve the two-step problem.
Question 10.
Wyatt has 16 crayons. He buys 24 new crayons. Then he finds 7 more crayons. How many crayons does Wyatt have now?

________ crayons
Answer:

Total number of crayon = 47

Set G

Thinking Habits
Construct Arguments
How can I use math to explain my work?
Am I using numbers and symbols correctly?
Is my explanation clear?

Solve the problem. Use words and numbers to make a math argument.
Question 11.
A second-grade class sets a goal to collect 70 cans. One week they collect 38 cans. The next week they collect 35 cans. Do they meet their goal?
Answer:
Given that,
A second-grade class set a goal to collect cans = 70
One week the second-grade class set collect cans = 38
Next week the second-grade class set collect cans = 35
Total number of cans they collected = 38 + 35 =73
Yes they meet their goal by collecting 73 cans out of 70

Topic 3 Assessment Practice

Question 1.
Which have a sum of 43? Choose all that apply.
☐ 33 + 10
☐ 28 + 13
☐ 10 + 33
☐ 19 + 24
☐ 10 + 21
Answer:
33 + 10 has a sum of 43
10 + 33 has a sum of 43
19 + 24 has a sum of 43
Question 2.
Terry has 63 crayons. She gets 25 more crayons. How many crayons does Terry have in all? Show your work.
________ crayons
Answer:
Given that,
Total number of crayons near Terry = 63
Tenny get more crayons = 25
Total number of crayons at Terry = 63 + 25 = 88
Question 3.
Which equation does this number line show?

A. 57 + 28 = 85
B. 57 + 38 = 95
C. 57 + 33 = 90
D. 57 + 39 = 96
Answer:
57 + 38 = 95
Question 4.
Use the numbers on the cards. Write the missing numbers under the number line to show how to find the sum of 40 + 35.

Answer:
Question 5.
Colin has 54 pennies and 28 nickels. How many coins does Colin have?
Break apart the second addend to solve. Show your work.
________ coins
Answer:
Given that,
Total number of pennies near Colin = 54
Total number of nickels near Colin = 28
Total number of coins near colin = 54 + 28
54 + (20 + 8)
(54 + 20) + 8
74 + 8 = 82

Question 6.
Show how to add 68 + 16 using the open number line.

68 + 16 = ___________
Answer:
68 + 16 = 84
First draw the Line.
Represent the number on the line.
The first number is 68 and counts by 10 then it gets 78 and jumps to 6 then it gets 84.
Count the numbers and draw an arrow.

Question 7.
Part A
Show how you can use an open number line to find 44 + 27.

44 + 27 = _________
Answer:
44 + 27 = 71
First draw the Line.
Represent the number on the line.
The first number is 44 and counts by 20 then it gets 64 and jumps to 7 then it gets 71.
Count the numbers and draw an arrow.

Part B
In words, tell how you used the open number line to find the sum.
Answer:
Suppose  we have a sum that is 14 + 13
Then draw a line and represent the numbers on a line and place a 14 on the line shift  10 from the 14 we get 24 then jump to 3 then we get 27.
The sum of 14 + 13 = 27.

Question 8.
Which have a sum of 70? Choose all that apply.
☐ 35 + 35
☐ 40 + 30
☐ 45 + 45
☐ 50 + 200
☐ 30 + 30
Answer:
35 + 35
40 + 30

Question 9.
Lisa has 18 markers. Adam has 22 markers. Will all of the markers fit in a box that can hold 38 markers?
Make a math argument. Explain.
Answer:
Given that,
Total number of markers near Lisa = 18
Total number of markers near Adam = 22
Total number of Markers fit in a box = 38
Total number of markers = 18 + 22 = 40
Total markers are not fit into a box.

Question 10.
Ted has 52 cards in a box. Tyrone has 48 more cards than Ted. How many cards does Tyrone have? Show your work to explain your thinking.
________ cards
Answer:
Given that
Ted has  cards in a box = 52
Tyrone has more card than Ted = 48
Total number of cards at Tyrone = 52 + 48 = 100
Question 11.
Which are equal to 47 + 25? Choose all that apply.
☐ 40 + 20 + 7 +5
☐ 40 + 20 + 12
☐ 50 + 12
☐ 50 + 22
Answer:
To find the sum of 47 + 25 we apply the 40 + 20 + 7 + 5

Question 12.
Emma has 46 rocks. She gets 25 more rocks from Gus. How many rocks does Emma have now?

________ rocks
Answer:
Given that,
Emma has rocks = 46
She get more rocks = 25
Total number of rocks at Emma = 46 + 25 = 71
Question 13.
Is each sum 64? Choose Yes or No.

Answer:

Question 14.
Break apart the second addend to find 56 + 38. Show your work.

56 + 38 = ________
Answer:
56 + 38
56 + 30 + 8
86 + 8 = 94

Question 15.
Write an equation to solve each part of the two-step problem.
Ken has 45 stamps. He uses 20 stamps. Then he buys 7 more stamps. How many stamps does he have now?

Ken has ________ stamps.
Answer:
Given that,
Ken has total number of stamps = 45
He used total number of stamps = 20
He buy another stamps = 7
Total number of stamps Ken have = 45 – 20 + 7
25 + 7 = 32

Question 16.
Show two different ways to find 28 + 49 using compensation.
Way 1
Way 2
Answer:
Way 1: 28 + 49 = 77
Way 2:  28 + 49
28 + 40 + 9
68 + 9 = 77

Topic 3 Performance Task

Popcorn Sales
A second-grade class is selling popcorn to help pay for a field trip.
This table shows how many boxes some students have sold.

Question 1.
How many boxes of popcorn did Ted and Mary sell in all? Use the open number line to solve. Show your work.

_________ boxes
Answer:
Given that,
Number of popcorn did Ted sell = 21
Number of popcorn did Mary sell = 34
Total number of popcorn box sell = 21 + 34 = 55
First draw the Line.
Represent the number on the line.
The first number is 21and counts by 30 then it gets 51and jumps to 4 then it gets 80.
Count the numbers and draw an arrow.

Question 2.
James says that Mary and Nancy sold more boxes in all than Darnell and Ted sold in all. Do you agree with him?
Circle:
Yes
No
Explain your answer.
Answer:
Given that,
Total number of boxes sold by Mary = 34
Total number of boxes sold by Nancy = 19
Total number of boxes sold by Mary and Nancy = 34 + 19 = 43
Total number of boxes sold by Darnell = 28
Total number of boxes sold by Ted = 21
A total number of boxes sold by Darnell and Ted = 21 + 28 = 49
James said wrong that Mary and Nancy sold fewer boxes than Darnell and Ted.
Question 3.
Which two students sold a total of 55 boxes? Use any strategy to solve. Show your work.
Circle the names of the two students.

Question 4.
Nancy sold 18 fewer boxes than Lucas. How many boxes did Lucas sell?

Part A
Solve the problem. Show your work and explain your thinking.
________ boxes
Answer:
Given that,
Nancy sold fewer boxes than Lucas = 18
Total number of boxes that Nancy sold = 19
Total number of boxes that Lucas sold more than Nancy = 19 – 18 = 1

Part B
Look at the list of strategies on the left. To show that your answer in Part A is correct, use a different strategy to solve the problem.
Answer:

Go through the enVision Math Common Core Grade 2 Answer Key Topic 14 More Addition, Subtraction, and Length regularly and improve your accuracy in solving questions.

enVision Math Common Core 2nd Grade Answers Key Topic 14 More Addition, Subtraction, and Length

Essential Question:
How can you add and subtract lengths?

enVision STEM Project: Modeling Land, Water, and Length
Find Out Find and share books and other sources that show the shapes and kinds of land and water in an area. Draw a picture or make a model to show the land or water in an area.
Journal: Make a Book Show what you learn in a book. In your book, also:

• Draw a picture to show the shape of some land or water in your area.
• Make up a math story about lengths. Draw a picture to show how to solve the problem in your story.

Review What You Know

Vocabulary
Question 1.
Circle the measuring unit that is better to estimate the length of a room.
meter
centimeter
Answer: centimeter

Question 2.
Circle the number of feet in 1 yard.
2 feet
3 feet
4 feet
12 feet
Answer: 3 feet

Question 3.
The clock shows the time a math class begins. Circle a.m. or p.m.

Answer: 10 a.m.

Estimate
Question 4.
Estimate the length of the eraser in centimeters.

About _______ centimeter
Answer: 4 centimeter

Compare
Question 5.
A sidewalk is 632 yards long. A jogging trail is 640 yards long.
Use <, >, or = to compare the lengths.
632 640
Answer: 632 < 640

Rectangles
Question 6.
Label the 2 missing lengths of the sides of the rectangle.

Answer: The missing lengths are 3cm and 4 cm.
In the rectangle opposite sides are equal. So, the 2 missing lengths of the sides of a rectangle are 3cm and 4cm.

Pick a Project

PROJECT 14A
How tall are Ferris wheels?
Project: Write a Ferris Wheel Story

PROJECT 14B
How big are insects?
Project: Make Insect Drawings

PROJECT 14C
How can you measure if you do not have tools?
Project: Make a Measurement Poster

PROJECT 14D
How is some food grown?
Project: Draw a Garden Plan

Lesson 14.1 Add and Subtract with Measurements

Solve & Share
The ant crawled along the edge of this blue rectangle. Measure the total distance the ant crawled. Show your work and be ready to explain it.
I can … solve problems by adding or subtracting length measurements.

Visual Learning Bridge

Convince Me! Explain how to find the distance around a square park that is 2 miles long on each side.

Guided Practice

Decide if you need to add or subtract. Then write an equation to help solve each problem.
Question 1.
What is the distance around the baseball card?

Question 2.
What is the distance around the puzzle?

Distance around: _________ in.
Answer:
The puzzle has four sides one side is 12in and 15in.
The opposite side of 12in is also 12in and the opposite side of 15in is also 15in.
The total distance around the puzzle is 15 + 15 + 12 + 12 = 54
The distance around the puzzle is 54in.
Independent Practice

Decide if you need to add or subtract. Then write an equation to help solve each problem.
Question 3.
What is the distance around the door?

_________
Distance around: ________ ft
Answer:
The door has four sides one side is 3ft and 7ft.
The opposite side of 3ft is also 3ft and the opposite side of 7ft is also 7ft.
The total distance around the door is 3 + 3 + 7 + 7 = 20
The distance around the door is 20ft.

Question 4.
What is the distance around the cell phone?

___________
Distance around: _________ in.
Answer:
The cell has four sides one side is 4in and 2in.
The opposite side of 2in is also 2in and the opposite side of 4in is also 4in.
The total distance around the cell is 2 + 2 + 4 + 4 = 12
The distance around the cell is 12in.

Question 5.
How much longer is the red scarf than the blue scarf?

________ in. longer
Answer:
Given that,
The length of the red scarf is 60in.
The length of the blue scarf is 45in.
Red scarf – blue scarf = 60 – 45 = 15
The red scarf is 15in longer than a blue scarf.

Question 6.
Algebra What is the length of the shorter side of the rectangle?

Complete the equation to solve.
20+ _______ + 20 + _______ = 60
The shorter side is ________ centimetres.
Answer:
The Given that,
The length of the longer side of the  rectangle is 20cm
The other side of the longer side is also 20cm
But the given equation is
20 + 20 = 60
40 = 60
60 – 40 = 20
20 can be divided into 2 shorter sides so, one shorter side is 10 and another shorter side is 10.
The shorter side is 20 centimetres.

Problem Solving

Decide if you need to add or subtract. Then write an equation to help solve each problem.
Question 7.
Model Ashley’s sunflower is 70 inches tall. Kwame’s sunflower is 60 inches tall. How much taller is Ashley’s sunflower than Kwame’s sunflower?

_________ inches taller
Answer:
Given that,
The length of Ashley’s sunflower is 70 inches.
The length of Kwame’s sunflower is 60 inches.
70 – 60 = 10
Ashley’s sunflower is 10inches longer than Kwame’s sunflower.

Question 8.
Model Ben compares the length of a leaf and a plant. The leaf is 15 centimetres. The plant is 37 centimetres. How much shorter is the leaf than the plant?

__________ centimeters shorter
Answer:
Given that,
The total length of the leaf is 15 centimeters.
The total length of the plant is 37 centimeters.
37 – 15 = 22
The length of the leaf is 22 centimeters shorter than the length of the plant.

Question 9.
Higher Order Thinking Tyler threw a ball 42 feet and then 44 feet. Sanjay threw a ball 38 feet and then 49 feet. Who threw the longer distance in all? Show you work.
Answer:
Given that,
Tyler threw a ball is 42 feet and then 44 feet.
Tyler threw a ball in total = 42 + 44 = 86
Sanjay threw a ball is 38 feet and then 49 feet.
Sanjay threw a ball in total = 38 + 49 = 87
Sanjay threw a ball longer distance than Tyler.

Question 10.
Assessment Practice What is the distance around the placemat?

A. 28 in.
B. 39 in.
C. 56 in.
D. 66 in.
Answer:
The placemat has four sides one side is 121in and 17in.
The opposite side of 11in is also 11in and the opposite side of 17in is also 17in.
The total distance around the placemat is 11 + 11 + 17 + 17 = 56
The distance around the placemat is 56in.
C is the correct option.

Lesson 14.2 Find Unknown Measurements

Solve & Share
Julie and Steve each cut a piece of yarn. The total length of both pieces is 12 cm. Measure each piece of yarn. Circle Julie and Steve’s pieces. Then explain your thinking.
I can … add or subtract to solve problems about measurements.

Visual Learning Bridge

Convince Me! How does drawing a yardstick help you solve the problem above?

Guided Practice

Write an equation using a ? for the unknown number. Solve with a picture or another way.
Question 1.
A square stamp measures 2 centimeters in length. How many centimeters long are two stamps?

Anawer: 2+2 = 4

Question 2.
Stuart’s desk is 64 centimeters long. His dresser is 7 centimeters longer than his desk. How long is Stuart’s dresser?
________ cm
Answer:
Given that,
Stuart’s desk is 64 centimeters long. His dresser is 7 centimeters longer than his desk.
64 + 7 = 71 centimeters
Thus his dresser is 71 centimeter long.

Independent Practice

Write an equation using a ? for the unknown number. Solve with a picture or another way.
Question 3.
Filipe’s pencil box is 24 centimeters long. Joe’s pencil box is 3 centimeters shorter than Filipe’s. How long is Joe’s pencil box?
_________ cm
Answer:
Given that
Filipe’s pencil box is 24 centimeters long. Joe’s pencil box is 3 centimeters shorter than Filipe’s.
24 – 3 = 21 centimeters
Thus Joe’s pencil box is 21 centimeters.

Question 4.
Clark threw a red ball and a blue ball. He threw the red ball 17 feet. He threw the blue ball 7 feet farther. How far did Clark throw the blue ball?
__________ ft
Answer:
Given that,
Clark threw a red ball and a blue ball. He threw the red ball 17 feet.
He threw the blue ball 7 feet farther.
17 + 7 = 24 feet.Question 5.
en Vision® STEM Ashlie’s map shows where animals, land, and water are at a zoo. The distance around her map is 38 inches. What is the length of the missing side?

____________ inches
Answer: The length of the missing side in the given map is 11 in.

Problem Solving

Solve each problem.
Question 6.
Make Sense A brown puppy is 43 centimeters tall. A spotted puppy is 7 centimeters shorter than the brown puppy. A white puppy is 14 centimeters taller than the brown puppy. How tall is the spotted puppy? Think about what you need to find.
_______ cm

Answer:
Given that,
the brown puppy is 43 centimeters tall.
A spotted puppy is 7 centimeters shorter than a brown puppy.
A white puppy is 14 centimeters taller than the brown puppy.
43 – 7 = 36 centimeters
Thus spotted puppy is 36 centimeters tall.

Question 7.
Vocabulary Complete the sentences using the terms below.
foot
yard
inch
A paper clip is about 1 _______ long.
My math book is about 1 ________ long.
A baseball bat is about 1 ________ long.
Answer:
A paper clip is about 1 inch long.
My math book is about 1 foot long.
A baseball bat is about 1 yard long

Question 8.
Higher Order Thinking Jack jumped 15 inches. Tyler jumped I inch less than Jack and 2 inches more than Randy. Who jumped the farthest? How far did each person jump?
Answer:
Given that,
Jack jumped = 15 inches
Tyler jumped 1 inch less than jack
Tyler jumped = 14 inches
Randy jumped = 14 + 2 = 16
Randy jumped farthest.

Question 9.
Assessment Practice Kim was 48 inches tall in January. She grew 9 inches during the year. How tall is Kim at the end of the year? Write an equation with an unknown and then draw a picture to solve.
Answer:
Given that,
Kim was tall in January = 48 inches
Kim grew during the year = 9 inches
Total Kim tall at the end of the year = 48 + 9 = 57 inches

Lesson 14.3 Continue to Find Unknown Measurements

Solve & Share
Alex has a piece of ribbon that is 45 feet long. He cuts the ribbon. Now he has 39 feet of ribbon. How many feet of ribbon did Alex cut off? Draw a picture and write an equation to solve. Show your work.
I can … add and subtract to solve measurement problems by using drawings and equations.

Visual Learning Bridge

Convince Me! How does writing an equation help you solve the problem above?

Guided Practice

Write an equation using a ? for the unknown number. Solve with a picture or another way.
Question 1.
A plant was 15 inches tall. It grew and is now 22 inches tall. How many inches did the plant grow?

Answer: 15 + 7 = 22

Question 2.
Each bus is 10 meters long. Each boat is 7 meters long. What is the total length of two buses and two boats?
Answer:
Given that,
Total number of buses = 2
Length of each bus = 10
Total length of two buses = 2 × 10 = 20
Total number of boats = 2
Length of each boats = 7
Total length of two boats = 7 × 2 = 14
Therefore, total length of two buses and two boats = 20 + 14 = 34

Independent Practice

Write an equation using a ? for the unknown number. Solve with a picture or another way.
Question 3.
Brent’s rope is 49 inches long. He cuts off some of the rope and now it is 37 inches long. How much rope did Brent cut off?
Answer:
Given that,
The total length of Brent’s rope = 49 inches
He cut off some of the rope and now it is = 37 inches
Brent cut off rope = 49 – 37 = 12inches
Question 4.
Sue ran for some meters and stopped. Then she ran another 22 meters for a total of 61 meters in all. How many meters did she run at first?
Answer:
Given that,
Sue ran total meters in all = 61 meters
Sue ran some meters from 61 meters = 22 meters
Sue rum at first time  = 61 – 22 = 39

Question 5.
Algebra Solve each equation. Use the chart.

Answer:
Problem Solving

Solve each problem.
Question 6.
Make Sense The yellow boat is 15 feet shorter than the green boat. The green boat is 53 feet long. How long is the yellow boat? Think about what you are trying to find. Write an equation to solve. Show your work.
________ ft
Answer:
Given that,
The total length of Green boat = 53 feets
Length of the yellow boat is 15 feet shorter than green boat = 53 – 15 = 38 feets
Length of the yellow boat is 38 feets

Question 7.

Vocabulary Steve measured the length of his desk. It measured 2 units.
Circle the unit Steve used.
meter
foot
centimeter
inch
Lori measured the length of her cat. It measured 45 units.
Circle the unit Lori used.
centimeter
yard
inch
foot
Answer:
Steve used:
Meter
Lori used
Centimeter

Question 8.
Higher Order Thinking Lucy’s ribbon is I foot long. Kathleen’s ribbon is 15 inches long. Whose ribbon is longer and by how many inches? Explain your thinking.
Answer:
Given that,
Lucy’s ribbon = 1 foot long
1 foot = 12 inches
Kathleen’s ribbon = 15 inches
Kathleen’s ribbon is longer than Lucy’s ribbon.

Question 9.
Assessment Practice Mary’s water bottle is 25 cm long. Joey’s water bottle is 22 cm long. Ella’s water bottle is 17 cm long.
Which statements are correct? Choose all that apply.
☐ Mary’s bottle is 8 cm longer than Ella’s.
☐ Joey’s bottle is 6 cm longer than Ella’s.
☐ Joey’s bottle is 3 cm shorter than Mary’s.
☐ Ella’s bottle is 8 cm longer than Mary’s.
Answer: Mary’s bottle is 8 cm longer than Ella’s and Joey’s bottle is 3 cm shorter than Mary’s are correct.

Lesson 14.4 Add and Subtract on a Number Line

Solve & Share
Amelia walks 18 blocks on Monday and 5 blocks on Tuesday. How many blocks does she walk in all?
Use the number line to show how many blocks Amelia walks. Then write an equation to show your work.
I can … add and subtract on a number line.

Visual Learning Bridge

Convince Me! Explain how to add 14 inches and 11 inches using a number line.

Guided Practice

Use the number lines to add or subtract.
Question 1.

Question 2.
28 – 14 = _______

Answer:
Subtraction of 28 and 14 is
28 – 14 = 14

Independent Practice

Use the number lines to add or subtract.
Question 3.
80 – 35 = ________

Answer:
Subtraction of 80 and 35 is
80 – 35 = 45

Question 4.
19+ 63 = ________

Answer:
Addition of 19 and 63
19 + 63 = 82

Question 5.
Higher Order Thinking Use the number line to show 15 inches plus O inches. Explain your thinking.

Answer:
15 inches + 0 inches = 15 inches

Question 6.
Number Sense Show each number below as a length from 0 on the number line. Draw four separate arrows.

Answer:

Problem Solving

Use the number line to solve each problem.
Question 7.
Use Tools A football team gains 15 yards 1 on its first play. The team gains 12 yards on its second play. How many yards does the team gain in two plays?

__________ yards
Answer:

Given that,
A football team gains on its first play = 15 yards.
A football team gains on its second play =12 yards.
Food ball team gains in two plays = 15 + 12 = 27 yards.

Question 8.
Use Tools Mia buys 25 feet of board. She uses 16 feet of board for a sandbox. How many feet of board does she have left?

_________ feet
Answer:
Given that,
Total length of board Mia buy = 25 feets
She uses a board for sand box = 16 feets
How many feets of board she left = 25 – 16 = 9

Question 9.
Higher Order Thinking The runners on the track team ran 12 miles on Monday. On Tuesday, they ran 6 more miles than they ran on Monday. How many miles did they run in all on both days?

_________ miles
Answer:
Given that,
The runners on the track team ran on Monday = 12 miles
The runners on the track team ran on Tuesday = 6 more miles than Monday = 6miles + 12miles = 18miles
They ran in all on both days = 12 miles+ 18 miles = 30 miles

Question 10.
Assessment Practice Deb has two pencils. One pencil is 9 cm long and the other pencil is 13 cm long. What is the total length of both pencils?
Use the number line to show your work.

___________ centimeters
Answer:
Given that,
Deb has two pencils
The total length of one pencil = 9 centimeters
The total length of other pencils = 13 centimeters
Total length of both the pencils = 9 centimetres + 13 centimetres = 22 centimetres

Lesson 14.5 Problem Solving

Use Appropriate Tools
Solve & Share

Choose a tool to solve each part of the problem. Be ready to explain which tools you used and why.
Which line is longer? How much longer? Draw a line that is that length.
I can … choose the best tool to use to solve problems.

Thinking Habits Which of these tools can I use?
counters
paper and pencil cubes
place-value blocks
measuring tools
string
number line
technology
Am I using the tool correctly?

Visual Learning Bridge

Convince Me! Explain why counters are NOT the best tool to use to solve the problem above.

Guided Practice

Choose a tool to use to solve the problem. \ Show your work. Explain why you chose that tool and how you got your answer.
Question 1.
Sara cut 19 centimeters of ribbon into two pieces. One piece is 11 centimeters long. How long is the other piece?
Answer:
Given that,
Sara cut 19 centimeters of ribbon into two pieces.
The length of one piece = 11 centimetres
The length of other piece = 19 centimetres – 11 centimetres = 8 centimetres.
The length of other pieces = 8 centimeters.

Independent Practice

Solve each problem. Show your work.
Question 2.
Work with a partner. Measure each other’s arm from the shoulder to the tip of the index finger. Measure to the nearest inch. Whose arm is longer and by how much?
Choose a tool to use to solve the problem. Explain why you chose that tool and how you got your answer.
Answer:

Question 3.
Marcel jumped 39 centimeters high. Jamal jumped 48 centimeters high. How much higher did Jamal jump than Marcel?
Which tool would you NOT use to solve this problem? Explain.
Answer:
Given that,
Marcel jumped = 39 centimetres
Jamal jumped = 48 centimetres
Jamal jumped more than Marcel.

Place value box tool is not used for solving the problem.

Problem Solving

Performance Task
Sailboats Zak is measuring sailboats at the dock. Mr. Lee’s sailboat is 64 feet long. Ms. Flint’s sailboat is 25 feet shorter than Mr. Lee’s boat. Help Zak find the length of Ms. Flint’s boat.

Question 4.
Use Tools Which tool would you NOT use to solve this problem? Explain.
Answer:

Question 5.
Be Precise Will you add or subtract to solve the problem?
______________
Write an equation. Use ? for the unknown.
______________
What unit of measure will you use?
______________
Answer:

Question 6.
Explain What is the length of Ms. Flint’s boat? Did you use a tool to solve the problem? Explain.
Answer:
Given that,
The length of Ms. Flint’s boat = 25 feet shorter than Mr. Lee’s boat.
Mr. Lee’s boat = 65 feets.
Length of the Ms. Flint’s boat = 65

Topic 14 Fluency Practice

Follow the path
Color a path from Start to Finish. Follow the sums and differences that are odd numbers. You can only move up, down, right, or left.
I can … add and subtract within 100.

Topic 14 Vocabulary Review

Understand Vocabulary
Choose a term from the Word List to complete each sentence.
Word List
• centimeter (cm)
• foot (ft)
• height
• inch (in.)
• length
• mental math
• meter (m)
• yard (yd)

Question 1.
The length of your finger can best be measured in centimeters or ___________.
Answer:
The length of your finger can best be measured in centimetres or inches.

Question 2.
100 ________ equals 1 meter.
Answer:
100 centimetres equals to 1 meter.

Question 3.
__________ is how tall an object is from bottom to top.
Answer:
Height is how tall an object is from bottom to top.

Write T for true or F for false.
Question 4.
_______ 1 yard is 5 feet long.
Answer:
False

Question 5.
________ 12 inches is I foot long.
Answer:
True

Question 6.
________ A centimeter is longer than a meter.
Answer:
False

Question 7.
_________ You can do mental math in your head.
Answer:
False

Use Vocabulary in Writing
Question 8.
Tell how to find the total length of two pieces of string. One piece of string is 12 inches long. The other piece is 9 inches long. Use terms from the Word List.
Answer:
Given that,
The total length of one piece of string = 12 inches
The total length of other pieces of string = 9 inches
The total length of two pieces = 12 inches + 9 inches = 21 inches

Topic 14 Reteaching

Set A

What is the distance around the front of the bookcase?

Add the lengths. Write an equation.
4+ 3+ 4+ 3 = 14
Distance around: 14 feet

Write an equation to help solve.
Question 1.
What is the distance around the front of the crayon box?

Distance around: _________ cm
Answer:
Given that,
The crayon box has four sides
The length of the two sides is 12cm and 9cm.
The opposite side of 12 cm is also 12 cm.
The opposite side of 9cm is also 9 cm
Total distance around crayon box = 12 + 12 + 9 + 9 = 42 centimetres.

Set B

A kite string is 27 feet long. Some of the string is cut off. Now the kite string is 18 feet long. How many feet of kite string were cut off?
Write an equation and draw a picture.
27 – ? = 18 or 18+? = 27

Write an equation using a ? for the unknown number. Then draw a picture to solve.
Question 2.
A piece of yarn is 42 inches long. Mia cuts some of it off. It is now 26 inches long. How much yarn did Mia cut off?
Answer:
Given that,
A piece of yarn = 42 inches long
Mia cuts some of it and now it is = 26 inches
Mia cut off yarn = 42 – 26 = 16 inches

Set C

A book measures 10 inches long. Another book measures 13 inches long. What is the total length of both books?
You can show 10 + 13 on a number line.

Solve the problem using the number line.
Question 3.
One room in Jackie’s house is 15 feet long. Another room is 9 feet long. What is the total length of both rooms?

Answer:
Given that,
The length of one room in Jackie’s house = 15 feets
The length of other room in Jackie’s house = 9 feets
Total length of two rooms in Jackie’s house = 15 + 9 = 24 feets

Set D

Thinking Habits
Use Tools
Which of these tools can I use?
counters
paper and pencil cubes
place-value blocks
measuring tools
string
number line
technology
Am I using the tool correctly?

Choose a tool to solve the problem.
Question 4.
Damon’s shoelace is 45 inches long. His shoelace breaks. One piece is 28 inches long. How long is the other piece?
Explain your solution and why you chose the tool you used.
Answer:
Given that,
The total length of Damon’s shoelace = 45 inches long.
His shoelace breaks into two pieces and one-piece length = 28 inches
The length of other piece = 45 inches – 28 inches = 17 inches

Topic 14 Assessment Practice

Question 1.
A notebook has a length of 7 in. and a width of 5 in. What is the total distance around the notebook? Use the image below for help.

Distance around: _______ in.
Answer:
Given that,
The note book has a length of 7 inches and 5 inches
Total distance around the note book = 7 + + 7 + 5 + 5 = 24
Total distance around the note book = 24 inches.

Question 2.
Kate is 48 inches tall. Tom is 2 inches taller than Kate. James is 3 inches shorter than Tom.
How tall is James?
A. 45 inches
B. 47 inches
C. 50 inches
D. 53 inches
Answer:
Given that,
Kate is 48 inches tall.
Tom is 2 inches tall than Kate = 48 + 2 = 50 inches
James is 3 inches shorter than Tom = 50 – 3 = 47 inches
James has 47 inches tall.
Option B is correct.

Question 3.
Alexis has a rope that is 7 feet long. Mariah’s rope is 9 feet long. Sam’s rope is 3 feet longer than Mariah’s rope.
Use the measurements on the cards to complete each sentence.

Sam’s rope is ________ long.
Alexis’s rope is ________ shorter than Mariah’s rope.
Sam’s rope is _________ longer than Alexis’s rope.
Answer:
Sam’s rope is 12 feet long.
Alexis’s rope is 2 feets shorter than Mariah’s rope.
Sam’s rope is 5 feet longer than Alexis’s rope.

Question 4.

Joe rides his bike 18 miles. Then he rides 7 more miles.
Use the number line to find how far Joe rides. Then explain your work.

Answer:
Given that,
Joe rides his bike = 18 miles.
He rides 7 more miles = 18 + 7 = 25 miles
Joe rides in total = 25 inches.

Question 5.
Pat says that each unknown equals 25 cm. Do you agree? Choose Yes or No.

Answer:

Question 6.
Grace got a plant that was 34 cm tall. The plant grew and now it is 42 cm tall. How many centimeters did the plant grow?
A. 8 cm
B. 12 cm
C. 42 cm
D. 76 cm
Answer:
Given that,
Grace got a plant that was 34 centimeters long.
The plant grows up to 42 centimeters tall.
How much the plant grow = 42 – 34 = 8 centimetres.
Option A is correct

Question 7.
Claire rides her bike 26 miles on Saturday and Sunday. She rides 8 miles on Sunday. How many miles does she ride on Saturday?
Write an equation to show the unknown. Then use the number line to solve the problem.

Answer:
Given that,
Claire rides her bike on Saturday and Sunday = 26 miles
She rides on Sunday = 8 miles
She rides on Saturday = 26 – 8 = 18 miles

Question 8.
Chris had a string that is 18 cm long. He cut off 7 cm. How much string is left?
A. Which of these tools could you use to solve the problem? Choose all that apply.
☐ centimeter ruler
☐ paper and pencil
☐ measuring cup
☐ number line
☐ inch ruler
Answer:

B. Write an equation to show the unknown.
Then draw a number line to solve.
________ _______ = _________
________ cm
Answer:

Topic 14 Performance Task

Fishing Fun Jim and his family go on a fishing trip. They use a boat and fishing gear to help them catch fish.

Question 1.
Jim takes this fishing box with him. What is the distance around the front of the fishing box? Write an equation to help solve the problem.

Distance around: _________ centimeters
Answer:
Jim takes this fishing box with him.
The length of the fishing box = 31
The breath of the fishing box = 16
Distance around the front of the fishing box = 31 + 16 = 47 centimetres

Question 2.
Jim’s fishing pole is 38 inches long. Performance His dad’s fishing pole is 96 inches Task long. How much shorter is Jim’s pole than his dad’s pole? Part A
Write a subtraction equation that shows the problem.

Part B
Solve the problem.
__________ inches shorter
Answer:
Jim’s fishing pole = 38 inches
His dad’s fishing pole = 96 inches
96 – 38 = 58
Jim’s fishing pole is 58 inches shorter than his dad’s fishing pole.

Question 3.
Jim catches a fish 49 yards away from the shore. Later, he helps row the boat closer to the shore. Now he is 27 yards away from the shore. How many yards closer to shore is Jim now than when he caught the fish?
Part A
Write an addition equation that shows the problem.
Answer:

Part B
Solve the problem.
______ yards
Answer:

Question 4.
Jim catches a silver fish that is 12 inches long. His sister catches a green fish that is 27 inches long. What is the total length of both fish?
Use the number line to solve.

__________ inches
Answer:
Given that,
Jim catches a silver fish that is 12 inches long.
His sister catches a green fish that is 27 inches long.
The total length of two fishes = 12 + 27 = 39 inches.

Question 5.
Jim has 27 yards of fishing line. He gives 12 yards of line to a friend. How many yards of line does Jim have left?

Answer:
Given that,
Jim has 27 yards of fishing line.
He gives 12 yards of line to a friend.
Jim left the fishing line = 27 – 12 = 15 yards

Question 6.
Jim’s family meets a man with a big boat. A parking spot at the dock is 32 feet long. Will the man’s car and boat fit in the parking spot?

Part A
What do you need to find?
Answer:
A parking spot at the dock is 32 feets
Length of the big boat = 27 feets.
Length of the car = 7 feets.
There is a space between car and boat = 2 feets.
Total length of car and boat = 34 feets
Yes the car and boat fit in the parking spot.

Part B
What is the total length? Write an equation to solve.
Will the car and boat fit in the parking spot? Explain.
_____________
What tool did you use? _______________
Answer:

Go through the enVision Math Common Core Grade 3 Answer Key Topic 13 Fraction Equivalence and Comparison regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 13 Fraction Equivalence and Comparison

Essential Question:
What are different ways to compare fractions?

enVision STEM Project: Life Cycles
Do Research A frog egg hatches into a tadpole that lives in water. The tadpole will change and eventually become an adult frog. Use the Internet or another source to gather information about the life cycle of a frog and other animals.

Journal: Write a Report Include what you found. Also in your report:

• Tell about what is in a frog’s habitat to support changes the frog goes through in its life cycle.
• Compare the life cycles of the different animals you studied.
• For the animals you studied, make up and solve problems using fractions. Draw fraction strips to represent the fractions.

Review What You Know

Choose the best term from the box. Write it on the blank.

• <
• >
• numerator
• unit fraction

Vocabulary

Question 1.
The symbol ___________ means is greater than.

Answer:
The symbol > means greater than.

Explanation:
In the above-given question,
given that,
greater than symbol is used to compare numbers.
for example:
3 > 1.
so the symbol > is used for large numbers when compared with small numbers.

Question 2.
The symbol _________ means is less than.

Answer:
The symbol < means less than.

Explanation:
In the above-given question,
given that,
less than a symbol is used to compare numbers.
for example:
1 < 3.
so the symbol < is used for small numbers when compared with large numbers.

Question 3.
A ________ represents one equal part of a whole.

Answer:
The fraction represents one equal part of a whole.

Explanation:
In the above-given question,
given that,
a fraction represents one equal part of a whole.
for example:
3/4.
the whole part is 4.
the 3/4 of the portion is filled.
so the fraction represents one equal part of a whole.

Comparing Whole Numbers

Compare. Write <, >, or =.
Question 4.
48 30

Answer:
48 > 30.

Explanation:
In the above-given question,
given that,
the two numbers are 48 and 30.
30 is less than 48.
48 is greater than 30.
48 > 30.

Question 5.
6 6

Answer:
6 = 6.

Explanation:
In the above-given question,
given that,
the two numbers are 6 and 6.
6 is equal to 6.
6 = 6.

Question 6.
723 732

Answer:
723 < 732.

Explanation:
In the above-given question,
given that,
the two numbers are 723 and 732.
723 is less than 732.
732 is greater than 723.
723 < 732.

Question 7.
152 183

Answer:
152 < 183.

Explanation:
In the above-given question,
given that,
the two numbers are 152 and 183.
152 is less than 183.
183 is greater than 152.
152 < 183.

Question 8.
100 10

Answer:
100 > 10.

Explanation:
In the above-given question,
given that,
the two numbers are 100 and 10.
100 is greater than 10.
10 is less than 100.
100 > 10.

Question 9.
189 99

Answer:
189 > 99.

Explanation:
In the above-given question,
given that,
the two numbers are 189 and 99.
189 is greater than 99.
99 is less than 189.
189 > 99.

Question 10.
456 456

Answer:
456 = 456.

Explanation:
In the above-given question,
given that,
the two numbers are 456 and 456.
456 is equal to 456.
456 = 456.

Question 11.
123 223

Answer:
123 < 223.

Explanation:
In the above-given question,
given that,
the two numbers are 123 and 223.
123 is less than 223.
223 is greater than 123.
123 < 223.

Question 12.
421 399

Answer:
421 > 399.

Explanation:
In the above-given question,
given that,
the two numbers are 421 and 399.
421 is greater than 399.
399 is less than 421.
421 > 399.

Question 13.
158 185

Answer:
158 < 185.

Explanation:
In the above-given question,
given that,
the two numbers are 158 and 185.
158 is less than 185.
185 is greater than 158.
158 < 185.

Question 14.
117 117

Answer:
117 = 117.

Explanation:
In the above-given question,
given that,
the two numbers are 117 and 117.
117 is equal to 117.
117 = 117.

Question 15.
900 893

Answer:
900 > 893.

Explanation:
In the above-given question,
given that,
the two numbers are 900 and 893.
900 is greater than 893.
893 is less than 900.
900 > 893.

Identifying Fractions

For each shape, write the fraction that is shaded.
Question 16.

Answer:
The fraction is 4/8.

Explanation:
In the above-given question,
given that,
the figure contains 8 boxes.
4 boxes are filled.
4/8 portion of the boxes are filled.
4/8 = 1/2.
so half portion of the boxes is filled.

Question 17.

Answer:
The fraction is 1/6.

Explanation:
In the above-given question,
given that,
there are 6 boxes in the figure.
1 box is filled.
so 1/6 portion is filled.

Question 18.

Answer:
The fraction is 2/4.

Explanation:
In the above-given question,
given that,
the figure contains 4 boxes.
2 boxes are filled.
2/4 portion of the boxes are filled.
2/4 = 1/2.
so half portion of the boxes is filled.

Division

Divide.
Question 19.
30 ÷ 5

Answer:
The answer is 6.

Explanation:
In the above-given question,
given that,
the two numbers are 30 and 5.
5 x 6 = 30.
30 / 5 = 6.

Question 20.
72 ÷ 8

Answer:
72 / 8 = 9.

Explanation:
In the above-given question,
given that,
the two numbers are 72 and 8.
8 x 9 = 72.
72 / 8 = 9.

Question 21.
28 ÷ 4

Answer:
28 / 4 = 7.

Explanation:
In the above-given question,
given that,
the two numbers are 28 and 4.
4 x 7 = 28.
28 / 4 = 7.

Question 22.
48 ÷ 6

Answer:
48 / 6 = 8.

Explanation:
In the above-given question,
given that,
the two numbers are 48 and 6.
6 x 8 = 48.
48 / 6 = 8.

Question 23.
81 ÷ 9

Answer:
81 / 9 = 9.

Explanation:
In the above-given question,
given that,
the two numbers are 81 and 9.
9 x 9 = 81.
81 / 9 = 9.

Question 24.
45 ÷ 5

Answer:
45 / 5 = 9.

Explanation:
In the above-given question,
given that,
the two numbers are 45 and 5.
5 x 9 = 45.
45 / 5 = 9.

Question 25.
32 ÷ 8

Answer:
32 / 8 = 4.

Explanation:
In the above-given question,
given that,
the two numbers are 32 and 8.
8 x 4 = 32.
32 / 8 = 4.

Question 26.
42 ÷ 6

Answer:
42 / 6 = 7.

Explanation:
In the above-given question,
given that,
the two numbers are 42 and 6.
6 x 7 = 42.
42 / 6 = 7.

Question 27.
49 ÷ 7

Answer:
49 / 7 = 7.

Explanation:
In the above-given question,
given that,
the two numbers are 49 and 7.
7 x 7 = 49.
49 / 7 = 7.

Question 28.
How can you check if the answer to 40 ÷ 5 is 8?

Answer:
40 / 5 = 8.

Explanation:
In the above-given question,
given that,
the two numbers are 40 and 5.
40 / 5 = 8.
8 x 5 = 40.

Pick a Project

PROJECT 13A
Do you want to ride a horse?
Project: Design a Racetrack for Horses

PROJECT 13B
How deep do you have to dig before you reach water?
Project: Create a Picture of a Well

PROJECT 13C
How many coffee beans does it take to fill up a container?
Project: Plot Fractions on a Number Line

3-ACT MATH PREVIEW

Math Modeling
What’s the Beef?

Lesson 13.1 Equivalent Fractions: Use Models

Solve & Share
Gregor threw a softball of the length of the yard in front of his house. Find as many fractions as you can that name the same part of the length of the yard that Gregor threw the ball. Explain how you decided
I can … find equivalent fractions that name the same part of a whole.

Answer:
1/9, 2/9, 3/9, 4/9.

Explanation:
In the above-given question,
given that,
Gregor threw a softball off the length of the yard in front of his house.
Gregor threw the 1st ball at 1 yard.
1/9.
the length of the yard is 9.
Gregor threw the 2nd ball at 2 yards.
2/9.
Gregor threw the 3rd ball at 3 yards.
3/9.
Gregor threw the 4th ball at 4 yards.
4/9.
so the fractions are 1/9, 2/9, 3/9, and 4/9.

Look Back! How can fraction strips help you tell if a fraction with a denominator of 2, 3, or 6 would name the same part of a whole as \(\frac{3}{4}\)?

Answer:
2/4 and 6/4.

Explanation:
In the above-given question,
given that,
the denominators are 2, 3, and 6.
3/4 and 2/4 = 1/2.
6/4 = 3/2.

Essentials Question
How Can Different Fractions Name the Same Part of a Whole?

Visual Learning Bridge
The Chisholm Trail was used to drive cattle to market. Ross’s herd has walked \(\frac{1}{2}\) the distance to market. What is another way to name \(\frac{1}{2}\)?

\(\frac{1}{2}\) = \(\frac{}{}\) You can use fraction strips.

The fractions \(\frac{1}{2}\) and \(\frac{2}{4}\) represent the same part of the whole.
Two \(\frac{1}{4}\) strips are equal to \(\frac{1}{2}\), so \(\frac{1}{2}\) = \(\frac{2}{4}\).
Another name for \(\frac{1}{2}\) is \(\frac{2}{4}\).

You can find other equivalent fractions. Think about fractions that name the same part of the whole.

Four \(\frac{1}{8}\) strips are equal to \(\frac{1}{2}\), so \(\frac{1}{2}\) = \(\frac{4}{8}\).
Another name for \(\frac{1}{2}\) is \(\frac{4}{8}\)

Convince Me! Look for Relationships In the examples above, what pattern do you see in the fractions that are equivalent to \(\frac{1}{2}\)? What is another name for \(\frac{1}{2}\) that is not shown above?

Answer:
The other name is 4/8.

Explanation:
In the above-given question,
given that,
Four \(\frac{1}{8}\) strips are equal to \(\frac{1}{2}\).
\(\frac{1}{2}\) = \(\frac{4}{8}\).
\(\frac{1}{2}\) is \(\frac{4}{8}\).
so the other name is 4/8.

Another Example!
You can find an equivalent fraction for \(\frac{4}{6}\) using an area model.

Both area models have the same-sized whole. One is divided into sixths. The other shows thirds. The shaded parts show the same part of a whole. Because \(\frac{4}{6}\) = \(\frac{2}{3}\), another name for \(\frac{4}{6}\) is \(\frac{2}{3}\).

Guided Practice

Do You Understand?
Question 1.
Divide the second area model into sixths. Shade it to show a fraction equivalent to \(\frac{1}{3}\):

Answer:
1/3 = 2/6.

Explanation:
In the above-given question,
given that,
divide the second area model into sixths.
\(\frac{1}{3}\) = \(\frac{2}{6}\).
\(\frac{1}{3}\) is \(\frac{2}{6}\).
2/6 = 1/3.

Do You Know How?
Question 2.
Use the fraction strips to help find an equivalent fraction.

Answer:
1/4 = 4/16.

Explanation:
In the above-given question,
given that,
\(\frac{1}{4}\) = \(\frac{4}{16}\).
\(\frac{4}{16}\) is \(\frac{1}{4}\).
1/4 = 4/16.

Independent Practice

Question 3.
Use the fraction strips to help find an equivalent fraction.

Answer:
1/2 = 4/8.

Explanation:
In the above-given question,
given that,
1/4 + 1/4 = 1/2.
1/2 + 1/2 = 1.
4/8 = 1/2.

Question 4.
Divide the second area model into eighths. Shade it to show a fraction equivalent to \(\frac{1}{2}\).

Answer:
1/2 = 4/8.

Explanation:
In the above-given question,
given that,
divide the second area model into eights.
\(\frac{1}{2}\) = \(\frac{4}{8}\).
\(\frac{1}{2}\) is \(\frac{4}{8}\).
1/2 = 4/8.

In 5-8, find each equivalent fraction. Use fraction strips or draw area models to help.
Question 5.
\(\frac{3}{4}\) = \(\frac{}{8}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\).

Explanation:
In the above-given question,
given that,
divide the 1st area model into fourths.
divide the second area model into eights.
3/4 = 6/8.
6/8 = 3/4.

Question 6.
\(\frac{6}{6}\) = \(\frac{}{8}\)

Answer:
\(\frac{6}{6}\) = \(\frac{1}{8}\).

Explanation:
In the above-given question,
given that,
divide the 1st area model into sixths.
divide the second area model into eights.
6/6 = 1.
1/8 = 6/6.

Question 7.
\(\frac{2}{6}\) = \(\frac{}{3}\)

Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\).

Explanation:
In the above-given question,
given that,
divide the 1st area model into sixths.
divide the second area model into thirds.
2/6 = 1/3.
1/3 = 2/6.

Question 8.
\(\frac{4}{8}\) = \(\frac{}{2}\)

Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\).

Explanation:
In the above-given question,
given that,
divide the 1st area model into eigths.
divide the second area model into halfs.
4/8 = 1/2.
1/2 = 4/8.

Problem Solving

In 9 and 10, use the fraction strips at the right.

Question 9.
Marcy used fraction strips to show equivalent fractions. Complete the equation.
\(\frac{}{4}\) = ________

Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\).

Explanation:
In the above-given question,
given that,
divide the 1st area model into fourths.
divide the second area model into eights.
1/4 = 2/8.
2/8 = 1/4.

Question 10.
Rita says the fraction strips show fractions that are equivalent to \(\frac{1}{2}\). Explain what you could do to the diagram to see if she is correct.

Answer:
\(\frac{2}{4}\) = \(\frac{1}{2}\).

Explanation:
In the above-given question,
given that,
divide the 1st area model into fourths.
divide the second area model into halves.
2/4 = 1/2.
1/2 = 2/4.

Question 11.
Reasoning A band learns 4 to 6 new songs every month. What is a good estimate for the number of songs the band will learn in 8 months? Explain.

Answer:
The number of songs the band will learn in 8 months = 80 songs.

Explanation:
In the above-given question,
given that,
A band learns 4 to 6 new songs every month.
4 + 6 = 10.
10 x 8 = 80.
so the number of songs the band will learn in 8 months = 80 songs.

Question 12.
Three-eighths of a playground is covered by grass. What fraction of the playground is NOT covered by grass?

Answer:
The fraction of the playground is not covered by grass = 5/8.

Explanation:
In the above-given question,
given that,
three-eights of a playground is covered by grass.
8 – 3 = 5.
so the fraction of the playground is not covered by grass = 5/8.

Question 13.
Higher Order Thinking Aiden folded 2 strips of paper into eighths. He shaded a fraction equal to \(\frac{1}{4}\) on the first strip and a fraction equal to \(\frac{3}{4}\) on the second strip. Use eighths to show the fractions Aiden shaded on the pictures to the right. Which fraction of each strip did he shade?

Answer:
The fraction he shaded = 6/8.

Explanation:
In the above-given question,
given that,
Aiden folded 2 strips of paper into eighths.
2/8.
He shaded a fraction equal to \(\frac{1}{4}\) on the first strip.
1/4.
fraction equal to \(\frac{3}{4}\) on the second strip.
3/4.
he shaded the 6/8 portion of each strip.
6/8 = 3/4.

Assessment Practice

Question 14.
Which fractions are equivalent? Select all that apply.

Answer:
1/4 and 2/8.
3/4 and 6/8.
2/4 and 4/8.

Explanation:
In the above-given question,
given that,
there are three equivalent fractions.
the fractions are:
2/8 = 1/4.
6/8 = 3/4.
4/8 = 2/4.

Lesson 13.2 Equivalent Fractions: Use the Number Line

Solve & Share
The top number line shows a point at \(\frac{1}{4}\). Write the fraction for each of the points labeled A, B, C, D, E, and F. Which of these fractions show the same distance from 0 as \(\frac{1}{4}\)?
I can … use number lines to represent equivalent fractions.

Look Back! How can number lines show that two fractions are equivalent?

Answer:
The fractions are 1/2, 2/4, 3/4, 2/8, 4/8, and 4/6.

Explanation:
In the above-given question,
given that,
The number line A shows the fraction 1/2.
B shows the fraction 2/4.
C shows the fraction 3/4.
D shows the fraction 2/8.
E shows the fraction 4/8.
F shows the fraction 4/6.
2/4 = 1/2.
2/8 = 1/4.
4/8 = 1/2.
4/6 = 2/3.

Essential Question
How Can You Use Number Lines to Find Equivalent Fractions?

Visual Learning Bridge
The Circle W Ranch 1-mile trail has water for cattle at each \(\frac{1}{4}\) mile mark. The Big T Ranch 1-mile trail has water for cattle at the \(\frac{1}{2}\)-mile mark. What fractions name the points on the trails where there is water for cattle at the same distance from the start of each trail?

You can use number lines to find the fractions.

The fractions \(\frac{2}{4}\) and \(\frac{1}{2}\) name the same points on the trails where there is water for cattle. They are at the same distance from the start of the trails.

Convince Me! Model with Math lan paints \(\frac{6}{8}\) of a fence. Anna paints \(\frac{3}{4}\) of another fence of equal size and length. How can you show that lan and Anna have painted the same amount of each fence?

Answer:
Yes, both Anna and Lan have painted the same amount of each fence.

Explanation:
In the above-given question,
given that,
Lan paints \(\frac{6}{8}\) of a fence.
Anna paints \(\frac{3}{4}\) of another fence of equal size and length.
3/4 = 6/8.
2 x 3 = 6.
4 x 2 = 8.
so both Anna and Lan have painted the same amount of each fence.

Guided Practice

Do You Understand?
Question 1.
Complete the number line to show that \(\frac{2}{6}\) and \(\frac{1}{3}\) are equivalent fractions.

Answer:
2/6 = 1/3.

Explanation:
In the above-given question,
given that,
the fractions on the number line are:
1/6, 2/6, 3/6, 4/6, and 5/6.
2/6 = 1/3.
4/6 = 2/3.

Question 2.
Sheila compares \(\frac{4}{6}\) and \(\frac{4}{8}\) she discovers that the fractions are NOT equivalent. How does Sheila know?

Answer:
Yes, both fractions are not equivalent.

Explanation:
In the above-given question,
given that,
Sheila compares \(\frac{4}{6}\) and \(\frac{4}{8}\).
4/6 = 2/3.
2 x 2 = 4.
2 x 3 = 6.
4/8 = 2/4.
2 x 2 = 4.
4 x 2 = 8.
so 4/6 is not equal to 4/8.

Do You Know How?
In 3 and 4, find the missing equivalent fractions on the number line. Then write the equivalent fractions below.
Question 3.

Answer:
The missing equivalent fractions on the number line is 3/6.

Explanation:
In the above-given question,
given that,
the fractions on the number line are:
1/6, 2/6, 3/6, 4/6, 5/6, and 1.
3/6 = 1/2.
so the 3/6 and 1/2 are the equivalent fractions.

Question 4.

Answer:
6/8 = 3/4.

Explanation:
In the above-given question,
given that,
the fractions on the number line are:
1/8, 2/8, 3/8, 4/8, 5/8, 6/8, and 7/8.
2/8 = 1/4.
4/8 = 1/2.
6/8 = 3/4.
2 x 3 = 6.
2 x 4 = 8.

Independent Practice

In 5-8, find the missing equivalent fractions on the number line. Then write the equivalent fractions below.
Question 5.

Answer:
The missing equivalent fractions on the number line are 2/8.

Explanation:
In the above-given question,
given that,
the fractions on the number line are 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, and 7/8.
2/8 = 1/4.
1 x 2 = 2.
4 x 2 = 8.
so the missing equivalent fraction is 2/8 = 1/4.

Question 6.

Answer:
The missing equivalent fractions on the number line are 4/6.

Explanation:
In the above-given question,
given that,
the fractions on the number line are 1/6, 2/6, 3/8, and 5/6.
2/6 = 1/3.
1 x 2 = 2.
3 x 2 = 6.
4/6 = 2/3.
2 x 2 = 4.
3 x 2 = 6.
so the missing equivalent fraction is 4/6 = 2/3.

Question 7.

Answer:
The missing equivalent fractions on the number line are 4/8.

Explanation:
In the above-given question,
given that,
the fractions on the number line are 1/8, 2/8, 3/8, 5/8, 6/8, and 7/8.
2/8 = 1/4.
1 x 2 = 2.
4 x 2 = 8.
4/8 = 2/4.
2 x 2 = 4.
4 x 2 = 8.
so the missing equivalent fraction is 4/8 = 2/4.

Question 8.

Answer:
The missing equivalent fractions on the number line are 6/6.

Explanation:
In the above-given question,
given that,
the fractions on the number line are 1/6, 2/6, 3/6, 4/6, and 5/6.
2/6 = 1/3.
1 x 2 = 2.
3 x 2 = 6.
4/6 = 2/3.
2 x 2 = 4.
3 x 2 = 6.
6/6 = 1.
1 x 6 = 6.
so the missing equivalent fraction is 6/6 = 1.

Problem Solving

Question 9.
Number Sense Bradley had 40 slices of pizza to share. How many pizzas did he have? Explain how you solved the problem.

Answer:
The number of pizzas did he have = 5.

Explanation:
In the above-given question,
given that,
Bradley had 40 slices of pizza to share.
each pizza was cut into 8 slices.
40/8 = 5.
5 x 8 = 40.
so the number of pizzas did he have = 5.

Question 10.
Ms. Owen has 15 magazines to share among 5 students for an art project. How many magazines will each student get? Use the bar diagram to write an equation that helps solve the problem.

Answer:
The number of magazines will each student get = 3.

Explanation:
In the above-given question,
given that,
Ms. Owen has 15 magazines to share among 5 students for an art project.
15 / 5 = 3.
3 + 3 + 3 + 3 + 3 = 15.
3 x 5 = 15.
so the number of magazines will each student get = 3.

Question 11.
Yonita has 28 different apps on her computer. Casey has 14 music apps and 20 game apps on his computer. How many more apps does Casey have than Yonita? Explain.

Answer:
The number of apps does Casey has more than Yonita = 6.

Explanation:
In the above-given question,
given that,
Yonita has 28 different apps on her computer.
Casey has 14 music apps and 20 game apps on his computer.
14 + 20 = 34.
34 – 28 = 6.
so the number of apps does Casey has more than Yonita = 6.

Question 12.
Construct Arguments How can you tell, just by looking at the fractions, that \(\frac{2}{4}\) and \(\frac{3}{4}\) are NOT equivalent? Construct an argument to explain.

Answer:
Yes, 2/4 and 3/4 are not equivalent fractions.

Explanation:
In the above-given question,
given that,
the fraction 2/4 = 1/2.
1 x 2 = 2.
2 x 2 = 4.
the fraction 3/4 is not an equivalent fraction.
so both the fractions are not equal.

Question 13.
Higher Order Thinking Fiona and Gabe each had the same length of rope. Fiona used \(\frac{2}{3}\) of her rope. Using sixths, what fraction of the length of rope will Gabe need to use to match the amount Fiona used? Draw a number line as part of your answer.

Answer:
The fraction of the rope Gabe used is 4/6.

Explanation:
In the above-given question,
given that,
Fiona and Gabe each had the same length of rope.
Fiona used \(\frac{2}{3}\) of her rope.
4/6 = 2/3.
2 x 2 = 4.
3 x 2 = 6.
so the fraction of rope Gabe used is 4/6.

Assessment Practice

Question 14.
Use the number line to find which fraction is equivalent to \(\frac{3}{6}\).

Answer:
Option A is the correct answer.

Explanation:
In the above-given question,
given that,
3/6 = 1/2.
1 x 3 = 3.
3 x 2 = 6.
1/2 = 3/6.
so option A is correct.

Question 15.
Use the number line to find which fraction is equivalent to \(\frac{4}{8}\).

Answer:
Option C is the correct answer.

Explanation:
In the above-given question,
given that,
4/8 = 2/4.
2 x 2 = 4.
4 x 2 = 8.
2/4 = 4/8.
so option C is correct.

Lesson 13.3 Use Models to Compare Fractions: Same Denominator

Solve & Share
Maria and Evan are both jogging a mile. Maria has jogged mile, and Evan has jogged mile. Show how far each has jogged. Use any model you choose. Who jogged farther? How do you know?
I can … compare fractions that refer to the same-sized whole and have the same denominator by comparing their numerators.

Look Back! Suppose Evan had jogged \(\frac{5}{8}\) mile instead of \(\frac{3}{8}\) mile. Now, who has jogged farther? Explain.

Answer:
Evan jogged farther than Maria.

Explanation:
In the above-given question,
given that,
Evan had jogged \(\frac{5}{8}\) mile instead of \(\frac{3}{8}\).
5/8 – 3/8 = 2/8.
so I think maria jogged very little when compared to Evan.
so Evan jogged farther than Maria.

Essential Question
How Can You Compare Fractions with the Same Denominator?

Visual Learning Bridge
Two banners with positive messages are the same size. One banner is \(\frac{4}{6}\) yellow, and the other banner is \(\frac{2}{6}\) yellow. Which is greater, \(\frac{4}{6}\) or \(\frac{2}{6}\)?

\(\frac{4}{6}\) is 4 of the unit fraction is \(\frac{1}{6}\).
\(\frac{2}{6}\) of the unit fraction \(\frac{1}{6}\).
So, \(\frac{4}{6}\) is greater than \(\frac{2}{6}\).

Record the comparison using symbols or words.
\(\frac{4}{6}\) > \(\frac{2}{6}\)
Four sixths is greater than two sixths.
If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction.

Convince Me! Reasoning Write a number for each numerator to make each comparison true. Use a picture and words to explain how you decided.

Guided Practice

Do You Understand?
Question 1.
Explain how you can use fraction strips to show whether \(\frac{5}{6}\) or \(\frac{3}{6}\) of the same whole is greater.

Answer:
5/6 > 3/6.

Explanation:
In the above-given question,
given that,
the fractions are 5/6 and 3/6.
so 5/6 is greater than 3/6.
3/6 < 5/6.
5/6 > 3/6.

Question 2.
Which is greater, \(\frac{3}{4}\) or \(\frac{2}{4}\)? Draw \(\frac{1}{4}\)-strips to complete the diagram and answer the question.

Answer:
3/4 is greater than 2/4.

Explanation:
In the above-given question,
given that,
3/4 is greater than 2/4.
the whole is 4.
but one time it is divided into 3 parts.
it is divided into 2 parts.
so 3/4 > 2/4.

Do You Know How?
In 3 and 4, compare. Write <, >, or =. Use the fraction strips to help.
Question 3.

Answer:
2/8 > 1/8.

Explanation:
In the above-given question,
given that,
the fractions are 2/8 and 1/8.
1/8 + 1/8 = 2/8.
2/8 is greater than 1/8.
so 2/8 > 1/8.

Question 4.

Answer:
3/6 < 5/6.

Explanation:
In the above-given question,
given that,
the fractions are 3/6 and 5/6.
5/6 is divided into 5 parts.
1/6 + 1/6 + 1/6 = 3/6.
so 3/6 < 5/6.

Independent Practice

Leveled Practice In 5-14, compare. Write <, >, or =. Use or draw fraction strips to help. The fractions refer to the same whole.
Question 5.

Answer:
3/8 < 4/8.

Explanation:
In the above-given question,
given that,
the two fractions are 3/8 and 4/8.
1/8 + 1/8 + 1/8 = 3/8.
1/8 + 1/8 + 1/8 + 1/8 = 4/8.
so 3/8 < 4/8.

Question 6.

Answer:
3/4 = 3/4.

Explanation:
In the above-given question,
given that,
the two fractions are 3/4 and 3/4.
1/4 + 1/4 + 1/4 = 3/4.
3/4 = 3/4.
so both of them are equal.

Question 7.
\(\frac{6}{8}\) \(\frac{3}{8}\)

Answer:
6/8 > 3/8.

Explanation:
In the above-given question,
given that,
the two fractions are 6/8 and 3/8.
6/8 = 3/4.
2 x 3 = 6.
4 x 2 = 8.
1/8 + 1/8 + 1/8 = 3/8.
6/8 > 3/8.

Question 8.
\(\frac{5}{8}\) \(\frac{7}{8}\)

Answer:
5/8 < 7/8.

Explanation:
In the above-given question,
given that,
the two fractions are 5/8 and 7/8.
1/8 + 1/8 + 1/8  + 1/8 + 1/8 = 5/8.
1/8 x 7 = 7/8.
5/8 < 7/8.

Question 9.
\(\frac{1}{2}\) \(\frac{1}{2}\)

Answer:
1/2 = 1/2.

Explanation:
In the above-given question,
given that,
the two fractions are 1/2 and 1/2.
1/2 x 1 = 1/2.
1/2 x 1 =1/2.
so both of them are equal.

Question 10.
\(\frac{1}{3}\) \(\frac{2}{3}\)
Answer:

1/3 < 2/3.

Explanation:
In the above-given question,
given that,
the two fractions are 1/3 and 2/3.
1/3 x 1 = 1/3.
1/3 + 1/3 = 2/3.
1/3 < 2/3.

Question 11.
\(\frac{6}{6}\) \(\frac{3}{6}\)
Answer:

6/6 > 3/6.

Explanation:
In the above-given question,
given that,
the two fractions are 6/6 and 3/6.
1/6 + 1/6 + 1/6  + 1/6 + 1/6 + 1/6 = 6/6.
1/6 + 1/6 + 1/6 = 3/6.
6/6 > 3/6.

Question 12.
\(\frac{2}{8}\) \(\frac{3}{8}\)
Answer:

2/8 < 3/8.

Explanation:
In the above-given question,
given that,
the two fractions are 2/8 and 3/8.
1/8 + 1/8 = 2/8.
1/8 + 1/8 +1/8 = 3/8.
2/8 < 3/8.

Question 13.
\(\frac{3}{3}\) \(\frac{1}{3}\)
Answer:

3/3 > 1/3.

Explanation:
In the above-given question,
given that,
the two fractions are 3/3 and 1/3.
1/3 + 1/3 + 1/3  = 3/3.
1/3 x 1 = 1/3.
3/3 > 1/3.

Question 14.
\(\frac{1}{4}\) \(\frac{3}{4}\)
Answer:

1/4 < 3/4.

Explanation:
In the above-given question,
given that,
the two fractions are 1/4 and 3/4.
1/4 x 1 = 1/4.
1/4 +1/4 + 1/4  = 3/4.
1/4 < 3/4.

Problem Solving

In 15 and 16, use the pictures of the strips that have been partly shaded.

Question 15.
Compare. Write <, >, or =
The green strips show \(\frac{1}{6}\) \(\frac{2}{6}\)

Answer:
1/6 < 2/6.

Explanation:
In the above-given question,
given that,
the two fractions are 1/6 and 2/6.
1/6 x 1 = 1/6.
1/6 +1/6 = 2/6.
1/6 < 2/6.

Question 16.
Do the yellow strips show \(\frac{2}{4}\) > \(\frac{3}{4}\)? Explain.

Answer:
No, 2/4 < 3/4.

Explanation:
In the above-given question,
given that,
the two fractions are 2/4 and 3/4.
1/4 +1/4 = 2/4.
1/4 +1/4 + 1/4  = 3/4.
2/4 < 3/4.

Question 17.
Izzy and Henry have two different pizzas. Izzy ate \(\frac{3}{8}\) of her pizza. Henry ate \(\frac{3}{8}\) of his pizza. Izzy ate more pizza than Henry. How is this possible? Explain.

Answer:
No, it was not possible.

Explanation:
In the above-given question,
given that,
Izzy and Henry have two different pizzas.
Izzy ate \(\frac{3}{8}\) of her pizza.
Henry ate \(\frac{3}{8}\) of his pizza.
3/8 = 1/8 + 1/8 + 1/8.
3/8 x 1 = 3/8.
3/8 = 3/8.
so both of them ate the equal.

Question 18.
Generalize Two fractions are equal. They also have the same denominator. What must be true of the numerators of the fractions? Explain.

Answer:
Yes, the two fractions are equal.

Explanation:
In the above-given question,
given that,
Izzy and Henry have two different pizzas.
Izzy ate \(\frac{3}{8}\) of her pizza.
Henry ate \(\frac{3}{8}\) of his pizza.
3/8 = 1/8 + 1/8 + 1/8.
3/8 x 1 = 3/8.
3/8 = 3/8.
so both of them ate the equal.

Question 19.
Number Sense Mr. Domini had $814 in the bank on Wednesday. On Thursday, he withdrew $250, and on Friday, he withdrew $185. How much money did he have in the bank then?

Answer:
The money he has in the bank = $379.

Explanation:
In the above-given question,
given that,
Mr. Domini had $814 in the bank on Wednesday.
On Thursday, he withdrew $250.
On Friday, he withdrew $185.
250 + 185 = 435.
814 – 435 = 379.
so Mr. Domini had $814 in the bank on Wednesday.

Question 20.
Higher Order Thinking Tom’s parents let him choose whether to play his favorite board game for \(\frac{7}{8}\) hour or for \(\frac{8}{8}\) hour. Explain which amount of time you think Tom should choose and why.

Answer:
Tom should choose 8/8 hour.

Explanation:
In the above-given question,
given that,
Tom’s parents let him choose whether to play his favorite board game for 7/8 hours.
8/8 hour = 1.
7/8 x 1 = 7/8.
1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 8/8.
1 = 8/8.
so i think Tom should choose 1 hour.

Assessment Practice

Question 21.
Paul and Enrique each have equal-sized pizzas cut into 8 equal slices. Paul eats 3 slices. Enrique eats 2 slices. Select numbers and symbols from the box to write a comparison for the fraction of pizza Paul and Enrique have each eaten.

Answer:
Paul eats more slices than Enriques.

Explanation:
In the above-given question,
given that,
Paul and Enrique each have equal-sized pizzas cut into 8 equal slices.
Paul eats 3 slices.
Enrique eats 2 slices.
1/8 + 1/8 + 1/8 = 3/8.
1/8 + 1/8 = 2/8.
so paul eats more slices than Enriques.

Lesson 13.4 Use Models to Compare Fractions: Same Numerator

Solve & Share
Krista, Jamal, and Rafe each had 1 serving of vegetables. Krista ate \(\frac{2}{6}\), Jamal ate \(\frac{2}{3}\), and Rafe ate \(\frac{2}{8}\) of his serving. Arrange the fractions in order from least to greatest to show who ate the least and who ate the greatest amount of vegetables.
I can … compare fractions that refer to the same whole and have the same numerator by comparing their denominators.

Answer:
Rafe, Krista, and Jamal.

Explanation:
In the above-given question,
given that,
Krista, Jamal, and Rafe each had 1 serving of vegetables.
Krista ate \(\frac{2}{6}\), Jamal ate \(\frac{2}{3}\).
Rafe ate \(\frac{2}{8}\) of his serving.
2/6 = 1/6 + 1/6.
2/3 = 1/3 + 1/3.
2/8 = 1/8 + 1/8.
so Rafe ate least when compared to Krista and Jamal.
so the order from least to highest.
Rafe, Krista, and Jamal.

Look Back! Tamika ate \(\frac{2}{2}\) of a serving of vegetables. In order from least to greatest, arrange the fractions of a serving Krista, Jamal, Rafe, and Tamika each ate. Explain your reasoning.

Answer:
Rafe, Krista, Jamal, and Tamika.

Explanation:
In the above-given question,
given that,
Tamika ate \(\frac{2}{2}\) of a serving of vegetables.
2/2 = 1.
so Tamika at more than Rafe, Krista, and Jamal.

Essential Question
How Can You Compare Fractions with the Same Numerator?

Visual Learning Bridge
Claire bought 2 scarves as souvenirs from her visit to a Florida university. The scarves are the same size. One scarf is \(\frac{5}{6}\) orange, and the other scarf is \(\frac{5}{8}\) orange. Which is greater, \(\frac{5}{6}\) or \(\frac{5}{8}\)?

What You Show
Use fraction strips to reason about the size of \(\frac{5}{6}\) a compared to the size of \(\frac{5}{8}\).

There are 5 sixths. There are 5 eighths. The parts are different sizes.
The greater the denominator, the smaller each part will be.

What You Write
Describe the comparison using symbols or words.
\(\frac{5}{6}\) > \(\frac{5}{8}\)
Five sixths is greater than five eighths.
If two fractions have the same numerator, the fraction with the lesser denominator is the greater fraction.

Convince Me! Critique Reasoning Julia says \(\frac{1}{8}\) is greater than \(\frac{1}{4}\) because 8 is greater than 4. Critique Julia’s reasoning. Is she correct? Explain.

Answer:
Yes, Julia’s reasoning was correct.

Explanation:
In the above-given question,
given that,
Julia says \(\frac{1}{8}\) is greater than \(\frac{1}{4}\).
1/8 = 1 x 1/8.
1/4 = 1 x 1/4.
so Julia’s reasoning was correct.

Guided Practice

Do You Understand?
Question 1.
How can fraction strips help you reason about whether \(\frac{4}{6}\) or \(\frac{4}{8}\) of the same whole is greater?

Answer:
4/6 > 4/8.

Explanation:
In the above-given question,
given that,
the two fractions are 4/6 and 4/8.
4/6 = 1/6 + 1/6 + 1/6 + 1/6.
4/8 = 1/8 + 1/8 + 1/8 + 1/8.
4/6 x 1 = 4/6.
4/8 x 1 = 4/8.
so 4/6 > 4/8.

Question 2.
Which is greater, \(\frac{1}{4}\) or \(\frac{1}{6}\)? Draw fraction strips to complete the diagram and answer the question.

Answer:
1/4 > 1/6.

Explanation:
In the above-given question,
given that,
the two fractions are 1/4 and 1/6.
1/4 x 1 = 1/4.
1/6 x 1 = 1/6.
1 is divided into 1/4 and 1/6.
1/4 > 1/6.

Do You Know How?
In 3 and 4, compare. Write <, >, or =. Use fraction strips to help.
Question 3.

Answer:
3/6 < 3/3.

Explanation:
In the above-given question,
given that,
the two fractions are 3/6 and 3/3.
3/6 = 1/6 + 1/6 + 1/6.
3/3 = 1.
so 3/6 < 3/3.

Question 4.

Answer:
4/6 < 4/8.

Explanation:
In the above-given question,
given that,
the two fractions are 4/6 and 4/8.
4/6 = 1/6 + 1/6 + 1/6 + 1/6.
4/8 = 1/8 + 1/8 + 1/8 + 1/8.
so 4/6 = 1 x 4/6.
so 4/6 < 4/8.

Independent Practice

Leveled Practice In 5-14, compare. Write <, >, or =. Use or draw fraction strips to help. The fractions refer to the same whole.
Question 5.

Answer:
2/4 < 2/3.

Explanation:
In the above-given question,
given that,
the two fractions are 2/4 and 2/3.
2/4 = 1/4 + 1/4.
2/3 = 1/3 + 1/3.
so 2/4 < 2/3.

Question 6.

Answer:
4/4 > 4/6.

Explanation:
In the above-given question,
given that,
the two fractions are 4/4 and 4/6.
4/4 = 1.
1/6 + 1/6 + 1/6 + 1/6 = 4/6.
so 4/4 > 4/6.

Question 7.
\(\frac{2}{3}\) \(\frac{2}{2}\)

Answer:
2/3 > 2/2.

Explanation:
In the above-given question,
given that,
the two fractions are 2/3 and 2/2.
2/2 = 1.
1/3 + 1/3 = 2/3.
so 2/3 > 2/2.

Question 8.
\(\frac{4}{8}\) \(\frac{4}{8}\)

Answer:
4/8 = 4/8.

Explanation:
In the above-given question,
given that,
the two fractions are 4/8 and 4/8.
4/8 = 1/8 + 1/8 + 1/8 + 1/8.
4/8 x 1 = 4/8.
so 4/8 = 4/8.

Question 9.
\(\frac{5}{6}\) \(\frac{5}{8}\)

Answer:
5/6 > 5/8.

Explanation:
In the above-given question,
given that,
the two fractions are 5/6 and 5/8.
5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6.
5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
so 5/6 > 5/8.

Question 10.
\(\frac{1}{4}\) \(\frac{1}{3}\)

Answer:
1/4 > 1/3.

Explanation:
In the above-given question,
given that,
the two fractions are 1/4 and 1/3.
1/4 = 1/4 x 1.
1/3 x 1 = 2/3.
so 1/4 > 1/3.

Question 11.
\(\frac{1}{3}\) \(\frac{1}{6}\)

Answer:
1/3 > 1/6.

Explanation:
In the above-given question,
given that,
the two fractions are 1/3 and 1/2.
1/3 = 1 x 1/3.
1/2 x 1 = 1/3.
so 1/3 > 1/6.

Question 12.
\(\frac{4}{6}\) \(\frac{4}{6}\)

Answer:
4/6 = 4/6.

Explanation:
In the above-given question,
given that,
the two fractions are 4/6 and 4/6.
4/6 = 1 x 4/6.
1/6 + 1/6 + 1/6 + 1/6 = 4/6.
so 4/6 = 4/6.

Question 13.
\(\frac{1}{8}\) \(\frac{1}{2}\)

Answer:
1/8 < 1/2.

Explanation:
In the above-given question,
given that,
the two fractions are 1/8 and 1/2.
1/8 = 1 x 1/8.
1/2 x 1 = 1/2.
so 1/8 < 1/2.

Question 14.
\(\frac{2}{6}\) \(\frac{2}{3}\)

Answer:
2/6 < 2/3.

Explanation:
In the above-given question,
given that,
the two fractions are 2/6 and 2/3.
2/6 = 1/6 + 1/6.
1/3 + 1/3 = 2/3.
so 2/6 < 2/3.

Problem Solving

Question 15.
James uses blue and white tiles to make the two designs shown here. James says that the total blue area in the top design is the same as the total blue area in the bottom design. Is he correct? Explain.

Answer:
Yes, James was correct.

Explanation:
In the above-given question,
given that,
James uses blue and white tiles to make the two designs.
James says that the total blue area in the top design is the same as the total blue area in the bottom design.
4/8 = 1/8 + 1/8 + 1/8 + 1/8.
1/8 x 4 = 4/8.
so James was correct.

Question 16.
Amy sold 8 large quilts and 1 baby quilt. How much money did she make from selling quilts?

Answer:
The money did she make from selling quilts = $520.

Explanation:
In the above-given question,
given that,
Amy sold 8 large quilts and 1 baby quilt.
60 x 8 = 480.
40 x 1 = 40.
480 + 40 = 520.
so the money did she make from selling quilts = $520.

Question 17.
Be Precise Write two comparison statements about the fractions shown below.

Answer:
3/3 > 3/4.

Explanation:
In the above-given question,
given that,
the two fractions are 3/3 and 3/4.
3/3 = 1/3 + 1/3 + 1/3.
3/4 = 1/4 + 1/4 + 1/4.
so 3/3 > 3/4.

Question 18.
Higher Order Thinking John says that when you compare two fractions with the same numerator, you look at the denominators because the fraction with the greater denominator is greater. Is he correct? Explain, and give an example.

Answer:
Yes, he was correct.

Explanation:
In the above-given question,
given that,
John says that when you compare two fractions with the same numerator,
3/3 and 3/4.
3/3 = 1.
3/4 = 1/4 + 1/4 + 1/4.
1 > 1/4.
so he was correct.

Assessment Practice

Question 19.
These fractions refer to the same whole. Which of these comparisons are correct? Select all that apply.

Answer:
2/4 > 2/3, 1/2 > 1/4, 5/6 = 5/6, and 3/4 > 3/6.

Explanation:
In the above-given question,
given that,
the fractions are 2/4 and 2/3.
2/4 = 1/4 + 1/4.
2/3 = 1/3 + 1/3.
the fractions are 1/2 and 1/4.
1/4 x 1 = 1/4.
1/2 x 1 = 1/2.
the fractions are 3/4 and 3/6.
3/4 = 1/4 + 1/4 + 1/4.
3/6 = 1/6 + 1/6 + 1/6.
so the four fractions are correct.

Lesson 13.5 Compare Fractions: Use Benchmarks

Solve & Share
Mr. Evans wrote \(\frac{2}{8}, \frac{4}{8}, \frac{6}{8}, \frac{1}{8}, \frac{3}{8}, \frac{5}{8}\) on and \(\frac{7}{8}\) on the board. Then he circled the fractions that are closer to 0 than to 1. Which fractions did he circle? Which fractions did he not circle? Explain how you decided.
I can … use what I know about the size of benchmark numbers to compare fractions.

Look Back! Eric says that \(\frac{3}{8}\) is closer to 1 than to 0 because \(\frac{3}{8}\) is greater than \(\frac{1}{8}\). Is he correct? Use benchmark numbers to evaluate Eric’s reasoning and justify your answer.

Answer:
Yes, Eric was correct.

Explanation:
In the above-given question,
given that,
Eric says that 3/8 is closer to 1.
3/8 is greater than 1/8.
3/8 = 1/8 + 1/8 + 1/8.
so 3/8 > 1/8.
so Eric was correct.

Essential Question
How Can Benchmark Numbers Be Used to Compare Fractions?

Visual Learning Bridge
Keri wants to buy of a container of roasted peanuts. Alan wants to buy of a container of roasted peanuts. The containers are the same size. Who will buy more peanuts?

Compare each fraction to the benchmark number \(\frac{1}{2}\). Then see how they relate to each other in size.

So, \(\frac{2}{6}\) is less than \(\frac{2}{3}\).
\(\frac{2}{6}\) < \(\frac{2}{3}\)
Alan will buy more peanuts than Keri.

Convince Me! Make Sense and Persevere Candice buys \(\frac{2}{8}\) of a container of roasted peanuts. The container is the same size as those used by Keri and Alan. She says \(\frac{2}{8}\) is between \(\frac{1}{2}\) and 1, so she buys more peanuts than Alan. Is Candice correct? Explain.

Answer:
Candice, she was correct.

Explanation:
In the above-given question,
given that,
Candice buys \(\frac{2}{8}\) of a container of roasted peanuts.
The container is the same size as those used by Keri and Alan.
She says \(\frac{2}{8}\) is between \(\frac{1}{2}\) and 1.
2/8 = 1/8 + 1/8.
1/2 x 1 = 1/2.
so Candice was correct.

Guided Practice

Do You Understand?
Question 1.
Tina used benchmark numbers to decide that \(\frac{3}{8}\) is less than \(\frac{7}{8}\). Do you agree? Explain.

Answer:
Yes, 3/8 is less than 7/8.

Explanation:
In the above-given question,
given that,
Tina used benchmark numbers to decide that 3/8 is less than 7/8.
3/8 = 1/8 + 1/8 + 1/8.
7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
so 3/8 is less than 7/8.

Question 2.
Write two fractions with a denominator of 6 that are closer to 0 than to 1.

Answer:
The two fractions are 3/6 and 4/6.

Explanation:
In the above-given question,
given that,
the two fractions are 3/6 and 4/6
3/6 = 1/6 + 1/6 + 1/6.
4/6 = 1/6 + 1/6 + 1/6 + 1/6.
so 3/6 and 4/6 equal to 0 and 1.

Question 3.
Write two fractions with a denominator of 8 that are closer to 1 than to 0.

Answer:
The two fractions are 2/8 and 7/8.

Explanation:
In the above-given question,
given that,
the two fractions with a denominator of 8 that are closer to 1 than to 0.
2/8 = 1/8 + 1/8.
7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
so the two fractions are 2/8 and 7/8 is equal to 0 and 1.

Do You Know How?
In 4-6, choose from the fractions \(\frac{1}{8}, \frac{1}{4}, \frac{6}{8}\) and \(\frac{3}{4}\). Use fraction strips to help.
Question 4.
Which fractions are closer to 0 than to 1?

Answer:
The two fractions are 3/4 and 1/4.

Explanation:
In the above-given question,
given that,
the fractions are 1/8, 1/4, 6/8, and 3/4.
3/4 = 1/4 + 1/4 + 1/4.
1/4 x 1 = 1/4
so the two fractions are 3/4 and 1/4.

Question 5.
Which fractions are closer to 1 than to 0?

Answer:
The fractions are 6/8 and 3/4.

Explanation:
In the above-given question,
given that,
the fractions are 1/8, 1/4, 6/8, and 3/4.
6/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
3/4 = 1/4 + 1/4 + 1/4.
so the fractions closer to 1 than to 0 are 6/8 and 3/4.

Question 6.
Use the two fractions with a denominator of 8 to write a true statement: < .

Answer:
1/8 < 6/8.

Explanation:
In the above-given question,
given that,
the fractions are 1/8, 1/4, 6/8, and 3/4.
6/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
3/4 = 1/4 + 1/4 + 1/4.
the two fractions with a denominator of 8.
so 1/8 < 6/8.

Independent Practice

In 7 and 8, choose from the fractions, \(\frac{2}{3}, \frac{7}{8}, \frac{1}{4}\), and \(\frac{2}{6}\).
Question 7.
Which of the fractions are closer to 0 than to 1?

Answer:
The fractions are closer to 0 than to 1 are 2/3 and 1/4.

Explanation:
In the above-given question,
given that,
the fractions are 2/3, 7/8, 1/4, and 2/6.
2/3 = 1/3 + 1/3.
1/4 x 1 = 1/4.
so the fractions are closer to 0 than to 1 are 2/3 and 1/4.

Question 8.
Which of the fractions are closer to 1 than to 0?

Answer:
The fractions are closer to 1 than to 0 are 7/8 and 2/6.

Explanation:
In the above-given question,
given that,
the fractions are 2/3, 7/8, 1/4, and 2/6.
7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
2/6 = 1/6 + 1/6.
so the fractions are closer to 1 than to 0 are 7/8 and 2/6.

In 9-14, use a strategy to compare. Write <, >, or =.

Question 9.
\(\frac{5}{8}\) \(\frac{7}{8}\)

Answer:
5/8 < 7/8.

Explanation:
In the above-given question,
given that,
the two fractions are 5/8 and 7/8.
5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
so 5/8 < 7/8.

Question 10.
\(\frac{5}{8}\) \(\frac{2}{8}\)

Answer:
5/8 > 2/8.

Explanation:
In the above-given question,
given that,
the two fractions are 5/8 and 2/8.
5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
2/8 = 1/8 + 1/8.
so 5/8 > 2/8.

Question 11.
\(\frac{3}{4}\) \(\frac{3}{6}\)

Answer:
3/4 > 3/6.

Explanation:
In the above-given question,
given that,
the two fractions are 3/4 and 3/6.
3/4 = 1/4 + 1/4 + 1/4.
3/6 = 1/6 + 1/6 + 1/6.
so 3/4 < 3/6.

Question 12.
\(\frac{4}{6}\) \(\frac{4}{8}\)

Answer:
4/6 < 4/8.

Explanation:
In the above-given question,
given that,
the two fractions are 4/6 and 4/8.
4/6 = 1/6 + 1/6 + 1/6 + 1/6.
4/8 = 1/8 + 1/8 + 1/8 + 1/8.
so 4/6 < 4/8.

Question 13.
\(\frac{2}{6}\) \(\frac{2}{4}\)

Answer:
2/6 > 2/4.

Explanation:
In the above-given question,
given that,
the two fractions are 2/6 and 2/4.
2/6 = 1/6 + 1/6.
2/4 = 1/4 + 1/4.
so 2/6 > 2/4.

Question 14.
\(\frac{2}{3}\) \(\frac{1}{3}\)

Answer:
2/3 > 1/3.

Explanation:
In the above-given question,
given that,
the two fractions are 2/3 and 1/3.
2/3 = 1/3 + 1/3.
1/3 = 1/3 x 1.
so 2/3 > 1/3.

Problem Solving

In 15-17, use the table at the right.

Question 15.
Which people have walked closer to 1 mile than to 0 miles?

Answer:
Mr. Nunez and Miss Lee have walked closer to 1 mile than to 0 miles.

Explanation:
In the above-given question,
given that,
there are 5 people in the chart.
they are 1/6, 5/6, 1/3, 4/8, and 4/6.
the people closer to 1 mile than to 0 miles are Mr. Nunez and Miss.
the fractions closer to 1 mile is 5/6 and 4/6.

Question 16.
Which people have walked closer to 0 miles than to 1 mile?

Answer:
Mrs. Avery and Miss Chang have walked closer to 0 miles than to 1 mile.

Explanation:
In the above-given question,
given that,
there are 5 people in the chart.
they are 1/6, 5/6, 1/3, 4/8, and 4/6.
the people closer to 0 miles than to 1 mile are Mrs. Avery and Miss chang.
the fractions closer to 0 miles is 1/6 and 1/3.

Question 17.
Who has walked a fraction of a mile that is closer to neither 0 nor 1? Explain.

Answer:
Mr. O’Leary has walked closer to neither 0 nor 1.

Explanation:
In the above-given question,
given that,
there are 5 people in the chart.
they are 1/6, 5/6, 1/3, 4/8, and 4/6.
the people closer to neither 0 nor 1.
the fractions are 4/8.

Question 18.
Rahul compares two wholes that are the same size. He says that \(\frac{2}{6}\) < \(\frac{2}{3}\) because \(\frac{2}{6}\) is less than \(\frac{1}{2}\), and \(\frac{2}{3}\) is greater than \(\frac{1}{2}\). Is he correct? Explain.

Answer:
Yes, he was correct.

Explanation:
In the above-given question,
given that,
Rahul compares two wholes that are the same size.
He says that \(\frac{2}{6}\) < \(\frac{2}{3}\).
\(\frac{2}{6}\) is less than \(\frac{1}{2}\).
2/6 < 2/3.
2/6 < 1/2.
2/3 > 1/2.
so he was correct.

Question 19.
Make Sense and Persevere Manish drives 265 more miles than Janice. Manish drives 642 miles. How many miles does Janice drive?

Answer:
The number of miles does Janice drive =

Explanation:
In the above-given question,
given that,
Manish drives 265 more miles than Janice.
Manish drives 642 miles.
642 – 265 = 377.
so the number of miles does Janice drives = 377.

Question 20.
Algebra Nika has 90 pencils. Forty of them are yellow, 13 are green, 18 are red, and the rest are blue. How many blue pencils does Nika have?

Answer:
The number of blue pencils does Nika have = 47.

Explanation:
In the above-given that,
given that,
Algebra Nika has 90 pencils.
Forty of them are yellow, 13 are green, 18 are red, and the rest are blue.
13 + 18 = 43.
90 – 43 = 47.
so the number of blue pencils does Nika have = 47.

Question 21.
Higher Order Thinking Omar says that \(\frac{2}{6}\) < \(\frac{4}{6}\) because \(\frac{2}{6}\) is between 0 and \(\frac{1}{2}\), and \(\frac{4}{6}\) is between \(\frac{1}{2}\) and 1. Is he correct? Explain.

Answer:
Yes, he was correct.

Explanation:
In the above-given question,
given that,
2/6 < 4/6.
2/6 is between 0 and 1/2.
4/6 is between 1/2 and 1.
0, 2/6, and 1/2.
1/2, 4/6, and 1.
so Omar was correct.

Assessment Practice

Question 22.
Each of the fractions in the comparisons at the right refer to the same whole. Use benchmark fractions to reason about the size of each fraction. Select all the correct comparisons.

Answer:
2/3 < 2/4, 3/6 > 3/8, and 3/8 > 5/8.

Explanation:
In the above-given question,
given that,
the fractions are 2/3 < 2/4, 2/4 < 2/3, 3/8 > 5/8, 1/4 < 2/4, and 3/6 > 3/8.
so the 2/3 < 2/4.
2/3 < 1 and 1/2 > 1.
3/6 > 3/8.
3/8 > 5/8.
so the correct fractions are 2/3 < 2/4, 3/6 > 3/8, and 3/8 > 5/8.

Lesson 13.6 Compare Fractions: Use the Number Line

Solve & Share
Tanya, Riaz, and Ryan each used a bag of flour to make modeling clay. The bags were labeled lb, á lb, and Ź lb. Show these fractions on a number line. How can you use the number line to compare two of these fractions?
I can … compare two fractions by locating them on a number line.

Look Back! If the bags were labeled \(\frac{4}{8}\) lb, \(\frac{3}{8}\) lb, and \(\frac{6}{8}\) lb, how could a number line help you solve this problem?

Answer:
3/8 < 4/8 < 6/8.

Explanation:
In the above-given question,
given that,
if the bags were labeled 4/8 lb, 3/8 lb, and 6/8 lb.
so the fractions from least to greatest are 3/8, 4/8, and 6/8.
3/8 is near to 0.
4/8 is in between 0 and 1.
6/8 is near to 1.

Essentials Question
How Can You Compare Fractions Using the Number Line?

Visual Learning Bridge
Talia has two different lengths of blue and red ribbon. Does she have more blue ribbon or more red ribbon?

The fractions both refer to 1 yard of ribbon. This is the whole.
You can use a number line to compare \(\frac{1}{3}\) and \(\frac{2}{3}\).
The farther the distance of the fraction from zero on the number line, the greater the fraction.

On the number line, \(\frac{2}{3}\) is farther to the right than \(\frac{1}{3}\).
So, \(\frac{2}{3}\) > \(\frac{1}{3}\).
Talia has more blue ribbon than red ribbon.

Convince Me! Use Structure Talia has an additional length of green ribbon that measures \(\frac{2}{4}\) yard. How can you compare the length of the green ribbon to the lengths of the blue and red ribbons?

Guided Practice

Do You Understand?
Question 1.
When two fractions refer to the same whole, what do you notice when the denominators you are comparing are the same?

Answer:
The denominators are greater than the numerators.

Explanation:
In the above-given question,
given that,
if two fractions are the same.
the denominators are greater than the numerators.

Question 2.
Write a problem that compares two fractions with different numerators.

Answer:
1/3 > 2/3.

Explanation:
In the above-given question,
given that,
the two different fractions are 1/3 and 2/5.
1/3 x 1 = 1/3.
2/3 = 1/3 + 1/3.
so 1/3 > 2/3.

Do You Know How?
In 3-5, compare fractions using <, >, or =. Use the number lines to help.
Question 3.

Answer:
2/4 < 2/3.

Explanation:
In the above-given question,
given that,
the two fractions are 2/4 and 2/3.
2/4 = 1/4 + 1/4.
2/3 = 1/3 + 1/3.
2/4 is the half portion in the number line.
so 2/4 > 2/3.

Question 4.

Answer:
2/6 < 2/3.

Explanation:
In the above-given question,
given that,
the two fractions are 2/6 and 2/3.
2/6 = 1/6 + 1/6.
2/3 = 1/3 + 1/3.
2/6 is below the half portion in the number line.
so 2/6 < 2/3.

Question 5.

Answer:
5/8 > 3/8.

Explanation:
In the above-given question,
given that,
the two fractions are 5/8 and 3/8.
5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
3/8 = 1/8 + 1/8 + 1/8.
3/8 is the half portion in the number line.
so 5/8 > 3/8.

Independent Practice

In 6-9, use the number lines to compare the fractions. Write >, <, or =.
Question 6.

Answer:
1/4 > 3/4.

Explanation:
In the above-given question,
given that,
the two fractions are 1/4 and 3/4.
1/4 = 1/4 x 1.
3/4 = 1/4 + 1/4 + 1/4.
1/4 is nearest to 0.
so 1/4 > 3/4.

Question 7.

Answer:
4/6 < 3/6.

Explanation:
In the above-given question,
given that,
the two fractions are 4/6 and 3/6.
4/6 = 1/6 + 1/6 + 1/6 + 1/6.
3/6 = 1/6 + 1/6 + 1/6.
so 4/6 < 3/6.

Question 8.

Answer:
1/2 > 1/4.

Explanation:
In the above-given question,
given that,
the two fractions are 1/4 and 1/2.
1/2 = 1/2 x 1.
1/4 = 1/4 x 1
1/4 is nearest to 0.
so 1/2 > 1/4.

Question 9.

Answer:
1/3 > 1/8.

Explanation:
In the above-given question,
given that,
the two fractions are 1/3 and 1/8.
1/3 = 1/3 x 1.
1/8 = 1/8 x 1.
1/8 is nearest to 0.
so 1/3 > 1/8.

Problem Solving

Question 10.
Number Sense Randy wants to save $39. The table shows how much money he has saved. Explain how you can use estimation to decide if he has saved enough money.

Answer:
Yes, he has saved enough money.

Explanation:
In the above-given question,
given that,
Randy wants to save $39.
in march month he saved $14.
in April he saved $11.
in May he saved $22.
14 + 11 + 22 = 47.
so he has saved enough money.

Question 11.
Scott ate \(\frac{2}{8}\) of a fruit bar. Anne ate \(\frac{4}{8}\) of a same-sized fruit bar. Can you tell who ate more of a fruit bar, Scott or Anne? Explain.

Answer:
Anne ate more of a fruit bar.

Explanation:
In the above-given question,
given that,
Scott ate \(\frac{2}{8}\) of a fruit bar.
Anne ate \(\frac{4}{8}\) of a same-sized fruit bar.
2/8 = 1/8 + 1/8.
4/8 = 1/8 + 1/8 + 1/8 + 1/8.
4 > 2.
so the whole is 8.
so Anne ate more of a fruit bar.

Question 12.
Be Precise Matt and Adara have identical pieces of cardboard for an art project. Matt uses \(\frac{2}{3}\) of his piece. Adara uses \(\frac{2}{6}\) of her piece. Who uses more, Matt or Adara? Draw two number lines to help explain your answer.

Answer:
Matt uses more cardboard.

Explanation:
In the above-given question,
given that,
Matt and Adara have identical pieces of cardboard for an art project.
matt uses 2/3 of his piece.
Adara uses 2/6 of her piece.
2/3 = 1/3 + 1/3.
2/6 = 1/6 + 1/6.
in 1st 3 is the whole part.
2 is near to 3.
so matt uses more cardboard.

Question 13.
Higher Order Thinking Some friends shared a pizza. Nicole ate \(\frac{2}{8}\) of the pizza. Chris ate \(\frac{1}{8}\) more than Johan. Mike ate \(\frac{1}{8}\) of the pizza. Johan ate more than Mike. Who ate the most pizza?

Answer:
Chris ate more pizza.

Explanation:
In the above-given question,
given that,
Some friends shared a pizza.
Nicole ate \(\frac{2}{8}\) of the pizza.
Chris ate \(\frac{1}{8}\) more than Johan.
Mike ate \(\frac{1}{8}\) of the pizza.
1/8 + 1 = 2/8.
2/8 + 1 = 3/8.
so Chris ate more pizza.

Question 14.
Inez has 2 rows of plants. There are 8 plants in each row. Each plant has 3 flowers. How many flowers are there in all?

Answer:
The number of flowers is there = 48.

Explanation:
In the above-given question,
given that,
Inez has 2 rows of plants.
there are 8 plants in each row.
each plant has 3 flowers.
8 x 2 =16.
16 x 3 = 48.
so the number of flowers is there = 48.

Assessment Practice

Question 15.
Daniel walked \(\frac{3}{4}\) of a mile. Theo walked \(\frac{3}{8}\) of a mile. Use the number lines to show 0 the fraction of a mile Daniel and Theo each walked. Then select all the correct statements that describe the fractions.

☐ \(\frac{3}{4}\) is equivalent to \(\frac{3}{8}\) because the fractions mark the same point.
☐ \(\frac{3}{4}\) is greater than \(\frac{3}{8}\) because it is farther from zero.
☐ \(\frac{3}{4}\) is less than \(\frac{3}{8}\) because it is farther from zero.
☐ \(\frac{3}{8}\) is less than \(\frac{3}{4}\) because it is closer to zero.
☐ \(\frac{3}{8}\) is greater than \(\frac{3}{4}\) because it is closer to zero.

Answer:
Option B is the correct answer.

Explanation:
In the above-given question,
given that,
Daniel walked \(\frac{3}{4}\) of a mile.
Theo walked \(\frac{3}{8}\) of a mile.
in the 1st line, the 3 is farther from the 0.
so 3/4 > 3/8.
so option B is the correct answer.

Lesson 13.7 Whole Numbers and Fractions

Solve & Share
Jamie’s family ate 12 pieces of apple pie during the week. Each piece was \(\frac{1}{6}\) of a whole pie. How many whole pies did Jamie’s family eat? What fraction of a pie was left over? Explain how you decided.
I can … use representations to find fraction names for whole numbers.

Look Back! Jamie cuts another pie into smaller pieces. Each piece of pie is \(\frac{1}{8}\) of the whole. Jamie gives away 8 pieces. Does Jamie have any pie left over? Explain how you know.

Answer:
Jamie does not have left any pie.

Explanation:
In the above-given question,
given that,
Jamie cuts another pie into smaller pieces.
Each piece of pie is \(\frac{1}{8}\) of the whole.
Jamie gives away 8 pieces.
8 – 8 = 0.
so Jamie does not have left any pie.

Essential Question
How Can You Use Fraction Names to Represent Whole Numbers?

Visual Learning Bridge
What are some equivalent fraction names for 1, 2, and 3?
You can write a whole number as a fraction by writing the whole number as the numerator and

The number line shows 3 wholes. Each whole is divided into 1 equal part.
1 whole divided into 1 equal part can be written as \(\frac{1}{1}\).
2 wholes each divided into 1 equal part can be written as \(\frac{2}{1}\).
3 wholes each divided into 1 equal part can be written as \(\frac{1}{1}\)
1 = \(\frac{1}{2}\)
2 = \(\frac{2}{1}\)
3 = \(\frac{3}{1}\)

You can find other equivalent fraction names for whole numbers.

Convince Me! Reasoning What equivalent fraction names can you write for 4 using denominators of 1, 2, or 4?

Another Example!
You can use fractions to name whole numbers.

Twelve \(\frac{1}{3}\) fraction strips equal 4 whole fraction strips.
All whole numbers have fraction names. You can write 4 = \(\frac{12}{3}\).
You also know 4 = \(\frac{4}{1}\), so you can write 4 = \(\frac{4}{1}\) = \(\frac{12}{3}\).

Guided Practice

Do You Understand?
Question 1.
Explain how you know that \(\frac{4}{1}\) = 4.

Answer:
4/1 = 4.

Explanation:
In the above-given question,
given that,
12/3 = 4/1.
3 x 1 = 3.
3 x 4 = 12.
so 4/1 = 4.

Do You Know How?
Question 2.
Complete the number line.

Answer:
The missing numbers in upside are 1/3, 3/3, 4/3, and 6/3.
the missing numbers on the downside are 1/6, 2/6, 4/6, 5/6, 6/6, 7/6, 9/6, 10/6, 11/6, and 12/6.

Explanation:
In the above-given question,
given that,
the number line is 1/3, 2/3, 3/3, 4/3, 5/3, 6/3.
2/6 = 1/3.
1 x 2 = 2.
3 x 2 = 6.
6/6 = 1.
9/6 = 3/2.
3 x 3 = 9.
3 x 2 = 6.
so the missing numbers are 1/3, 3/3, 4/3, and 6/3.
1/6, 2/6, 4/6, 5/6, 6/6, 7/6, 9/6, 10/6, 11/6, and 12/6.

Question 3.
Look at the number line. Write two equivalent fractions for each whole number.

Answer:
1 = 3/3 = 6/6.
2 = 6/3 = 12/6.

Explanation:
In the above-given question,
given that,
the two numbers are 1 and 2.
1 = 3/3.
6 / 6 = 1.
6/3 = 2.
12 / 6 = 2.

Independent Practice

In 4-7, write two equivalent fractions for each whole number. You can draw number lines to help.
Question 4.

Answer:
4 = 8/2 = 4/1.

Explanation:
In the above-given question,
given that,
the number is 4.
8/2 = 4.
2 x 1 = 2.
2 x 4 = 8.
4 / 1 = 4.
so the missing numbers are 8 and 4.

Question 5.

Answer:
1 = 4/4 = 1/1.

Explanation:
In the above-given question,
given that,
the number is 1.
4/4 = 1.
4 x 1 = 4.
1 x 4 = 4.
1 / 1 = 1.
so the missing numbers are 4 and 1.

Question 6.

Answer:
2 = 6/3 = 2/1.

Explanation:
In the above-given question,
given that,
the number is 2.
6/3 = 2.
3 x 1 = 3.
3 x 2 = 6.
2 / 1 = 2.
so the missing numbers are 6 and 1.

Question 7.

Answer:
5 = 10/2 = 5/1.

Explanation:
In the above-given question,
given that,
the number is 5.
10/2 = 5.
2 x 1 = 2.
2 x 5 = 10.
5 / 1 = 5.
so the missing numbers are 10 and 5.

In 8-11, for each pair of fractions, write the equivalent whole number.
Question 8.
\(\frac{6}{2}\) = \(\frac{3}{1}\) =

Answer:
\(\frac{6}{2}\) = \(\frac{3}{1}\) = 3.

Explanation:
In the above-given question,
given that,
for each pair of fractions, write the equivalent whole number.
6/2 = 3.
3/1 = 3.
so \(\frac{6}{2}\) = \(\frac{3}{1}\) = 3.

Question 9.
\(\frac{3}{3}\) = \(\frac{6}{6}\) =

Answer:
\(\frac{3}{3}\) = \(\frac{6}{6}\) = 1.

Explanation:
In the above-given question,
given that,
for each pair of fractions, write the equivalent whole number.
3/3 = 1.
6/6 = 1.
so \(\frac{3}{3}\) = \(\frac{6}{6}\) = 1.

Question 10.
\(\frac{8}{4}\) = \(\frac{6}{3}\) =

Answer:
\(\frac{8}{4}\) = \(\frac{6}{3}\) = 2.

Explanation:
In the above-given question,
given that,
for each pair of fractions, write the equivalent whole number.
8/4 = 2.
6/3 = 2.
so \(\frac{8}{4}\) = \(\frac{6}{3}\) = 2.

Question 11.
\(\frac{9}{3}\) = \(\frac{12}{4}\) =

Answer:
\(\frac{9}{3}\) = \(\frac{12}{4}\) = 3.

Explanation:
In the above-given question,
given that,
for each pair of fractions, write the equivalent whole number.
9/3 = 3.
12/4 = 3.
so \(\frac{9}{3}\) = \(\frac{12}{4}\) = 3.

Problem Solving

Question 12.
Henry needs to fix or replace his refrigerator. It will cost $376 to fix it. How much more will it cost to buy a new refrigerator than to fix the current one?

Answer:
The more it costs to buy a new refrigerator = $593.

Explanation:
In the above-given question,
given that,
Henry needs to fix or replace his refrigerator.
It will cost $376 to fix.
the new refrigerator cost is $969.
969 – 376 = 593.
so more it costs to buy a new refrigerator = $593.

Question 13.
Declan says, “To write an equivalent fraction name for 5, I can write 5 as the denominator and 1 as the numerator.” Do you agree with Declan? Explain.

Answer:
No, Declan was wrong.

Explanation:
In the above-given question,
given that,
To write an equivalent fraction name for 5, I can write 5 as the denominator and 1 as the numerator.
5/1 = 5.
so Declan was wrong.

Question 14.
Look for Relationships Describe a pattern in fractions equivalent to 1 whole.

Answer:

Question 15.
enVision® STEM There are four stages in a butterfly’s life cycle: egg, caterpillar, chrysalis, and butterfly. Dan makes one whole poster for each stage. Use a fraction to show the number of whole posters Dan makes.

Answer:
Dan makes the fractions 1/4, 2/4, 3/4, and 4/4.

Explanation:
In the above-given question,
given that,
There are four stages in a butterfly’s life cycle: egg, caterpillar, chrysalis, and butterfly.
1st stage is egg = 1/4.
2nd stage is caterpillar = 2/4.
3rd stage is chrysalis = 3/4.
4th stage is butterfly = 4/4.
so the fractions are 1/4, 2/4, 3/4, and 4/4.

Question 16.
Karen bought 4 movie tickets for $9 each. She has $12 left over. How much money did Karen have to start? Explain.

Answer:
The money Karen has to start = $48.

Explanation:
In the above-given question,
given that,
Karen bought 4 movie tickets for $9 each. She has $12 left over
4 x 9 = 36.
36 + 12 = 48.
so the money Karen has to start = $48.

Question 17.
Higher Order Thinking Peggy has 4 whole sandwiches. She cuts each whole into halves. Then Peggy gives away 1 whole sandwich. Show the number of sandwiches Peggy has left as a fraction.

Each sandwich is cut into equal parts.

Answer:
The number of sandwiches Peggy has left as a fraction = 6/8.

Explanation:
In the above-given question,
given that,
Peggy has 4 whole sandwiches.
She cuts each whole into halves.
4 x 2 = 8.
Then Peggy gives away 1 whole sandwich.
8 – 2 = 6.
so the number of sandwiches Peggy has left as a fraction = 6/8.

Assessment Practice

Question 18.
Complete the equations. Match the fractions with their equivalent whole numbers.

Answer:
6/1 = 12/2 = 6.
6/3 = 4/2 = 2.
4/4 = 1/1 = 1.
8/2 = 16/4 = 4.

Explanation:
In the above-given question,
given that,
the numbers are 1, 2, 4, and 6.
6/1 = 12/2 = 6.
6/3 = 4/2 = 2.
4/4 = 1/1 = 1.
8/2 = 16/4 = 4.

Lesson 13.8 Problem Solving

Construct Arguments
Solve & Share
Lindsey and Matt are running in a 1-mile race. They have both run the same distance so far. Write a fraction that shows how far Lindsey could have run. Write a different fraction that shows how far Matt could have run. Construct a math argument to support your answer.
I can … construct math arguments using what I know about fractions.

Thinking Habits
Be a good thinker! These questions can help you.

• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?
  

Look Back! Construct Arguments Are the two fractions you wrote equivalent? Construct a math argument using pictures, words, and numbers to support your answer.

Essential Question
How Can You Construct Arguments?

Visual Learning Bridge
Clara and Ana are making rugs. The rugs will be the same size. Clara has finished of her rug. Ana has finished of her rug. Who has finished more of her rug? Conjecture: Clara has finished a greater portion of her rug than Ana.

A conjecture is a statement that you think is true. It needs to be proved.

How can I explain why my conjecture is correct?
I need to construct an argument to justify my conjecture.

How can I construct an argument?
I can

• use numbers, objects, drawings, or actions correctly to explain my thinking.
• make sure my explanation is simple, complete, and easy to understand.

Here’s my thinking…
I will use drawings and numbers to explain my thinking.
The number lines represent the same whole. One is divided into fourths. One is divided into eighths.

The number lines show that 3 of the fourths is greater than 3 of the eighths.
So, \(\frac{3}{4}\) > \(\frac{3}{8}\). The conjecture is correct.

Convince Me! Construct Arguments Use numbers to construct another math argument to justify the conjecture above. Think about how you can look at the numerator and the denominator.

Guided Practice

Construct Arguments Paul and Anna were eating burritos. The burritos were the same size. Paul ate \(\frac{2}{6}\) of a burrito. Anna ate \(\frac{2}{3}\) of a burrito. Conjecture: Paul and Anna ate the same amount.
Question 1.
Draw a diagram to help justify the conjecture.

Answer:
No, Paul and Anna were correct.

Explanation:
In the above-given question,
given that,
Paul and Anna were eating burritos.
The burritos were the same size.
Paul ate \(\frac{2}{6}\) of a burrito.
Anna ate \(\frac{2}{3}\) of a burrito.
paul ate 2 of the sixths is less than the 2 of the thirds.
2/6 = 1/6 + 1/6.
2/3 = 1/3 + 1/3.
yes, the conjecture is not correct.

Question 2.
Is the conjecture correct? Construct an argument to justify your answer.

Answer:
No, the conjecture was not correct.

Explanation:
In the above-given question,
given that,
Paul and Anna were eating burritos.
The burritos were the same size.
Paul ate \(\frac{2}{6}\) of a burrito.
Anna ate \(\frac{2}{3}\) of a burrito.
paul ate 2 of the sixths is less than the 2 of the thirds.
2/6 = 1/6 + 1/6.
2/3 = 1/3 + 1/3.
yes, the conjecture is not correct.

Independent Practice

Construct Arguments Reyna has a blue ribbon that is 1 yard long and a red ribbon that is 2 yards long. She uses \(\frac{2}{4}\) of the red ribbon and \(\frac{2}{4}\) of the blue ribbon.

Conjecture: Reyna uses the same amount of red and blue ribbon.
Question 3.
Draw a diagram to help justify the conjecture.

Answer:
Yes, the conjecture was correct.

Explanation:
In the above-given question,
given that,
Reyna has a blue ribbon that is 1 yard long and a red ribbon that is 2 yards long.
She uses \(\frac{2}{4}\) of the red ribbon and \(\frac{2}{4}\) of the blue ribbon.
2/4 = 1/4 + 1/4.
2/4 = 1/4 + 1/4.
yes, the conjecture is correct.

Question 4.
Is the conjecture correct? Construct an argument to justify your answer.

Answer:
Yes, the conjecture is correct.

Explanation:
In the above-given question,
given that,
Reyna has a blue ribbon that is 1 yard long and a red ribbon that is 2 yards long.
She uses \(\frac{2}{4}\) of the red ribbon and \(\frac{2}{4}\) of the blue ribbon.
2/4 = 1/4 + 1/4.
2/4 = 1/4 + 1/4.
yes, the conjecture is correct.

Question 5.
Explain another way you could justify the conjecture.
Answer:

Problem Solving

Performance Task School Fair Twenty-one students worked at the school fair. Mrs. Gold’s students worked at a class booth. The table shows the fraction of 1 hour that her students worked. Mrs. Gold wants to know the order of the work times for the students from least to greatest.

Question 6.
Make Sense and Persevere What comparisons do you need to make to find out who worked the least?

Answer:
The student who worked least is Pedro.

Explanation:
In the above-given question,
given that,
School Fair Twenty-one students worked at the school fair.
Gold’s students worked at a class booth.
The table shows the fraction of 1 hour that her students worked.
Tim worked 4 hours.
Cathy worked 2/4 hours.
Jose worked 2/6 hours.
Pedro worked 3/4 hours.
3/4 < 2/4 < 2/6.
so the student who worked least is Pedro.

Question 7.
Be Precise What is the whole for each student’s time? Do all the fractions refer to the same whole?

Answer:
The same whole is 4.

Explanation:
In the above-given question,
given that,
School Fair Twenty-one students worked at the school fair.
Gold’s students worked at a class booth.
The table shows the fraction of 1 hour that her students worked.
Tim worked 4 hours.
Cathy worked 2/4 hours.
Jose worked 2/6 hours.
Pedro worked 3/4 hours.
3/4 < 2/4 < 2/6.
so the students who worked least is Pedro.

Question 8.
Use Appropriate Tools What tool could you use to solve this problem? Explain how you would use this tool.

Answer:

Question 9.
Construct Arguments What is the order of the work times from least to greatest? Construct a math argument to justify your answer.

Answer:
The student who worked the least is Pedro.

Explanation:
In the above-given question,
given that,
School Fair Twenty-one students worked at the school fair.
Gold’s students worked at a class booth.
The table shows the fraction of 1 hour that her students worked.
Tim worked 4 hours.
Cathy worked 2/4 hours.
Jose worked 2/6 hours.
Pedro worked 3/4 hours.
3/4 < 2/4 < 2/6.
so the student who worked least is Pedro.

Topic 13 Fluency Practice Activity

Find a Match
Work with a partner. Point to a clue. Read the clue.
Look below the clues to find a match. Write the clue letter in the box next to the match.
Find a match for every clue.
I can … multiply and divide within 100.

Clues
A. ls equal to 3 × 3
B. is equal to 4 × 4
C. is equal to 9 × 4
D. is equal to 0 ÷ 10
E. is equal to 35 ÷ 5
F. is equal to 12 ÷ 4
G. is equal to 5 × 4
H. is equal to 3 × 8
I. Is equal to 2 × 5
J. Is equal to 3 × 10
K. is equal to 9 × 2
L. is equal to 2 × 4

Answer:
6 x 6 = 36, 40 / 4 = 10, 0 x 9 = 0, 3 x 6 = 18, 32 / 4 = 8, 10 x 2 = 20, 5 x 6 = 30, 7 / 21 = 3, 8 x 2 = 16, and 6 x 4 = 24.

Explanation:
In the above-given question,
given that,
A is not equal to 9.
B is equal to 16.
C is equal to 36.
D is equal to 0.
E is equal to 35 / 5 = 7.
F is equal to 3.
G is equal to 20.
H is equal to 24.
I is equal to 10.
J is equal to 30.
K is equal to 18.
L is equal to 8.

Topic 13 Vocabulary Review

Word List

• denominator
• equivalent fractions
• fraction
• number line
• numerator
• unit fraction

Understand Vocabulary

Write T for true or F for false.
Question 1.
______ \(\frac{1}{6}\) and \(\frac{2}{6}\) have the same numerator.

Answer:
True.

Explanation:
In the above-given question,
given that,
the fractions are 1/6 and 2/6.
2/6 = 1/3.
2 x 1 = 2.
2 x 3 = 6.
so both the fractions have the same numerator.

Question 2.
________ \(\frac{1}{2}\) and \(\frac{4}{8}\) are equivalent fractions.

Answer:
True.

Explanation:
In the above-given question,
given that,
the fractions are 1/2 and 4/8.
4/8 = 1/2.
4 x 1 = 4.
4 x 2 = 8.
so both the fractions are equivalent fractions.

Question 3.
_______ \(\frac{3}{8}\) is a unit fraction.

Answer:
True.

Explanation:
In the above-given question,
given that,
the fraction is 3/8.
3/8 = 1/8 + 1/8 + 1/8.
so 3/8 is a unit fraction.

Question 4.
_________ A whole number can be written as a fraction.

Answer:
True.

Explanation:
In the above-given question,
given that,
A whole number can be written as a fraction.
2 / 2 = 1.
so the whole number can be written as a fraction.

Question 5.
________ The denominators in \(\frac{1}{3}\) and \(\frac{2}{3}\) in are the same.

Answer:
True.

Explanation:
In the above-given question,
given that,
the fractions are 1/3 and 2/3.
2/3 = 1/3 + 1/3.
in both the fractions, the numerator, and denominator are the same.
so both the fractions have the same denominators.

Question 6.
_______ A number line always shows fractions.

Answer:
A unit fraction is a number line that always shows fractions.

Explanation:
In the above-given question,
given that,
3/8 is a unit fraction.
3 is the numerator and 8 is a denominator.
so the unit fraction is a number line that always shows fractions.

For each of these terms, give an example and a non-example.

Answer:
1/2 is a fraction.
3/8 is a unit fraction.
1/2 = 2/4 are equivalent fractions.

Explanation:
In the above-given question,
given that,
the terms are fraction, unit fraction, and equivalent fractions.
1/2 is a fraction.
3/8 is a unit fraction.
1/2 = 2/4 are equivalent fractions.

Use Vocabulary in Writing
Question 10.
Use at least 2 terms from the Word List to explain how to compare \(\frac{1}{2}\) and \(\frac{1}{3}\).

Answer:
The two terms have different denominators.