Category: Envision Math

Go through the enVision Math Common Core Grade 1 Answer Key Topic 13 Time and Money regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 13 Time and Money

Essential Question:
What are the values of coins, and what are some different ways to tell time?
Musical instruments can make many different sounds.
Almost all of these sounds are made when some part of the instrument vibrates.


The Sound of Vibration
Find Out Talk to friends and relatives about the sounds that different musical instruments make. Ask them if they know what part of the instrument vibrates to make the sound.

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

• Draw pictures of different musical instruments.
• Circle or highlight the part of the instrument that

Review What You Know
Vocabulary

Question 1.
Count to find the missing numbers. 28, 29, __, __, 32, __, 34, __
Answer:

28, 29, 30, 31, 32, 33, 34, 35

Question 2.
Circle the number in the ones place.
1 2
Answer:

Question 3.
Write the missing numbers to complete the pattern.

Answer:

Counting
Question 4.
Count by 1 s to write the missing numbers. 47, 48, __, __, __, 52, 53, __
Answer:

47, 48, 49, 50, 51, 52, 53, 54

Question 5.
Count by 10s to write the missing numbers. __, 20, 30, __, __, __
Answer:

10, 20, 30, 40, 50, 60

Use Tools to Count
Question 6.
Use what you know about counting on a hundred chart to fill in the missing numbers.

Answer:

Pick a Project

PROJECT 13A
What are your favorite library books?
Project: Keep a Reading Log

PROJECT 13B
Where did all these coins come from? Project:
Make a Coin Poster

PROJECT 13C
Would you like to work in a store?
Project: Play Store

3-ACT MATH PREVIEW

Math Modeling
Drip Dry

I can model with math to solve a problem about time and measurement.

Lesson 13-1 Tell the Value of Coins

Solve & Share
Jennifer has 8 coins. She wants to share them with her friend. She says, “We each get 4 coins like this.” Do you think this is a fair way to share the coins? Explain.

I can … Identify coins and tell their value.

Answer:

No, this Is Not the fair way to share the coins because,

1 nickel = 5 cents

So, 4 nickels = 4 x 5 = 20 cents

1 dime = 10 cents

So, 4 dimes = 4 x 10 = 40 cents

Therefore, it is not the correct way to share the coins.

Visual Learning Bridge

Convince Me! Look at the penny and the nickel. Write 2 ways they are alike. Then write 2 ways they are different.

Guided Practice

Write the name of the coin. Then tell its value and how many are in a dollar.
Question 1.

Answer:

Name of the Coin = Dime

Value = 10 cents

How many in A dollar = 10

Question 2.

Answer:

Name of the coin = Penny

Value = 1 cent

How Many in a dollar = 100

Independent Practice

Circle the coins. Then complete the sentences.
Question 3.
Circle every quarter.

A quarter is worth _______ ¢.
There are _______ quarters in a dollar.
Answer:

1 quarter = 25 cents.

$1 = 100 cents

4 quarter = 100 cents

Therefore, There are 4 quarters in a dollar.

Question 4.
Circle every coin with a value of 5¢.

А _______ is worth 5¢.
How many in a dollar? _______
Answer:

A  nickel is worth 5¢

1 Dollar = 100 cents

20 nickels = 5 x 20 = 100 cents

Therefore, 20 nickels = 100 cents.

Question 5.
Mark has 6 dimes. How many more dimes does he need in order to have 1 dollar? _______ more dimes
Answer:

1 dime = 10 cents

So, 6 dimes = 6 x 10 = 60 cents

$1 = 100 cents

100 – 60 = 40

40 cents = 4 dimes

Therefore, Mark need 4 more dimes.

Question 6.
Higher Order Thinking Beth has a stack of nickels worth 1 dollar. She also has a stack of quarters worth 1 dollar. How many coins does she have in all? _______ coins in all
Answer:

$1 = 100 cents

1 nickel = 5 cents

20 nickels = 1 dollar

1 quarter = 25 cents

4 quarters = 1 dollar

Now, 20 nickels + 4 quarters = 24 coins

Therefore, 24 Coins are there in all.

Problem Solving

Solve the problems below.
Question 7.
Draw lines to show which coins go in which bank.

Answer:

Question 8.
Higher Order Thinking Jake has a dollar’s worth of dimes. Henry has a dollar’s worth of nickels. Who has more coins? How many more?
Answer:

$1 = 100 cents

1 dime = 10 cents

So, 10 dimes = 1 dollar

1 nickel = 5 cents

So, 20 Nickels = $1

Therefore, Henry has more coins than Jake.

Henry Has 10 coins more.

Question 9.
Number Sense Solve the riddle. I am a coin that is worth more than a nickel and less than a quarter. What coin am I?
Answer:

Dime

Explanation:

1 nickel = 5 cents

1 Quarter = 25 cents

1 dime = 10 cents

Therefore, Dime coin worth more than a nickel and less than a quarter.

Question 10.
Explain Kate wants to buy a bottle of juice. It costs a dollar. Kate has 3 quarters. How many more quarters does she need?
Answer:

Kate Need 1 quarter To buy a bottle of juice.

$1 = 100 cents

1 quarter = 25 cents

Which means, 3 quarters = 25+25+25 = 75

Now, 100 – 75 = 25

Therefore, Kate Need 1 Quarter To buy a bottle of juice.

Question 11.
Assessment Practice which coins have the same value as a dollar? Choose two that apply.
☐ 50 dimes
☐ 20 nickels
☐ 100 pennies
☐ 10 quarters
Answer:

1 dollar = 100 cents

1 Nickel = 5 cents

Which means, 20 Nickels = 20 x 5 = 100 cents

1 penny = 1 cent

Which means, 100 pennies = 100 cents

Therefore The answer is 20 Nickels and 100 pennies.

Lesson 13.2 Find the Value of a Group of Coins

Solve & Share
Julia has dime and 2 pennies. How many pop beads can she buy? Use words or pictures to explain how you know.

I can … find the value of a group of coins.

Answer:

Given That Julia Have 1 Dime And 2 Pennies

1 Dime = 10 Cents

And 2 pennies = 2 Cents

Total = 10¢ + 2¢ = 12¢

Also Given That, The Cost Of Pop Beads = 1¢

Therefore She can buy 12 Pop Beads.

Visual Learning Bridge

Convince Me! How is counting dimes and pennies like counting by tens and counting by ones?

Guided Practice 

Count on. Then write how much money in all.
Question 1.

Answer:

1 Dime = 10 Cents

So, 6 Dimes = 10 + 10 + 10 + 10 +10 + 10 = 60¢

Therefore, There are 60¢ In All.

Question 2.

Answer:

1 Dime = 10 Cents

So, 2 Dimes = 10 + 10 = 20¢

1 penny = 1 cent

So, 3 Pennies = 3 cents

Total : 20¢ +3¢ = 23¢

Therefore There are 23¢ in all.

Independent Practice

Count on. Then write how much in all.
Question 3.

Answer:

1 penny = 1 cent

So, 5 pennies = 5 Cents
Therefore, there are 5 Cents in all.

Question 4.

Answer:

1 Dime = 10 Cents

So, 3 Dimes = 10 + 10 + 10 = 30¢

1 penny = 1 cent

So, 3 pennies = 3¢

Total : 30¢ + 3¢ = 33¢

Therefore, There are 33¢ In All.

Question 5.

Answer:

1 Dime = 1 Cents

So, 3 Dimes = 10 + 10+ 10 = 30¢

1 penny = 1 cent

Total : 30¢ + 1¢ = 31¢

Therefore, There Are 31¢ In All.

Question 6.
Higher-Order Thinking Find the total value of the coins.

Answer:

I Will Count Dimes First Because It Will Be Easy While Calculating The Total.

1 Dime = 10 Cents

So, 7 Dimes = 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70¢

1 penny = 1 cent

So, 5 Pennies = 5¢

Total : 70¢ + 5¢ = 75¢

Therefore, The value Of The Coins = 75¢

Problem Solving

Solve each problem below.
Question 7.
Sally has 45¢. She has dimes and pennies. Draw a picture to show the coins Sally could have.

Answer:

45¢ Can Be Shown In Dimes And Pennies As

4 Dimes And 5 pennies.

1 dime = 10 cents

So, 4 Dimes = 10+ 10+ 10+ 10 = 40¢

1 penny = 1 cent

So, 5 pennies = 5¢

Total: 40¢ + 5¢ = 45¢

Question 8.
Be Precise Jack has 5 dimes and 17 pennies. How many cents does Jack have?
Answer:

1 Dime = 10 Cents

So, 5 Dime = 10+ 10 +10 + 10 + 10 = 50¢

1 penny = 1 cent

So, 17 Pennies = 17¢

Total : 50¢ + 17¢ = 67¢

Therefore, Jack Have 67¢

Question 9.
Higher-Order Thinking Tom has 4 dimes. He wants to buy the marker. How many more cents does he need?

Answer:

Given That Tom Have 4 dimes.

1 Dime = 10 Cents

So, 4 Dimes = 10 + 10 + 10 + 10 = 40¢

Tom Has 40 Cents.

The Cost Of The Marker 54¢

Now, 54¢ – 40¢ = 14¢

Therefore, Tom Need 14¢ To Buy The Marker.

Question 10.
Assessment Practice Rita has the 2 coins below in her purse.

Which coins does Rita need to have 31¢ exactly?

Answer: D

Rita Have 2 dimes in her purse.

1 dime = 10 cents

so, 2 dimes = 10+10 = 20 cents

To make 31 cents Rita needs 11 cents

11 cents can be shown as 1 dime and 1 penny.

1 dime = 10 cents + 1 penny = 1 cents

Total : 11 cents

So, The answer is D.

Lesson 13.3 Understand the Hour and Minute Hands

Solve & Share
Look at the clock. Ria says this clock shows 12 o’clock. Pat says this clock shows 3 o’clock. Do you agree with Ria or Pat? Tell why.

I can … tell time to the hour.

Visual Learning Bridge

Convince Me! How is the hour hand different from the minute hand?

Guided Practice

Write the time shown on each clock. Practice
Question 1.

Answer:

hour
hand: 4
minute
hand: 12
4 o’clock

Question 2.

hour
hand: _______
minute
hand: _______
_______ o’clock

Answer:

hour
hand: 9
minute
hand: 12
9 o’clock

Question 3.

hour
hand: _______
minute
hand: _______
_______ o’clock

Answer:

hour
hand: 3
minute
hand: 12
3 o’clock

Independent Practice

Draw the hour and minute hands to show the time.
Question 4.

10 o’clock
Answer:

Question 5.

2 o’clock
Answer:

Question 6.

11 o’clock
Answer:

Question 7.

12 o’clock
Answer:

Question 8.

6 o’clock
Answer:

Question 9.

1 o’clock
Answer:

Question 10.

5 o’clock
Answer:

Question 11.

8 o’clock
Answer:

Question 12.
Higher Order Thinking Write a time. Draw the hour and minute hands to show the time. Draw a picture to show an activity you do at that time.
_______ o’clock

Answer:

6 o’clock

Problem Solving

Solve each problem below.
Question 13.
Look for Patterns Sarah wakes up at 7 o’clock. Draw the hands on the clock to show 7 o’clock.

Answer:

Question 14.
enVision® STEM Each string on a guitar makes a different sound when it vibrates. Joe starts tuning his guitar at 9 o’clock. It takes him one hour to finish. What time does he finish? _______ o’clock
Answer:

At 10 o’clock

Question 15.
Higher Order Thinking Karen starts playing soccer one hour after 5 o’clock. Draw the hour and minute hands on the clock to show what time Karen starts playing soccer.
Then write a sentence about an activity you might do at that time.

Answer:

I play Cricket for 1 hour

Question 16.
Assessment Practice Bill likes to read after 3 o’clock and before 5 o’clock. Which clock shows the time Bill might read?

Answer:

Lesson 13.4 Tell and Write Time to the Hour

Solve & Share
Both of the clocks show the same time. Tell me what time is shown. Then write one way the clocks are alike and one way they are different.
I can … tell time to the hour using 2 different types of clocks.

Visual Learning Bridge

Convince Me! Do the clocks show the same time? Explain.

Answer:

No. The left side clock time is 7:00 and right side clock time showing is 8:00.

Guided Practice

Draw the hands on the clock face. Then write the time on the other clock.
Question 1.

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Independent Practice

Draw the hands on the clock face. Then write the time on the other clock.
Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.

Answer:

Think about how hands move on a clock to help solve the problem.

Question 11.
Number Sense Mary writes a pattern. Then she erases some of the times. Write the missing times.
6:00, 8:00, ______ : _______, 12:00, _____ : ______
Answer:

6:00, 8:00, 10:00, 12:00, 2:00

Problem Solving

Solve each problem below.
Question 12.
Reasoning Raul starts riding his bike at 1:00. He rides for 1 hour. What time does Raul stop? Draw the hands on the clock face. Then write the time on the other clock.

Answer:

Question 13.
Vocabulary Lucy reads for 1 hour. She starts reading at 8:00. What time did Lucy stop reading? Draw the hands on the clock face. Then write the hour Lucy stops reading.

_______ o’clock
Answer:

9 o’clock

Question 14.
Higher Order Thinking David goes to bed 2 hours before his mother. David’s mother goes to bed at 11:00.
Write the time David goes to bed on the clock.

Answer:

Question 15.
Assessment Practice Maribel washes dishes after 6:00 and before 9:00. Which clocks show a time Maribel might wash dishes? Choose two that apply.

Answer:

Lesson 13.5 Tell and Write Time to the Half Hour

Solve & Share
The minute hand travels all the way around the clock every hour. Each little mark is 1 minute of time.
Count how many minutes make up I hour. How many marks are there if the minute hand goes only halfway around the clock? Explain your answer.
I can … tell time to the half hour.

Visual Learning Bridge

Convince Me! Why is the hour hand between 6 and 7 when it is 6:30?

Guided Practice

Write the numbers to complete each sentence. Then write the time on the other clock.
Question 1.

Question 2.
The hour hand is between ________ and ______.
The minute hand is on _______.

Answer:

The hour hand is between 4 and 5.
The minute hand is on 6

Independent Practice

Write the time shown on each clock.
Question 3.

Answer:

The hour hand is between 8 and 9.
The minute hand is on 6

Question 4.

Answer:

The hour hand is between 5 and 6.
The minute hand is on 6

Question 5.

Answer:

The hour hand is between 12 and 1.
The minute hand is on 6

Look at the pattern. Write the missing times./
Question 6.
6:00, 6:30, 7:00, ______,8:00, _______, _______
Answer:

6:00, 6:30, 7:00, 7:30, 8:00, 8:30, 9:00

Question 7.
2:30, 3:30, ______,5:30, _______, _______
Answer:

2:30, 3:30, 4:30, 5:30, 6:30, 7:30, 8:30

Question 8.
Higher Order Thinking Carlos plays basketball for 30 minutes each day. He always starts playing at half past an hour. Write times he might start and stop playing basketball. Draw the hands on each clock face to show the times.

Answer:

Problem Solving

Solve each problem below.
Question 9.
Be Precise Sandy walks her dog at 3:00. She walks for 30 minutes. What time does Sandy stop walking her dog? Draw the hands on the clock face. Write the time on the other clock.

Answer:

Sandy stop walking her dog at 3:30

Question 10.
Be Precise Robin gets to school at 9:00. Her math class starts at half-past 9. What time does Robin’s math class start? Draw the hands on the clock face. Write the time on the other clock.

Answer:

Robin’s math class start at 9:30

Question 11.
Higher Order Thinking Show 8:00 on the first clock. On the second clock, show the time 30 minutes later. Is the hour hand still at 8? Explain.

Answer:

No, The hour hand will rotate and it will lie between 8 to 9.

Question 12.
Assessment Practice Which clock below shows the same time as the clock face?

Answer:

‘C’ clock shows the same time as the clock face.

Lesson 13.6 Problem Solving

Reasoning
Solve & Share
Noel has a music lesson at 3:30. At 4:30, he goes to the library. He gets ready at 5:00 so he can have dinner at 5:30. After dinner ends at 6:00, he plays a game. Organize Noel’s schedule in a way that makes sense to you.
I can … use reasoning to tell and write time.

Thinking Habits What do the numbers stand for? How are the numbers in the problem related?

Visual Learning Bridge

Convince Me! What happens 1 hour after Art begins? Explain how you know.

Guided Practice

Use Mr. Diaz’s Class Schedule above to answer the questions. Circle the activity that starts at the time shown. Then explain your reasoning.
Question 1.

Question 2.

Answer:

Independent Practice

Use the Nature Trip Schedule to answer the questions.

Question 3.
Which activity do children do just before the Bird Watch? Explain your reasoning.
Answer:

‘Walk’ is the activity children do just before the Bird. It is at 10:00 before Bird Watch which is at 11:00.

Question 4.
Which activity or activities do children do after Lunch? Explain your reasoning.
Answer:

‘Make a bird house’ is the activity children do after Lunch. It is at 12:30 after lunch which is at 12:00

Question 5.
Which activity starts at the time shown? Explain your reasoning.

Answer:

‘Make a Birdhouse’ is the activity. It is at 12:30.

Question 6.
Vocabulary Circle the time that shows a half hour past 3:00.
2:00
3:00
3:30
4:00
Answer:

3:30

Problem Solving

Performance Task
Visiting the City Andrew’s family takes a day trip to the city.
Help him solve the problems below using the Family Schedule.

Question 7.
Model The minute hand fell off this clock. What time should the clock show when Andrew’s family arrives at the Aquarium?
Draw the minute hand and write the time shown.

Answer:

Question 8.
Reasoning Andrew writes down all the activities his family is doing at 30 minutes after the hour. How many activities did Andrew write? Explain how you found out.
Answer:

Topic 13 Fluency Practice Activity

Point&Tally
Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue. Partner I and Partner 2 each point to a black number at the same time. Both partners add those numbers. If the answer is on your color, you get a tally mark. Work until one partner gets twelve tally marks.
I can … add and subtract within 10.

Topic 13 Vocabulary Review

Word List
• cent (c)
• minute
• dime
• minute
• dollar hand
• half hour
• nickel
• hour o’clock
• hour hand
• quarter

Understand Vocabulary
Question 1.
Circle the hour hand.

Answer:

Question 2.
Circle the minute hand.

Answer:

Question 3.
Fill in the blank.
Use a word from the Word List.
A 5¢ coin is called a __________
Answer:

Question 4.
Fill in the blank.
Use a word from the Word List.
A 25¢ coin is called a ___________ .
Answer:

Question 5.
Fill in the blank.
Use a word from the Word List.
There are 10 dimes in one __________.
Answer:

Use Vocabulary in Writing
Question 6.
Tell what time is shown on the clock using a word from the Word List.

Answer:

Topic 13 Reteaching

Set A

You can draw the hour and minute hands to show the time. Show 8:00

This clock shows 5 o’clock.

Answer:

Draw or write the time.
Question 1.

Answer:

Question 2.

_________ 0′ clock
Answer:

6 0′ clock

Draw the hands on the clock face. Then write the time on the other clock.
Question 3.

Answer:

Set B

What time do the clocks show?

Remember: Half past means 30 minutes after the hour.

Write the time shown on each clock.
Question 4.

half past _______
or ______ : ______
Answer:

half past 7

or 7:30

Question 5.

half past _______
or ______ : ______
Answer:

half past 2
or 2:30

Set C

Thinking Habits
Reasoning
What do the numbers stand for?
How are the numbers in the problem related?

Use the schedule to answer the questions.

Question 6.
What activity starts 2 hours after Reading?
Answer:

Recess is the activity starts 2 hours after Reading

Question 7.
What time does Math begin?
_______ : _______
Answer:

9:30

Topic 13 Assessment Practice

Question 1.
Lisa rides her bike after 2 o’clock and before 6 o’clock every Friday.
Choose two clocks that show the time Lisa might ride her bike.

Answer:

Question 2.
Which clock shows the same time as the clock face?

Answer:

D

Question 3.
Draw the time on the clock.

5 o’clock
Answer:

Question 4.
Draw hands on the clock face to show the time that Story Time starts.

Answer:

Question 5.
Show the same time on both clocks. How do you know you are correct?

Answer:

Minute hand is at12  and hour hand is at 3, so the time is 3 o’clock.  same time is displayed on the other clock also.

Topic 13 Performance Task

A Trip to the Zoo Carol and her class take a trip to the zoo. The chart shows their schedule.

Question 1.
Show another way to write the time for each activity.
Large Animals _________
Train Ride _________
Answer:

Large Animals – 10 o’ clock
Train Ride – Half past 9 o’ clock

Question 2.
Draw the hands on the clock to show the time for the Dolphin Show.

Answer:

Question 3.
The class left school at half past 8.
Draw the hands and write the time on the clocks to show what time they left school.

Answer:

Question 4.
Carol says that this clock shows the same time that Lunch starts.

Do you agree with her?
Circle Yes or No.
Explain your answer.
Answer:

No. I won’t agree with her.

Because the time at Lunch starts is 11:30 but the clock is showing the time 10:30.

Question 5.
The class finishes seeing the Small Animals at 1:30. They will get back at school in 30 minutes. What time will it be then? Choose a way to show the time.
Answer:

The time will be 2:00

Go through the enVision Math Common Core Grade 1 Answer Key Topic 10 Use Models and Strategies to Add Tens and Ones regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 10 Use Models and Strategies to Add Tens and Ones

enVision STEM Project: Watch the Stars

Find Out Talk to friends and relatives about stars. Discuss why the stars you see in the sky change from night to night.
Journal: Make a Book Show what you found out. In your book, also:

• Draw the stars you can see from where you live.
• Make up and solve addition problems about the stars.

Review What You Know

Vocabulary

Question 1.
Circle the digit that shows how many ones.
91

Answer:
The digit that shows many ones is 1.

Explanation:
In the above-given question,
given that,
the number is 91.
9 is in the tens place.
1 is in one place.
so we have to circle for one.

Question 2.
Circle the digit that shows how many tens.
13

Answer:
The digit that shows many tens is 1.

Explanation:
In the above-given question,
given that,
the number is 13.
1 is in the tens place.
3 is in one place.
so we have to circle for one.

Question 3.
Circle the symbol that tells you add.
+ – =

Answer:
The symbol is +.

Explanation:
In the above-given question,
given that,
for example:
3 + 2.
5.
here we did the addition operation.

Understanding Addition

Question 4.
Write an addition equation to match the picture.

Answer:
The equation is 9 + 5 = 14.

Explanation:
In the above-given question,
given that,
there are 9 blue flowers.
there are 5 red flowers.
9 + 5 = 14.

Question 5.
Noah mows 7 lawns. Mari mows 13 lawns. How many lawns did the two friends mow in all? Write an addition equation to solve.
__ + __ = ____

Answer:
The addition equation is 7 + 13 = 20.

Explanation:
In the above-given question,
given that,
Noah mows 7 lawns.
Mari mows 13 lawns.
7 + 13 = 20.

Hundred Chart

Question 6.
Fill in the missing numbers on the part of the hundred chart.

Answer:
The missing numbers are 42, 55, 58, 63, and 70.

Explanation:
In the above-given question,
given that,
the numbers are from 41 to 70.
the missing numbers on the part of the hundred charts:
42, 55, 58, 63, and 70.

pick a Project

PROJECT 10A

Has anyone ever called you the wrong name?
Project: Make a Manatee Facts Book

PROJECT 10B
Have you ever aimed at a target?
Project: Play a Target Toss Game

PROJECT 10C
What is as colorful as a butterfly?
Project: Make a Leaf and Egg Model

PROJECT 10D
What would life be like without bones?
Project: Write and Draw an Octopus Story

Lesson 10.1 Add Tens Using Models

Solve & Share

How are these addition problems alike? Talk to a partner about how you can use the first sum to help you find the second.

Answer:
3 + 5 = 8.
30 + 50 = 80.

Explanation:
In the above-given question,
given that,
add the numbers.
3 + 5 = 8.
3 is in the tens place and 0 is in one place.
30 + 50 = 80.

Visual Learning Bridge

Convince Me!
How is adding 6 + 3 like adding 60 + 30?

Answer:
6 tens + 3 tens = 90.

Explanation:
In the above-given question,
given that,
6 + 3 = 9.
6 tens + 3 tens.
6 tens = 60.
3 tens = 30.
60 + 30 = 90.

Guided Practice

Write the numbers to complete each equation.

Question 1.

Answer:
30 + 40 = 70.

Explanation:
In the above-given question,
given that,
3 tens + 4 tens.
3 tens = 30.
4 tens = 40.
3 tens + 4 tens = 70.

Question 2.

Answer:
10 + 50 = 60.

Explanation:
In the above-given question,
given that,
1 tens + 5 tens.
1 tens = 10.
5 tens = 50.
1 tens + 5 tens = 60.

Independent Practice

Write the numbers to complete each equation.

Question 3.

Answer:
20 + 20 = 40.

Explanation:
In the above-given question,
given that,
2 tens + 2 tens.
2 tens = 20.
2 tens = 20.
2 tens + 2 tens = 40.

Question 4.

Answer:
50 + 30 = 80.

Explanation:
In the above-given question,
given that,
5 tens + 3 tens.
5 tens = 50.
3 tens = 30.
5 tens + 3 tens = 80.

Question 5.

Answer:
30 + 10 = 40.

Explanation:
In the above-given question,
given that,
3 tens + 1 tens.
3 tens = 30.
1 tens = 10.
3 tens + 1 tens = 40.

Question 6.

Answer:
10 + 10 = 20.

Explanation:
In the above-given question,
given that,
1 tens + 1 tens.
1 tens = 10.
1 tens = 10.
1 tens + 1 tens = 20.

Question 7.

Answer:
40 + 40 = 80.

Explanation:
In the above-given question,
given that,
4 tens + 4 tens.
4 tens = 40.
4 tens = 40.
4 tens + 4 tens = 80.

Question 8.

Answer:
20 + 50 = 70.

Explanation:
In the above-given question,
given that,
2 tens + 5 tens.
2 tens = 20.
5 tens = 50.
2 tens + 5 tens = 70.

Question 9.

Answer:
30 + 30 = 60.

Explanation:
In the above-given question,
given that,
3 tens + 3 tens.
3 tens = 30.
3 tens = 30.
3 tens + 3 tens = 60.

Question 10.

Answer:
10 + 40 = 50.

Explanation:
In the above-given question,
given that,
1 tens + 4 tens.
1 tens = 10.
4 tens = 40.
1 tens + 4 tens = 50.

Question 11.

Answer:
50 + 40 = 90.

Explanation:
In the above-given question,
given that,
5 tens + 4 tens.
5 tens = 50.
4 tens = 40.
5 tens + 4 tens = 90.

Problem Solving
Add tens to solve. Use place-value blocks if needed.

Question 12.
Make Sense Alex and Annie each have 5 boxes of crayons. Each box has 10 crayons.
How many crayons do Alex and Annie have in all?
___ + ___ = ___
___ crayons

Answer:
The number of crayons do Alex and Annie have in all = 100.

Explanation:
In the above-given question,
given that,
Alex and Annie each have 5 boxes of crayons.
Each box has 10 crayons.
5 x 10 = 50.
50 + 50 = 100.
so the number of crayons do Alex and Annie have in all = 100.

Question 13.
Make Sense Becky and Dan buy some bottles of juice. Becky buys 6 bottles. Dan buys 2 bottles. Each bottle of juice is enough for 10 people. How many people do Dan and Becky have enough juice for?
___ + __ = ___
___ people

Answer:
The number of people do Dan and Becky have enough for = 80.

Explanation:
In the above-given question,
given that,
Becky and Dan buy some bottles of juice.
Becky buys 6 bottles.
Dan buys 2 bottles.
Each bottle of juice is enough for 10 people.
6 x 10 = 60.
2 x 10 = 20.
60 + 20 = 80.

Question 14.
Higher Order Thinking Bree says that she knows 4 + 3 = 7, so she also knows that 30 + 40 = 70. Is she correct? Explain how you know.

Answer:
Yes, she was correct.

Explanation:
In the above-given question,
given that,
4 + 3 = 7.
30 + 40 = 70.
3 tens + 4 tens = 7 tens.
so she was correct.

Question 15.
Assessment Practice Which equation matches the picture?
A. 2 + 3 = 5
B. 3 + 2 = 5
C. 20+ 3 = 23
D. 20 + 30 = 50

Answer:
Option D is correct.

Explanation:
In the above-given question,
given that,
2 tens + 3 tens.
2 tens = 20.
3 tens = 30.
20 + 30 = 50.
so option D is correct.

Lesson 10.2 Mental Math: Ten More Than a Number

Solve & Share

Solve each problem. What pattern do you see in the totals?

Answer:
15 + 10 = 25.
25 + 10 = 35.
55 + 10 = 65.

Explanation:
In the above-given question,
given that,
Add the numbers.
15 + 10 = 25.
25 + 10 = 35.
55 + 10 = 65.

Visual Learning Bridge

Convince Me!
Explain how you can use mental math to add 10 to 47.

Answer:
10 + 47 = 57.

Explanation:
In the above-given question,
given that,
4 + 1 = 5.
47 + 10 = 57.
5 tens + 7 ones = 57.

Guided Practice

Use mental math to solve the problems.

Question 1.

Answer:
10 + 25 = 35.

Explanation:
In the above-given question,
given that,
2 + 1 = 3.
25 + 10 = 35.
3 tens + 5 ones = 35.

Question 2.

Answer:
10 + 12 = 22.

Explanation:
In the above-given question,
given that,
1 + 1 = 2.
12 + 10 = 22.
2 tens + 2 ones = 22.

Independent Practice

Use mental math to solve each equation.

Question 3.

58 + 10 = ___

Answer:
10 + 58 = 68.

Explanation:
In the above-given question,
given that,
5 + 1 = 6.
58 + 10 = 68.
6 tens + 8 ones = 68.

Question 4.

44 + 10 = ___

Answer:
10 + 44 = 54.

Explanation:
In the above-given question,
given that,
4 + 1 = 5.
44 + 10 = 54.
5 tens + 4 ones = 54.

Question 5.

35 + 10 = ___

Answer:
10 + 35 = 45.

Explanation:
In the above-given question,
given that,
3 + 1 = 4.
35 + 10 = 45.
4 tens + 5 ones = 45.

Question 6.
10 + 72 = ___

Answer:
10 + 72 = 82.

Explanation:
In the above-given question,
given that,
7 + 1 = 8.
72 + 10 = 82.
8 tens + 2 ones = 82.

Question 7.
87 + 10 = ___

Answer:
10 + 87 = 97.

Explanation:
In the above-given question,
given that,
8 + 1 = 9.
87 + 10 = 97.
9 tens + 7 ones = 97.

Question 8.
31 + 10 = ___

Answer:
10 + 31 = 41.

Explanation:
In the above-given question,
given that,
3 + 1 = 4.
31 + 10 = 41.
4 tens + 1 ones = 41.

Question 9.
18 + 10 = ___

Answer:
10 + 18 = 28.

Explanation:
In the above-given question,
given that,
1 + 1 = 2.
18 + 10 = 28.
2 tens + 8 ones = 28.

Question 10.
10 + 26 = ___

Answer:
10 + 26 = 36.

Explanation:
In the above-given question,
given that,
2 + 1 = 3.
26 + 10 = 36.
3 tens + 6 ones = 36.

Question 11.
9 + 10 = ___

Answer:
10 + 9 = 19.

Explanation:
In the above-given question,
given that,
9 + 1 = 10.
9 + 10 = 19.
1 tens + 9 ones = 19.

Question 12.
Number Sense Winnie used place-value blocks to show 29 + 10. She said the answer is 30. Is Winnie correct? Explain how you know.

Answer:
No, Winnie was not correct.

Explanation:
In the above-given question,
given that,
Winnie used place-value blocks to show 29 + 10.
29 + 10 = 39.
so Winnie was not correct.

Problem Solving

Use mental math to solve the problems below.

Question 13.
Reasoning Sam makes 15 dollars mowing lawns one day. He makes 10 dollars the next day. How many dollars did Sam make in all?
____ dollars

Answer:
The number of dollars did Sam make in all = 25.

Explanation:
In the above-given question,
given that,
Sam makes 15 dollars mowing lawns one day.
He makes 10 dollars the next day.
15 + 10 = 25.
so the number of dollars did Sam make in all = 25.

Question 14.
Reasoning Tess solves 22 math problems. Then she solves 10 more math problems. How many math problems did Tess solve in all?

___ math problems

Answer:
The math problems did Tess solve in all = 32.

Explanation:
In the above-given question,
given that,
Tess solves 22 math problems.
Then she solves 10 more math problems.
22 + 10 = 32.
2 + 1 = 3.
so the math problems did Tess solve in all = 32.

Question 15.
Higher Order Thinking Roger collects 75 cans. Ella collects some cans. Roger and Ella have 85 cans together. How many cans did Ella collect?
___ cans

Answer:
The number of cans Ella collect = 10.

Explanation:
In the above-given question,
given that,
Roger collects 75 cans.
Ella collects some cans.
Roger and Ella have 85 cans together.
85 – 75 = 10.
so the number of cans Ella collect = 10.

Question 16.
Assessment Practice Match each pair of addends with their sum.

Answer:
27 = 17 + 10.
86 = 76 + 10.
43 = 33 + 10.
51 = 41 + 10.
69 = 59 + 10.

Explanation:
In the above-given question,
given that,
27 = 2 tens + 7 ones.
86 = 8 tens + 6 ones.
43 = 4 tens + 3 ones.
51 = 5 tens + 1 ones.
69 = 6 tens + 9 ones.
27 = 17 + 10.
86 = 76 + 10.
43 = 33 + 10.
51 = 41 + 10.
69 = 59 + 10.

Lesson 10.3 Add Tens and Ones Using a Hundred Chart

Solve & Share
Use a hundred chart to find these sums. 8 + 40 = ? 30 + 40 = ? 80 + 12 = ?
Show your work and tell how you found each sum.

Visual Learning Bridge

Convince Me!
How could you use the hundred chart to find the sum of 6 and 50?

Guided Practice

Use the part of the hundred chart to add.

Question 1.
2 + 12 = 14

Answer:
2 + 12 = 14.

Explanation:
In the above-given question,
given that,
12 has 1 ten and 2 ones.
so 12 is 1 row down on the chart.
2 is 2 ones.
2 + 12 = 14.

Question 2.
5 + 40 = ___

Answer:
5 + 40 = 45.

Explanation:
In the above-given question,
given that,
40 has 4 tens and 0 ones.
so 40 is 1 row down on the chart.
5 is 5 ones.
5 + 40 = 45.

Question 3.
13 + 20 = ___

Answer:
13 + 20 = 33.

Explanation:
In the above-given question,
given that,
33 has 3 tens and 3 ones.
so 33 is 1 row down on the chart.
13 is  1 ten 3 ones.
13 + 20 = 33.

Question 4.
10 + 31 = ___

Answer:
10 + 31 = 41.

Explanation:
In the above-given question,
given that,
41 has 4 ten and 1 ones.
so 31 is 1 row down on the chart.
10 is 10 ones.
10 + 31 = 41.

Question 5.

32 + 6 = ___

Answer:
6 + 32 = 38.

Explanation:
In the above-given question,
given that,
32 has 3 ten and 2 ones.
so 32 is 1 row down on the chart.
6 is 6 ones.
6 + 32 = 38.

Independent Practice

Use the hundred chart to add.

Question 6.
7 + 60 = ____

Answer:
7 + 60 = 67.

Explanation:
In the above-given question,
given that,
67 has 6 ten and 7 ones.
so 67 is 1 row down on the chart.
7 is 7 ones.
7 + 60 = 67.

Question 7.
33 + 20 = ___

Answer:
33 + 20 = 53.

Explanation:
In the above-given question,
given that,
53 has 5 ten and 3 ones.
so 53 is 1 row down on the chart.
20 is 20 ones.
33 + 20 = 53.

Question 8.
20 + 18 = ___

Answer:
18 + 20 = 38.

Explanation:
In the above-given question,
given that,
38 has 3 ten and 8 ones.
so 18 is 1 row down on the chart.
2 is 2 tens.
18 + 20 = 38.

Question 9.
5 + 13 = ___

Answer:
5 + 13 = 18.

Explanation:
In the above-given question,
given that,
13 has 1 ten and 3 ones.
so 5 is 1 row down on the chart.
5 is 5 ones.
5 + 13 = 18.

Question 10.
3 + 26 = ___

Answer:
3 + 26 = 29.

Explanation:
In the above-given question,
given that,
29 has 2 ten and 9 ones.
so 3 is 2 rows down on the chart.
3 is 3 ones.
3 + 26 = 29.

Question 11.
1 + 41 = ___

Answer:
1 + 41 = 51.

Explanation:
In the above-given question,
given that,
51 has 5 ten and 1 ones.
so 1 is 4 rows down on the chart.
1 is 1 one.
1 + 41 = 51.

Question 12.
4 + 32 = ___

Answer:
4 + 32 = 36.

Explanation:
In the above-given question,
given that,
36 has 3 ten and 6 ones.
so 3 is 3 rows down on the chart.
4 is 4 ones.
4 + 32 = 36.

Question 13.
56 + 2 = ___

Answer:
2 + 56 = 58.

Explanation:
In the above-given question,
given that,
58 has 5 tens and 8 ones.
so 2 is 5 rows down on the chart.
2 is 2 ones.
2 + 56 = 58.

Question 14.
10 + 85 = __

Answer:
10 + 85 = 95.

Explanation:
In the above-given question,
given that,
85 has 8 ten and 5 ones.
so 10 is 8 rows down on the chart.
10 is 10 ones.
10 + 85 = 95.

Question 15.
7 + 12 = ___

Answer:
7 + 12 = 19.

Explanation:
In the above-given question,
given that,
19 has 1 ten and 9 ones.
so 7 is 1 row down on the chart.
7 is 7 ones.
7 + 12 = 19.

Question 16.
50 + 13 = ___

Answer:
13 + 50 = 63.

Explanation:
In the above-given question,
given that,
63 has 6 ten and 3 ones.
so 13 is 4 rows down on the chart.
13 is 13 ones.
13 + 50 = 63.

Question 17.
71 + 5 = ___

Answer:
71 + 5 = 76.

Explanation:
In the above-given question,
given that,
76 has 7 ten and 6 ones.
so 71 is 1 row down on the chart.
5 is 5 ones.
71 + 5 = 76.

Question 18.
Higher Order Thinking Sue had some stickers in a book. She bought 30 more stickers. Now she has 36 stickers in her book. How many stickers did Sue have in the book at the start?
_____ stickers

Answer:
The number of stickers did Sue have in the book at start = 6.

Explanation:
In the above-given question,
given that,
Sue had some stickers in a book.
She bought 30 more stickers.
Now she has 36 stickers in her book.
36 – 30 = 6.
so the number of stickers did Sue have in the book at start = 6.

Problem Solving

Use the hundred chart to solve each problem below.

Question 19.
Use Tools Some hens lay 40 eggs. Then they lay 45 more eggs. How many eggs did the hens lay in all?
___ eggs

Answer:
The number of eggs did the hens lay in all = 85.

Explanation:
In the above-given question,
given that,
Some hens lay 40 eggs.
Then they lay 45 more eggs.
40 + 45 = 85.
so the number of eggs did the hens lay in all = 85.

Question 20.
Use Tools 22 students are at the book fair. More students came to the book fair later. There are 72 students in all at the book fair. How many students came later?
____ students

Answer:
The number of students who came later = 52.

Explanation:
In the above-given question,
given that,
22 students are at the book fair.
More students came to the book fair later.
There are 72 students in all at the book fair.
72 – 22 = 52.
so the number of students who came later = 52.

Question 21.
Higher Order Thinking Write a number story for 3 + 42.

Answer:
3 + 42 = 45.

Explanation:
In the above-given question,
given that,
3 + 42 = 45.
42 + 1 = 43.
43 + 1 = 44.
44 + 1 = 45.
3 + 42 = 45.

Question 22.
Assessment Practice Use the hundred chart. Which equations show the correct sum for 50 + 8? Choose two that apply.
8 + 50 = 85
50 + 8 = 13
8 + 50 = 58
50 + 8 = 58

Answer:
Options B and D are correct.

Explanation:
In the above-given question,
given that,
50 + 8 = 58.
8 + 50 = 58.
so options B and D are correct.

Lesson 10.4 Add Tens and Ones Using an Open Number LineName

Solve & Share

Use the open number lines to find the sums.
43 + 6 = ? 5+ 19 = ? 10+ 32 = ?

Visual Learning Bridge

Convince Me!
Think about the problem 20 + 17. Would it be easier to start with 20 or 17 on the number line to solve the problem?

Guided Practice
Add using the number lines.

Question 1.

Answer:
37 + 30 = 67.

Explanation:
In the above-given question,
given that,
add the numbers.
37 + 30 = 67.
37 + 10 = 47.
47 + 10 = 57.
57 + 10 = 67.

Question 2.

Answer:
26 + 50 = 76.

Explanation:
In the above-given question,
given that,
add the numbers.
26 + 50 = 76.
26 + 10 = 36.
36 + 10 = 46.
46 + 10 = 56.
56 + 10 = 66.
66 + 10 = 76.

Question 3.

11 + 8 = ___

Answer:
11 + 8 = 19.

Explanation:
In the above-given question,
given that,
11 + 8 = 19.
11 + 1 = 12.
12 + 1 = 13.
13 + 1 = 14.
14 + 1 = 15.
15 + 1 = 16.
16 + 1 = 17.
17 + 1 = 18.
18 + 1 = 19.

Question 4.

40 + 16 = ___

Answer:
40 + 16 = 56.

Explanation:
In the above-given question,
given that,
40 + 16 = 56.
40 + 10 = 50.
50 + 1 = 51.
51 + 1 = 52.
52 + 1 = 53.
53 + 1 = 54.
54 + 1 = 55.
55 + 1 = 56.

Question 5.

48 + 20 = ___

Answer:
48 + 20 = 68.

Explanation:
In the above-given question,
given that,
48 + 20 = 68.
48 + 10 = 58.
58 + 10 = 68.
so 48 + 20 = 68.

Question 6.

22 + 7 = ___

Answer:
22 + 7 = 9.

Explanation:
In the above-given question,
given that,
22 + 7 = 29.
22 + 1 = 23.
23 + 1 = 24.
24 + 1 = 25.
25 + 1 = 26.
26 + 1 = 27.
27 + 1 = 28.
28 + 1 = 29.

Question 7.
Higher Order Thinking Write an addition equation using a two-digit and one-digit number. Then solve by showing your work on the number line.

Answer:
10 + 10 = 20.

Explanation:
In the above-given question,
given that,
10 + 10 = 20.
1 + 1 = 2.
2 + 1 = 3.
3 + 1 = 4.
4 + 1 = 5.
5 + 1 = 6.
6 + 1 = 7.
7 + 1 = 8.
8 + 1 = 9.
9 + 1 = 10.
10 + 10 = 20.

Problem Solving

Solve the problems below.

Question 8.
Use Tools Danny writes 20 pages of his paper on Monday. He writes 32 pages on Tuesday. How many pages did Danny write in all? Use the number line to solve.

20 + 32 = ___ ___ pages

Answer:
The number of pages did Danny write in all = 52.

Explanation:
In the above-given question,
given that,
Danny writes 20 pages of his paper on Monday.
He writes 32 pages on Tuesday.
20 + 32 = 52.
so the number of pages did Danny write in all = 52.

Question 9.
Use Tools Last year, Leah watched 41 movies. This year, she has watched 30 movies. How many movies has Leah watched in all? Use the number line to solve.

41 + 30 = ___ ___ movies.

Answer:
The number of movies has Leah watched in all = 71.

Explanation:
In the above-given question,
given that,
Last year, Leah watched 41 movies.
this year, she has watched 30 movies.
41 + 30 = 71.
so the number of movies has Leah watched in all = 71.

Question 10.
Higher Order Thinking Explain how you would solve 57 + 7 on a number line.

Answer:
57 + 7 = 64.

Explanation:
In the above-given question,
given that,
57 + 7 = 64.
57 + 1 = 58.
58 + 1 = 59.
59 + 1 = 60.
60 + 1 = 61.
61 + 1 = 62.
62 + 1 = 63.
63 + 1 = 64.

Question 11.
Assessment Practice
Add 60 + 26 on a number line. Show your work.

60 + 26 = ___

Answer:
60 + 26 = 86.

Explanation:
In the above-given question,
given that,
26 + 10 = 36.
36 + 10 = 46.
46 + 10 = 56.
56 + 10 = 66.
66 + 10 = 76.
76 + 10 = 86.

Lesson 10.5 Add Tens and Ones Using Models

Solve & Share

Maddy has 50 stickers. Jill gives Maddy 5 more stickers. Use place-value blocks to show how many stickers Maddy has now. Then use numbers and pictures to show your work.

Answer:
The number of stickers Maddy has now = 60.

Explanation:
In the above-given question,
given that,
Maddy has 50 stickers.
Jill gives Maddy 5 more stickers.
50 + 5 = 60.
so the number of stickers Maddy has now = 60.

Visual Learning Bridge

Convince Me!
Could you count on by 10s to add 21 + 20?

Answer:
21 + 20 = 41.

Explanation:
In the above-given question,
given that,
21 + 20 = 41.
21 + 10 = 31.
31 + 10 = 41.

Guided Practice
Use blocks to add. Then draw what you did.

Question 1.

Answer:
24 + 4 = 28.

Explanation:
In the above-given question,
given that,
24 + 4 = 28.
24 + 1 = 25.
25 + 1 = 26.
26 + 1 = 27.
27 + 1 = 28.

Question 2.
16 + 30 = __

Answer:
16 + 30 = 46.

Explanation:
In the above-given question,
given that,
16 + 30 = 46.
16 + 10 = 26.
26 + 10 = 36.
36 + 10 = 46.

Question 3.
32 + 20 = ___

Answer:
32 + 20 = 52.

Explanation:
In the above-given question,
given that,
32 + 20 = 52.
32 + 10 = 42.
42 + 10 = 52.
32 + 20 = 52.

Question 4.
33 + 6 = ___

Answer:
33 + 6 = 39.

Explanation:
In the above-given question,
given that,
33 + 6 = 39.
33 + 1 = 34.
34 + 1 = 35.
35 + 1 = 36.
36 + 1 = 37.
37 + 1 = 38.
38 + 1 = 39.

Independent Practice

Add. Draw blocks to show your work.

Question 5.
37 + 2 = ___

Answer:
37 + 2 = 39.

Explanation:
In the above-given question,
given that,
37 + 2 = 39.
37 + 1 = 38.
38 + 1 = 39.
so 37 + 2 = 39.

Question 6.
21 + 40 = ___

Answer:
21 + 40 = 61.

Explanation:
In the above-given question,
given that,
21 + 40 = 61.
21 + 10 = 31.
31 + 10 = 41.
41 + 10 = 51.
51 + 10 = 61.

Question 7.
42 + 10 = ___

Answer:
42 + 10 = 52.

Explanation:
In the above-given question,
given that,
42 + 10 = 52.
42 + 1 = 43.
43 + 1 = 44.
44 + 1 = 45.
45 + 1 = 46.
46 + 1 = 47.
47 + 1 = 48.
48 + 1 = 49.
49 + 1 = 50.
50 + 1 = 51.
51 + 1 = 52.

Question 8.
4 + 33 = ___

Answer:
4 + 33 = 37.

Explanation:
In the above-given question,
given that,
33 + 4 = 37.
33 + 1 = 34.
34 + 1 = 35.
35 + 1 = 36.
36 + 1 = 37.

Question 9.
50 + 14 = ___

Answer:
50 + 14 = 64.

Explanation:
In the above-given question,
given that,
14 + 50 = 64.
14 + 10 = 24.
24 + 10 = 34.
34 + 10 = 44.
44 + 10 = 54.
54 + 10 = 64.

Look for a pattern to help you find the missing numbers.

Question 10.
Algebra Write the missing numbers. Then write the last addition problem in the pattern.

Answer:
40 + 5 = 45.
40 + 6 = 46.
40 + 7 = 47.
40 + 8 = 48.
40 + 9 = 49.

Explanation:
In the above-given question,
given that,
40 + 5 = 45.
45 + 1 = 46.
46 + 1 = 47.
47 + 1 = 48.
48 + 1 = 49.

Problem Solving

Write an equation to solve each problem below. Use blocks to help if needed.

Question 11.
Model Jamal has 32 coins in his piggy bank. Jamal’s dad gives him 4 more coins. How many coins does Jamal have now?
___ + ___ = ___
__ coins

Answer:
The number of coins did Jamal has now = 36.

Explanation:
In the above-given question,
given that,
Jamal has 32 coins in his piggy bank.
Jamal’s dad gives him 4 more coins.
32 + 4 = 36.
so the number of coins did Jamal have now = 36.

Question 12.
Model Julie sells 18 muffins on Monday. She sells 20 muffins on Friday. How many muffins did Julie sell in all?
___ + __ = ___
___ muffins

Answer:
The number of muffins did Julie sell in all = 38.

Explanation:
In the above-given question,
given that,
Julie sells 18 muffins on Monday.
She sells 20 muffins on Friday.
18 + 20 = 38.
so the number of muffins did Julie sell in all = 38.

Question 13.
Higher Order Thinking Jake has 9 marbles. He gets some more marbles. Now Jake has 79 marbles. How many marbles did Jake get? Draw a picture to solve.

Answer:
The number of marbles did Jake get = 70.

Explanation:
In the above-given question,
given that,
Jake has 9 marbles.
He gets some more marbles.
Now Jake has 79 marbles.
79 – 9 = 70.
so the number of marbles did Jake get = 70.

Question 14.
Assessment Practice Which is the sum for 40 + 37?
A 47
B 57
C 67
D 77

Answer:
Option D is correct.

Explanation:
In the above-given question,
given that,
40 + 37 = 57.
37 + 10 = 47.
47 + 10 = 57.
57 + 10 = 67.
67 + 10 = 77.
so option D is correct.

Lesson 10.6 Make a Ten to Add

Solve & Share

What strategy can you use to find 8 + 5?
How can you use the sum for 8 + 5 to help you find 28 + 5? Show your work and be ready to explain your thinking.

Visual Learning Bridge

Convince Me!
When you add two numbers, how do you know if you can make a 10?

Guided Practice
Draw blocks and make a 10 to add.

Question 1.
Find 37 + 7.

Answer:
37 + 7 = 44.

Explanation:
In the above-given question,
given that,
37 + 3 = 40.
7 = 3 + 4.
40 + 4 = 44.
37 + 7 = 44.

Independent Practice

Draw blocks and make a 10 to add.

Question 2.
17 + 7
Think: 17 + ___ = 20
So, break apart 7 into ___ + ___.
20 + ___ = ___
So, 17 + 7 = ___

Answer:
17 + 7 = 24.

Explanation:
In the above-given question,
given that,
17 + 3 = 20.
7 = 3 + 4.
20 + 4 = 24.
17 + 7 = 24.

Question 3.
38 +4
Think: 38 + ___ = 40
So, break apart 4 into __ + ___
40 + ___ = ___
So, 38 + 4 = __

Answer:
38 + 4 = 42.

Explanation:
In the above-given question,
given that,
38 + 2 = 40.
4 = 2 + 2.
40 + 2 = 42.
38 + 4 = 42.

Question 4.
42 + 8 = ___

Answer:
42 + 8 = 50.

Explanation:
In the above-given question,
given that,
30 + 6 = 36.
6 = 3 + 3.
36 + 3 = 39.
39 + 11 = 50.

Question 5.
29 +5 = ___

Answer:
29 + 5 = 34.

Explanation:
In the above-given question,
given that,
25 + 4 = 29.
4 = 2 + 2.
29 + 2 = 31.
31 + 2 = 34.

Algebra Write each missing number. Use place-value blocks if you need to.

Question 6.
23 + = 32

Answer:
The missing number is 9.

Explanation:
In the above-given question,
given that,
23 + x = 32.
32 – 23 = x.
x = 9.
so the missing number is 9.

Question 7.
35 + = 40

Answer:
35 + 5 = 40.

Explanation:
In the above-given question,
given that,
35 + x = 40.
x = 40 – 35.
x = 5.
so the missing number is 5.

Problem Solving

Solve each problem below.

Question 8.
Model Jamie has 28 cards. His sister gives him 6 more cards. How many cards does Jamie have now? Draw blocks to show your work.
__ cards

Answer:
The number of cards does Jamie has now = 34.

Explanation:
In the above-given question,
given that,
Jamie has 28 cards.
His sister gives him 6 more cards.
28 + 6 = 34.
so the number of cards does Jamie has now = 34.

Question 9.
Model Lisa knits 15 scarves. Then she knits 8 more. How many scarves does Lisa knit in all? Draw blocks to show your work.
cards
___ scarves

Answer:
The number of scarves does Lisa knit in all = 23.

Explanation:
In the above-given question,
given that,
Lisa knits 15 scarves.
Then she knits 8 more.
15 + 8 = 23.
so the number of scarves does Lisa knit in all = 23.

Question 10.
Higher Order Thinking Explain how to find 19 + 6. Use equations to show your thinking.

Answer:
19 + 6 = 25.

Explanation:
In the above-given question,
given that,
19 + 1 = 20.
20 + 1 = 21.
21 + 1 = 22.
22 + 1 = 23.
23 + 1 = 24.
24 + 1 = 25.

Question 11.
Assessment Practice Explain how to use the make a 10 strategy to find 37 + 5.

Answer:
37 + 5 = 42.

Explanation:
In the above-given question,
given that,
37 + 1 = 38.
38 + 1 = 39.
39 + 1 = 40.
40 + 1 = 42.

Lesson 10.7 Add Using Place Value

Solve & Share

Grace is solving 35 + 8. First she adds 35 + 5 = 40. What should she do next to find the answer? Draw a model to explain.

Visual Learning Bridge

Convince Me!
Do you need to make a 10 to add 23 + 15? How do you know?

Guided Practice
Add. Draw blocks to help.

Question 1.
Find 36 + 24.
6 + 4 = 10
30 + 20 = ___
So, 36 + 24 = ___

Answer:
36 + 24 = 60.

Explanation:
In the above-given question,
given that,
6 + 4 = 10.
30 + 20 = 50.
36 + 24 = 60.
50 + 10 = 60.

Question 2.
Find 19 + 25.
9 + 5 = 14
10 + 20 = 30
So, 19 + 25 = ___

Answer:
19 + 25 = 44.

Explanation:
In the above-given question,
given that,
9 + 5 = 14.
10 + 20 = 30.
30 + 14 = 44.
19 + 25 = 44.

Independent Practice

Add. Draw blocks or an open number line to help./

Question 3.
Find 19 + 42.
9 + 2 = ___
10 + 40 = ___
19 + 42 = ___

Answer:
19 + 42 = 61.

Explanation:
In the above-given question,
given that,
9 + 2 = 11.
10 + 40 = 50.
19 + 42 = 61.
50 + 11 = 61.

Question 4.
Find 27 + 25.
7 + 5 = ___
20 + 20 = ___
27 + 25 = ___

Answer:
27 + 25 = 32.

Explanation:
In the above-given question,
given that,
7 + 5 = 12.
20 + 20 = 40.
27 + 25 = 32.

Add. You can draw blocks or an open number line to help.

Question 5.
37 + 33 = ___

Answer:
37 + 33 = 70.

Explanation:
In the above-given question,
given that,
7 + 3 = 10.
30 + 30 = 60.
60 + 10 = 70.
37 + 33 = 70.

Question 6.
28 + 44 = ___

Answer:
28 + 44 = 72.

Explanation:
In the above-given question,
given that,
8 + 4 = 12.
20 + 40 = 60.
60 + 12 = 72.
28 + 44 = 72.

Question 7.
25 + 26 = ___

Answer:
25 + 26 = 51.

Explanation:
In the above-given question,
given that,
5 + 6 = 11.
20 + 20 = 40.
40 + 11 = 51.
25 + 26 = 51.

Question 8.
56 + 33 = ___

Answer:
56 + 33 = 89.

Explanation:
In the above-given question,
given that,
6 + 3 = 9.
50 + 30 = 80.
80 + 9 = 89.
56 + 33 = 89.

Problem Solving

Solve. You can draw blocks or an open number line to help you.

Question 9.
Reasoning Sara mows 15 lawns. Bill mows 12 lawns. How many lawns did they mow in all? Write an addition equation to show the problem.
__ lawns

Answer:
The number of lawns did they mow in all = 27.

Explanation:
In the above-given question,
given that,
Sara mows 15 lawns.
Bill mows 12 lawns.
15 + 12 = 27.
so the number of lawns did they mow in all = 27.

Question 10.
Reasoning Jon reads 24 pages. Then he reads 27 more pages. How many pages does he read in all? Write an addition equation to show the problem.
___ pages

Answer:
The number of pages does he read in all = 51.

Explanation:
In the above-given question,
given that,
Jon reads 24 pages.
Then he reads 27 more pages.
24 + 27 = 51.
so the number of pages does he read in all = 51.

Question 11.
Higher Order Thinking Explain how to find 27 + 15 by adding the tens first. Use equations to show your thinking.

Answer:
27 + 15 = 42.

Explanation:
In the above-given question,
given that,
27 + 15 = 42.
7 + 5 = 12.
20 + 10 = 30.
30 + 12 = 42.

Question 12.
Assessment Practice For which addition equations can you make a 10 to add? Choose two that apply.
12 + 29 = ?
61 +26 = ?
33 + 35 = ?
34 + 18 = ?

Answer:
Option A is correct.

Explanation:
In the above-given question,
given that,
12 + 29 = 41.
9 + 2 = 11.
10 + 20 = 30.
30 + 11 = 41.

Lesson 10.8 Practice Adding Using Strategies

Solve & Share

A puzzle has 59 green pieces and 25 orange pieces. Solve 59 + 25 to find how many pieces in all. Use any of the strategies you have learned.

Answer:
59 + 25 = 84.

Explanation:
In the above-given question,
given that,
9 + 5 = 14.
50 + 20 = 70.
70 + 14 = 84.

Visual Learning Bridge

Convince Me!
Why can you use different strategies to solve the same problem?

Guided Practice

Find each sum. Solve any way you choose. Draw or explain what you did.

Question 1.
37 + 24 = 61

Answer:
37 + 24 = 61.

Explanation:
In the above-given question,
given that,
37 + 24 = 61.
7 + 4 = 11.
30 + 20 = 50.
50 + 11 = 61.
so 37 + 24 = 61.

Question 2.
48 + 10 = ___

Answer:
48 + 10 = 58.

Explanation:
In the above-given question,
given that,
48 + 10 = 58.
8 + 0 = 8.
40 + 10 = 50.
50 + 8 = 58.

Independent Practice

Find each sum. Solve any way you choose. Draw or explain what you did.

Question 3.

Answer:
27 + 9 = 36.

Explanation:
In the above-given question,
given that,
9 + 7 = 16.
20 + 0 = 20.
20 + 16 = 36.

Question 4.

Answer:
50 + 23 = 73.

Explanation:
In the above-given question,
given that,
0 + 3 = 3.
50 + 20 = 70.
70 + 3 = 73.

Question 5.

Answer:
32 + 28 = 60.

Explanation:
In the above-given question,
given that,
32 + 28 = 60.
8 + 2 = 10.
30 + 20 = 50.
50 + 10 = 60.
32 + 28 = 60.

Question 6.

Answer:
62 + 19 = 81.

Explanation:
In the above-given question,
given that,
62 + 19 = 81.
60 + 10 = 70.
2 + 9 = 11.
70 + 11 = 81.
62 + 19 = 81.

Problem Solving

Find each sum. Solve any way you choose.

Question 7.
Reasoning Lilly makes necklaces. She has 43 blue beads. She has 20 pink beads. How many beads does Lilly have in all?
___ beads

Answer:
The number of beads does Lilly has in all = 63.

Explanation:
In the above-given question,
given that,
Lilly makes necklaces.
She has 43 blue beads.
she has 20 pink beads.
43 + 20 = 63.
so  the number of beads does Lilly have in all = 63.

Question 8.
Reasoning Jay has a hat collection. He has 27 hats from football teams. He has 33 hats from baseball teams. How many hats does Jay have in all?
___ hats

Answer:
The number of hats does Jay has in all = 60.

Explanation:
In the above-given question,
given that,
Jay has a hat collection.
He has 27 hats from football teams.
He has 33 hats from baseball teams.
27 + 33 = 60.
so the number of hats does Jay has in all = 60.

Question 9.
Higher Order Thinking Connie’s soccer team has a bake sale. The team sells 18 banana muffins and 24 oat muffins. They sell 12 granola bars. How many muffins did Connie’s team sell? Draw a picture and write an equation to show your work.
___ muffins

Answer:
The number of muffins did Connie’s team sell = 54 muffins.

Explanation:
In the above-given question,
given that,
Connie’s soccer team has a bake sale.
The team sells 18 banana muffins and 24 oat muffins.
They sell 12 granola bars.
18 + 24 + 12.
18 + 24 = 42.
42 + 12 = 54.
so the number of muffins did Connie’s team sell = 54 muffins.

Question 10.
Assessment Practice Garret uses place-value blocks to show 53 + 18. Which of the following model this problem? Choose two that apply.

Answer:
Option B is correct.

Explanation:
In the above-given question,
given that,
53 + 18 = 71.
3 + 8 = 11.
50 + 10 = 60.
60 + 11 = 71.
so option B is correct.

Lesson 10.9 Model with Math

Solve & Share
Pam has 13 buttons. Julie gives her some more. Now Pam as 30 buttons. Use blocks or a number line to figure out how many buttons Julie gave Pam.

Thinking Habits
How can I use numbers and symbols to solve this problem? How can I use the math I know to show this problem?

Visual Learning Bridge

Convince Me!
If Miko has 23 green marbles and 30 blue marbles, how many marbles does he have in all? Draw a picture to solve the problem.

Guided Practice
Use drawings to show and solve the problem. Then write the equation.

Question 1.
Ellen has 27 stickers. Her brother gives her 26 stickers. How many stickers does Ellen have in all?
___ + ___= ___

Answer:
27 + 26 = 53.

Explanation:
In the above-given question,
given that,
Ellen has 27 stickers.
Her brother gives her 26 stickers.
27 + 26 = 53.

Independent Practice

Use drawings to show and solve the problem. Then write the equation.

Question 2.
Barry has 12 red cars. He has 14 blue cars. How many cars does Barry have in all?
___ + ___ = ___ cars

Answer:
The number of cars does Barry have in all = 26.

Explanation:
In the above-given question,
given that,
Barry has 12 red cars.
He has 14 blue cars.
12 + 14 = 26.
so the number of cars does Barry have in all = 26.

Question 3.
Amy picks 18 roses. Roger picks 36 tulips. How many flowers do Amy and Roger pick in all?
___ + ___ = ___ flowers

Answer:
The number of flowers do Amy and Roger pick in all = 54.

Explanation:
In the above-given question,
given that,
Amy picks 18 roses.
Roger picks 36 tulips.
18 + 36 = 54.
so the number of flowers do Amy and Roger pick in all = 54.

Question 4.
There are 16 apples in the bowl. George buys 15 more apples. How many apples are there in all?
__ + ___ = __ apples

Answer:
The number of apples is there in all = 31.

Explanation:
In the above-given question,
given that,
There are 16 apples in the bowl.
George buys 15 more apples.
16 + 15 = 31.
so the number of apples are there in all = 31.

Problem Solving

Performance Task

Stamp Collection
Manuel, Matt, and Jessica each have their own stamp collection.

Question 5.
Model Manuel has 18 stamps. Matt gives Manuel 30 stamps. Now, how many stamps does Manuel have in all? Draw a picture to show the problem.

Answer:
The number of stamps does Manuel has in all = 48.

Explanation:
In the above-given question,
given that,
Manuel has 18 stamps.
Matt gives Manuel 30 stamps.
18 + 30 = 48.
so the number of stamps does Manuel has in all = 48.

Question 6.
Model Write an equation that matches the story.

Answer:
The number of stamps does Manuel has in all = 48.

Explanation:
In the above-given question,
given that,
Manuel has 18 stamps.
Matt gives Manuel 30 stamps.
18 + 30 = 48.
so the number of stamps does Manuel has in all = 48.

Question 7.
Explain Matt has 24 red stamps. He asks Jessica for enough red stamps to make 50 red stamps. Jessica gives him 25 red stamps. Did Jessica give Matt enough red stamps? Explain how you know using words or pictures.

Can you make a 10? Why or why not.

Answer:
Jessica did not give Matt enough red stamps.

Explanation:
In the above-given question,
given that,
Matt has 24 red stamps.
He asks Jessica for enough red stamps to make 50 red stamps.
Jessica gives him 25 red stamps.
24 + 26 = 50.
no, Jessica did not give Matt enough red stamps.

Topic 10 Fluency Practice

Color these sums and differences. Leave the rest white.

Topic 10 Vocabulary Review

Understand Vocabulary

Question 1.
Use the models to add the tens.

___ tens + ___ tens = ___ tens

Answer:
3 tens + 2 tens = 50.

Explanation:
In the above-given question,
given that,
3 tens = 30.
2 tens = 20.
30 + 20 = 50.

Question 2.
Use the models to add the tens.

___ tens + ___ tens = ___ tens

Answer:
2 tens + 4 tens = 6 tens.

Explanation:
In the above-given question,
given that,
2 tens + 4 tens.
2 tens = 20.
4 tens = 40.
20 + 40 = 60.

Question 3.
Find 19 + 12.
Add the ones. 9 + 2 = ___
Then add the tens. 10 + 10 = ___
Draw blocks to help. 19 + 12 = ___

Answer:
19 + 12 = 31.

Explanation:
In the above-given question,
given that,
9 + 2 = 11.
10 + 10 = 20.
19 + 12 = 31.

Use Vocabulary in Writing

Question 4.
Solve 20 + 6 using an open number line. Explain how you solved it using terms from the Word List.

Answer:
20 + 6 = 26.

Explanation:
In the above-given question,
given that,
20 + 1 = 21.
21 + 1 = 22.
22 + 1 = 23.
23 + 1 = 24.
24 + 1 = 25.
25 + 1 = 26.

Topic 10 Reteaching

Set A

You can add groups of 10.

Write the numbers to complete each equation.

Question 1.

Answer:
4 tens + 1 ten = 5 tens.

Explanation:
In the above-given question,
given that,
4 tens + 1 ten = 5 tens.
4 tens = 40.
1 tens = 10.
40 + 10 = 50.

Question 2.

Answer:
3 tens + 3 ten = 6 tens.

Explanation:
In the above-given question,
given that,
3 tens + 3 tens = 6 tens.
3 tens = 30.
3 tens = 30.
30 + 30 = 60.

Set B

You can also use mental math to add 10. When you add 10, the tens digit goes up by 1. The ones digit stays the same.

Answer:
2 tens + 1 ten = 3 tens.
3 tens + 4 ones = 34.

Explanation:
In the above-given question,
given that,
2 tens + 1 ten = 3 tens.
3 tens = 30.
4 ones = 4.
30 + 4 = 34.

Use mental math to solve the problems below.

Question 3.
36 + 10 = ___

Answer:
36 + 10 = 46.

Explanation:
In the above-given question,
given that,
6 + 0 = 6.
30 + 10 = 40.
40 + 6 = 46.

Question 4.
53 + 10 = ___

Answer:
53 + 10 = 63.

Explanation:
In the above-given question,
given that,
3 + 0 = 3.
50 + 10 = 60.
60 + 3 = 63.
so 53 + 10 = 63.

Question 5.
71 + 10 = ___

Answer:
71 + 10 = 81.

Explanation:
In the above-given question,
given that,
1 + 0 = 1.
70 + 10 = 80.
80 + 1 = 81.
so 71 + 10 = 81.

Set C

You can use part of a hundred chart to add tens and ones.
3+ 40 = ?

Use the part of the hundred chart to add tens and ones.

Question 6.
4 + 50 = ___

Answer:
4 + 50 = 54.

Explanation:
In the above-given question,
given that,
4 + 0 = 4.
50 + 0 = 50.
50 + 4 = 54.

Question 7.
8 + 30 = ___

Answer:
8 + 30 = 38.

Explanation:
In the above-given question,
given that,
8 + 0 = 8.
30 + 0 = 30.
30 + 8 = 38.

Set D

You can use an open number line to add.

Use an open number line to add.

Question 8.

11 + 6 = ___

Answer:
11 + 6 = 17.

Explanation:
In the above-given question,
given that,
10 + 7 = 17.
11 + 6 = 17.

Set E

You can use blocks to add tens to a number.

Add the tens and the ones. Use blocks to help you.

Question 9.
44 + 30 = ___

Answer:
4 + 0 = 4.

Explanation:
In the above-given question,
given that,
40 + 30 = 70.
4 tens = 40.
3 tens = 30.
40 + 30 = 70.

Question 10.
20 + 5 = ___

Answer:
20 + 5 = 25.

Explanation:
In the above-given question,
given that,
0 + 5 = 5.
20 + 0 = 20.
20 + 5 = 25.

Question 11.
30 + 28 = ___

Answer:
30 + 28 = 58.

Explanation:
In the above-given question,
given that,
0 + 8 = 8.
30 + 20 = 50.
50 + 8 = 58.
30 + 28 = 58.

Question 12.
19 + 60 = ___

Answer:
19 + 60 = 79.

Explanation:
In the above-given question,
given that,
9 + 0 = 9.
10 + 60 = 70.
70 + 9 = 79.
19 + 60 = 79.

Set F

Sometimes you can make 10 when you add.

Draw blocks and make a 10 to add.

Question 13.
33 + 9

Think: 33 + __ = 40
So, break apart 9 into ___ + ___.
40 + __ = ___
So, 33 + 9 = ___

Answer:
33 + 9 = 42.

Explanation:
In the above-given question,
given that,
33 + 7 = 40.
9 = 5 + 4.
33 + 9 = 42.

Set G

You can draw blocks to help you add. First add the ones. Then add the tens.

There are 4 tens and 3 ones. 24 + 19 = 43

Add. Draw blocks to help.

Question 14.
Find 67 + 16.
7 + 6 = ___
60 + 10 = ___
67 + 16 = ___

Answer:
67 + 16 = 83.

Explanation:
In the above-given question,
given that,
7 + 6 = 13.
60 + 10 = 70.
67 + 16 = 83.

Set H

Thinking Habits
Model with Math

Can I use a drawing, diagram, table, or graph to model the problem? Can I write an equation to show the problem?

Use drawings to show and solve the problem. Then write the equation.

Question 15.
Sally sees 15 birds. Then she sees 17 more. How many birds did Sally see in all?
___ + ___ = ___

Answer:
The number of birds did Sally see in all = 32.

Explanation:
In the above-given question,
given that,
Sally sees 15 birds.
Then she sees 17 more.
15 + 17 = 32.
so the number of birds did Sally see in all = 32.

Topic 10 Assessment Practice

Question 1.
Write an equation that matches the place-value blocks below.

Answer:
5 tens + 8 ones = 58.

Explanation:
In the above-given question,
given that,
5 tens = 50.
8 ones = 8.
5 tens + 8 ones = 58.

Question 2.
Find the sum. Draw place-value blocks to show how you found it. 50 + 3 = ___

Answer:
50 + 3 = 53.

Explanation:
In the above-given question,
given that,
0 + 3 = 3.
5 tens = 5 tens.
3 ones = 3.
5 tens + 3 ones = 53.

Question 3.
Find the sum of 16 and 18.
Use words, pictures, or a model to solve. Write the equation.

Answer:
16 + 18 = 34.

Explanation:
In the above-given question,
given that,
16 + 18 = 34.
6 + 8 = 14.
10 + 10 = 20.
20 + 14 = 34.
16 + 18 = 34.

Question 4.
Which equation matches the place-value blocks shown below? Choose two that apply.

Answer:
60 + 30 = 90
6 tens + 3 tens = 9 tens
60 + 10 = 70
4 tens + 3 tens = 7 tens
6 tens + 3 ones = 9 ones

Answer:
Options A and B are correct.

Explanation:
In the above-given question,
given that,
60 + 30 = 90.
6 tens + 3 tens = 9 tens.
so options A and B are correct.

Question 5.
Find the sum of 18 and 11. Explain how you solved the problem. Did you need to make a 10?

Answer:
The sum of 18 and 11 = 29.

Explanation:
In the above-given question,
given that,
18 + 11 = 29.
10 + 10 = 20.
8 + 1 = 9.
20 + 9 = 29.
so the sum of 18 and 11 = 29.

Question 6.
Solve the problem.
Use place-value blocks if needed. 28 + 13 = Can you make a 10? Explain.
Circle Yes or No.

Answer:
28 + 13 = 41.

Explanation:
In the above-given question,
given that,
28 + 13 = 41.
20 + 10 = 30.
8 + 3 = 11.
28 + 13 = 41.

Question 7.
Use the part of the hundred chart to add. Choose the possible explanation for how to find 46 + 20.

A. I start at 46 and then move two rows up to get 26. So, 46 + 20 = 26.
B. I start at 46 and then move one row down and four columns to the right to get 60. So, 46 + 20 = 60.
C. I start at 46 and then move two rows down to get 66. So, 46 + 20 = 66.
D. I start at 46 and then move two rows down to get 68. So, 46 + 20 = 68.

Answer:
Option C is correct.

Explanation:
In the above-given question,
given that,
46 + 20 = 66.
I start at 46 and then move two rows down to get 66.
46 + 20 = 66.
so option C is correct.

Use the part of the hundred chart to solve each problem. What is one way to explain your answer?

Question 8.
10 + 27 = ?
A. 17; I started at 27 and subtracted 1 ten.
B. 28; I started at 27 and added 1 ten.
C. 37; I started at 27 and added 1 ten.
D. 40; I started at 10 and added 3 tens.

Answer:
Option C is correct.

Explanation:
In the above-given question,
given that,
10 + 27 = 37.
I started at 27 and added 1 ten.
27 + 10 = 37.
so option C is correct.

Question 9.
4 + 35 = ?
A. 95; I started at 35 and added 4 tens.
B. 39; I started at 35 and added 4 ones.
C. 31; I started at 35 and subtracted 4 ones.
D. 12; I started at 32 and subtracted 2 tens.

Answer:
Option B is correct.

Explanation:
In the above-given question,
given that,
4 + 35 = 39.
I started at 35.
added the 4 ones to 35.
35 + 4 = 39.

Use mental math to solve. Then explain how you found your answer.

Question 10.
53 + 10 = ___

Answer:
53 + 10 = 63.

Explanation:
In the above-given question,
given that,
3 + 0 = 3.
50 + 10 = 60.
60 + 3 = 63.
53 + 10 = 63.

Question 11.
48 + 10 = ___

Answer:
48 + 10 = 58.

Explanation:
In the above-given question,
given that,
48 + 10 = 58.
40 + 10 = 50.
8 + 0 = 8.
50 + 8 = 58.
48 + 10 = 58.

Question 12.
64 + 10 = ___

Answer:
64 + 10 = 74.

Explanation:
In the above-given question,
given that,
64 + 10 = 74.
4 + 0 = 4.
60 + 10 = 70.
70 + 4 = 74.

Find the correct number to complete each equation.

Question 13.
20 + 70 = ___

Answer:
20 + 70 = 90.

Explanation:
In the above-given question,
given that,
2 tens + 7 tens.
2 tens = 20.
7 tens = 70.
20 + 70 = 90.

Question 14.
30 + ___ = 60

Answer:
30 + 30 = 60.

Explanation:
In the above-given question,
given that,
3 tens =30.
3 tens =30

30 + 30 = 60.

Question 15.
__ + 20 = 40

Answer:
20 + 20 =40.

Explanation:
In the above-given question,
given that,
2 tens = 20.
2 tens =20.

20 + 20 = 40.

Question 16.
Use the open number line to find 40 + 23. Show your work.

Answer:
40 + 23 = 63.

Explanation:
In the above-given question,
given that,
23 + 10 = 33.
33 + 10 = 43.
43 + 10 = 53.
53 + 10 = 63.

Question 17.
Find 43 + 8. Do the models correctly show the sum? Explain how you know.

Answer:
43 + 8 = 51.

Explanation:
In the above-given question,
given that,
8 + 3 = 11.
40 + 0 = 40.
40 + 11 = 51.
43 + 8 = 51.

Solve each problem. Can you make a 10? Use place-value blocks if needed.

Answer:
42 + 37 = 79.
16 + 35 = 51.
14 + 16 = 30.

Explanation:
In the above-given question,
given that,
40 + 2 = 42.
30 + 7 = 37.
42 + 37 = 79.

10 + 6 = 16.
30 + 5 = 35.
16 + 35 = 51.

10 + 4 = 14.
10 + 6 = 16.
14 + 16 = 30.

Pet Survey

Maria asked other students what kind of pet they have. She made this chart.

Question 1.
How many Fish and Cats in all? Use the open number line to solve.

___ fish and cats

Answer:
The number of fish and cats = 57.

Explanation:
In the above-given question,
given that,
there are 27 fish in the chart.
there are 30 cats in the chart.
27 + 30 = 57.
so the number of fish and cats = 57.

Question 2.
How many Dogs and Birds in all? Use the hundred chart to add.

__ + __ = ___
__ dogs and birds

Answer:
The number of dogs and birds = 47.

Explanation:
In the above-given question,
given that,
there are 8 birds in the chart.
there are 39 dogs in the chart.
8 + 39 = 47.
so the number of dogs and birds = 47.

Question 3.
Maria asks 18 students about their pets on Monday. She asks 17 students about their pets on Tuesday. How many students did she ask on both days?
Use place-value blocks to solve. Draw the blocks you used.

Did you need to make a 10 when you added the ones? Explain your answer.

Answer:
The number of students did she ask on both days = 35.

Explanation:
In the above-given question,
given that,
Maria asks 18 students about their pets on Monday.
She asks 17 students about their pets on Tuesday.
18 + 17 = 35.
so the number of students did she ask on both days = 35.

Question 4.
Maria adds other pets to her chart. 19 students in first grade have a rabbit. 24 students in second grade have a rabbit. How many students in all have rabbits?
Part A
Draw blocks to help you solve the problem.
Part B
Write an equation that matches the story.

Answer:
The number of students in all has rabbits = 43.

Explanation:
In the above-given question,
given that,
Maria adds other pets to her chart.
19 students in first grade have a rabbit.
24 students in second grade have a rabbit.
19 + 24 = 43.
so the number of students in all has rabbits = 43.

Go through the enVision Math Common Core Grade 3 Answer Key Topic 12 Understand Fractions as Numbers regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 12 Understand Fractions as Numbers

Essential Question:
What are different interpretations of a fraction?
Answer:
There are five different interpretations of fractions.
Explanation:
 Fractions as parts of wholes or parts of sets.
Fractions as the result of dividing two numbers.
Fractions as the ratio of two quantities.
Fractions as operators.
Fractions as measures. 

EnVision STEM Project: Fossils and Environment
Do Research Use the Internet or other sources to find out more about what fossils tell us about past environments. Research and make a booklet of fossils found in your state. Find at least 5 fossils and use one page for each fossil. Include where each fossil was found and what type of environment each location is now.

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

• List the types of food each of the 5 creatures ate when they were alive.
• Explain whether each of the 5 creatures on your list could live in today’s environment.
• Find the lengths of different fossils to the nearest half inch. Record the lengths in a line plot.

Review What You Know

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

• halves
• thirds
• inch
• yard

Question 1.
If a shape is divided into 2 equal parts, the parts can be called _________.
Answer:
Halves

Question 2.
The width of an adult’s thumb is about 1 _________.
Answer:
Inch

Question 3.
If a shape is divided into 3 equal parts, the parts can be called _________.
Answer:
Thirds

Skip Counting on the Number Line

Skip count on the number line. Write the missing numbers.
Question 4.

Answer:
125, 130, 135, 140, 145, 150, 155
Explanation:
Add 5 to each number present on number line.
110 + 5 = 115
115 + 5 = 120
120 + 5 = 125
125 + 5 = 130
130 + 5 = 135
135 + 5 = 140
140 + 5 = 145
145 + 5 = 150
150 + 5 = 155

Question 5.

Answer:
240, 260
Explanation:
Add 20 to each number present on number line
180 + 20 = 200
200 + 20 = 220
220 + 20 = 240
240 + 20 = 260

Equal Parts

Question 6.
Circle the shapes that show halves.

Answer:

Question 7.
Circle the shapes that show fourths.
Answer:

Measurement

Question 8.
How long is the nail to the nearest inch? Explain how you know.

Answer :
2 inches
Explanation :
The nail is in between the 1.5 marks and 2 inch mark
so the nearest inch the nail is 2 inches

Pick a Project

PROJECT 12A
How long would it take to drive across the Florida Keys?
Project: Make a Map

Answer:

The Florida Keys Overseas Highway is 113 miles in length, joining the mainland of Florida (starting in Florida City, just south of Homestead) to Key West. If you drove directly from Key Largo to Key West, it would take you roughly 2.5 hours, traveling distance of 100 miles.

PROJECT 12B
Why are there so many different floors in a building?
Project: Create a flooring design

Answer:
A floor is the bottom surface of a room or vehicle. Floors vary from simple dirt in a cave to many-layered surfaces made with modern technology. Floors may be stone, wood, bamboo, metal or any other material that can support the expected load. The levels of a building are often referred to as floors, although a more proper term is storey.

PROJECT 12C
What is the most common hat size?
Project: Collect Hat Size Data and Create a Line Plot

Answer:
Head sizes and shapes differ from region to region. The most common male size is 7-5/8 and the average hat size for females 7-2/8

PROJECT 12D
What are the most popular fruits and vegetables?
Project: Draw a Garden Plot

Answer:
The most popular fruits and vegetables are,
Fruits like Mango ,Banana ,Apple, Grapes, Water melon.. so on
Vegetables like Carrot, Potato, Tomato, Brinjal … So on

Lesson 12.1 Partition Regions into Equal Parts

Solve & Share
Show two different ways to divide a 2 x 6 region into 6 equal parts. How do you know the parts are equal?
I can … read and write a unit fraction.

Look Back! How are the parts of the regions alike? How are they different?

Essential Question
How Can You Name the Equal Parts of a Whole?
Answer:
Each equal part of a whole is called one-half.
Explanation:
One half is expressed as 1/2 and read as one over two or one upon two.

Visual Learning Bridge
You can divide a whole into equal parts. What fraction can you write to represent one of these equal parts?
A fraction is a part of a whole.
Divide each green whole into four equal parts.

Divide each green whole into six equal parts.

In the green wholes:

• All parts have an equal area.
• Each part is one sixth of the area of the whole.
• One sixth can be written as the fraction \(\frac{1}{6}\).

Convince Me! Critique Reasoning Kim says that the figure at the right is divided into fourths because there are 4 equal parts. Carrie says it is not divided into fourths because the parts are not the same shape. Who is correct? Explain.

Answer:
Carrie is correct.
Explanation:
In the given figure it is not divided into fourths because the parts are not of the same shape.

Guided Practice

Do You Understand?
Question 1.
In the examples in Box A on the previous page, explain how you know the 4 parts are equal.
Answer:
All parts are equal.
Explanation:
All parts have an equal area.
Each part is one-fourth or a quarter of the whole sheet.

In 2 and 3, tell if each shape shows equal or unequal parts. If the parts are equal, label 1 of the parts using a unit fraction.
Question 2.

Answer:
Equal parts
Explanation:
The area and size of each part of the figure are equal so the figure is divided into equal parts.

Question 3.

Answer:
Unequal parts
Explanation:
The area and size of each part of the figure are not equal so the figure is divided into unequal parts.

Do You Know How?
Question 4.
Draw lines to divide the shape into 8 equal parts. Then write the fraction that represents 1 part.

Answer:

1/8 unit fraction
Explanation:
The area and size of each part of the figure must be equal .
Then the figure is divided into equal parts
The total area of the figure is 24
So we need 8 parts
24 ÷ 8 = 3

Independent Practice

In 5-7, tell if each shape shows equal or unequal parts. If the parts are equal, label 1 of the parts using a unit fraction.
Question 5.

Answer:
Unequal parts
Explanation:
The given square has unequal parts, so it is difficult to denote in fraction

Question 6.

Answer:
Equal parts
Explanation:
The area and size of each part of the figure must be equal.
Then the figure is divided into equal parts.

Question 7.

Answer:
Equal parts
Explanation:
The area and size of each part of the figure must be equal.
Then the figure is divided into equal parts.

In 8-10, draw lines to divide the shape into the given number of equal parts. Then write the fraction that represents one part.
Question 8.
6 equal parts

Answer:

Question 9.
3 equal parts

Answer:

Question 10.
4 equal parts

Answer:

Problem Solving

In 11-14, use the table of flags to answer the questions.

Question 11.
What fraction represents the white part of Nigeria’s flag?
Answer:
one third[1/3]

Question 12.
Which nation’s flag is \(\frac{1}{2}\) red?
Answer:
Poland

Question 13.
Higher Order Thinking The flag of this nation has more than 3 equal parts. Which nation is it, and what fraction represents 1 part of its flag?
Answer:
Mauritius has more than 3 equal parts.
One fourth fraction represents 1 part of its flag.

Question 14.
Which nation’s flag is NOT divided into equal parts?
Answer:
Seychelles

Question 15.
Maryann buys 24 cans of soda. The soda comes in packs of 6 cans. How many packs does she purchase? Write a multiplication equation and a division equation to show your answer.
Answer:
4 packs of can soda
Explanation:
Maryann buys 24 cans of soda
1 pack of soda cans consist of 6 cans
so :
24 ÷ 6 = 4
Maryann buys 4 packs of soda cans
6 x 4 = 24

Question 16.
Make Sense and Persevere Jim has stickers in an array of 8 rows and 4 columns. He also has a packet of 14 stickers. How many stickers does Jim have in all?
Answer:
46 stickers
Explanation:
Jim has stickers in an array of 8 rows and 4 columns.
No of stickers in array are:
8 x 4 = 32 stickers
He also has a packet of 14 stickers.
total no of stickers Jim has are:
32 + 14 = 46 stickers

Assessment Practice

Question 17.
Draw lines to show how to divide this square into 8 equal pieces. Then select the fraction that represents 1 of the pieces.

A. \(\frac{1}{2}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{8}\)
Answer:

option D
1/8 unit fracttion

Lesson 12.2 Fractions and Regions

Solve & Share
Pat made a garden in the shape of a rectangle and divided it into 4 equal parts. She planted flowers in 3 of the parts. Draw a picture of what Pat’s garden might look like.
Answer:
Pat’s garden might look like this.

I can… use a fraction to represent multiple copies of a unit fraction.

Look Back! How many parts of Pat’s garden do NOT have flowers? Explain.
Answer:
1/4 part of Pat’s garden do NOT have flowers.
Explanation:
As  she planted only 3/4 of his garden with flowers.

Essential Question
How Can You Show and Name Parts of a Region?
Answer:
Fractions name parts of a whole region.
Explanation:
When an object is divided into a number of equal parts then each part is called a faction.
There are 2 parts that make up a faction:
Numerator: Which is the number that goes on top of the fraction, tells how many parts of the whole.
Denominator: Which is the number that goes on the bottom of the fraction, tells how many equal parts in all.

Visual Learning Bridge
Mr. Peters served part of a pan of enchiladas to a friend. What does each part of the whole pan represent? What part was served? What part is left?

Answer:
Each part of the whole represent fraction.
2/6 part is served.
4/6 part is left.

Convince Me! Be Precise Below is a picture of a pie pan. Draw lines and use shading to show that five \(\frac{1}{8}\)-pieces are still in the pan, and that three \(\frac{1}{8}\)-pieces were eaten. Use a fraction to label the part of the pie that is in the pan.

Answer:
3/8 pie in the pan is eaten.
5/8 pie in the pan is left over.

Guided Practice

Do You Understand?
Question 1.
In the problem in Box A on the previous page, what fraction names all of the pieces in the pan?
Answer:
The whole pan is divided into 6 equal parts. Each part is 1/6 of the whole
Explanation:
6 copies of 1/6 is 6/6.
So the whole is 6/6.
The unit fraction is 1/6.

Question 2.
Mrs. Patel made a cake. What fraction of the whole cake does each piece represent?

Answer:
1/8 fraction of the whole cake represents each piece

Question 3.
In the picture in Exercise 2, how many \(\frac{1}{8}\)-pieces were eaten? What fraction of the whole cake was eaten?
Answer:
2 pieces were eaten.
2/8 pieces were eaten.
Explanation:
In the given picture cake is divided into 8 equal parts.
Out of which 2 pieces were eaten.

Do You Know How?
In 4-6, use the figure below.

Question 4.
How many \(\frac{1}{3}\)-parts are blue?
Answer:
Two
Explanation:
Out of 3 parts in a given picture 2 parts are blue and 1 part is yellow.

Question 5.
What fraction of the whole is blue?
Answer:
Two third
Explanation:
In the given picture 2/3 of the whole is colored with blue

Question 6.
What fraction names all of the parts in the whole?
Answer:
1/3 one thirds

Independent Practice

In 7-10, write the unit fraction that represents each part of the whole. Then write the number of blue parts and the fraction of the whole that is blue.
Question 7.

Answer:
One part is blue
The fraction of whole is 1/2
Explanation:
The given triangle is equally divided into two,
one half colored with blue and the the other with yellow.
So the fraction of whole is 1/2.

Question 8.

Answer:
3 parts are blue
The fraction of whole is 3/6
Explanation:
Given hexagon is equally divided into six equal parts,
out of six, three are colored with blue and three with yellow
So the fraction of hexagon is written as 3/6.

Question 9.

Answer:
2 parts are blue
The fraction of whole is 2/4
Explanation:
Given circle is equally divided into 4 parts,
out of which 2 are colored with blue and 2 with yellow.
So the fraction of circle is written as 2/4.

Question 10.

Answer:
6 parts are blue
The fraction of whole is 6/8
Explanation:
Given picture is equally divided into 8 parts,
Out of which 6 are colored with blue and 2 with yellow.
So the fraction of given picture is written as 6/8.

Question 11.
Draw a rectangle that shows 6 equal parts. Write the unit fraction that represents each part. Then shade \(\frac{2}{6}\) of the rectangle. Explain how you know you shaded \(\frac{2}{6}\) of the rectangle.
Answer:

The unit fraction that represents the part of the rectangle is 116

Problem Solving

Question 12.
Vocabulary Fill in the blanks.
In the fraction \(\frac{4}{7}\), 4 is the ______ and 7 is the ________.
Answer:
4 is the numerator and 7 is denominator

Question 13.
Generalize Divide the grid below into fourths. Shade 3 of the parts. Write a fraction that represents the shaded area. Write a fraction that represents the unshaded area. What can you generalize about your fractions?

Answer:

Question 14.
Christine has 6 red scarves and 3 blue scarves. Each scarf has 2 stripes. How many stripes does Christine have on her scarves? Write equations to represent and solve the problem.
Answer:
Christine has 18 stripes in total on her scarves.
Explanation:
No of red scarves = 6
No of stripes on red scarves = 6 x 2 = 12
No of blue scarves + 3
No of stripes on blue scarves = 3 x 2 = 6
Total no of stripes = 12 + 6 = 18

Question 15.
Higher Order Thinking Draw a circle that shows 6 equal parts. Shade more than \(\frac{3}{6}\) of the circle, but less than \(\frac{5}{6}\) of the circle. What fraction have you shaded?
Answer:

Explanation:
A fraction more than 3/6 is 4/6 and a fraction less than 5/6 is 4/6
so we have to shade 4/6 of the circle

Question 16.
Number Sense What is the area of the baseball card? Show your work.

Answer:
The area of baseball card is 70 cm.
Explanation:
Baseball card is in the shape of rectangle.
So the area of rectangle is length X breadth  ( l x b )
Length = 10 cm
Breadth = 7 cm
Area = length x breadth
= 10 x 7
= 70 cm.

Assessment Practice

Question 17.
Select numbers from the box to write fractions to show 3 parts of each of these vegetable trays.

Answer:

Explanation:
The first plate is divided into 4 parts out of which three parts are removed
The second plate is divided into 6 parts out of which three parts are removed
The third plate is divided into 8 parts out of which three parts are removed

Lesson 12.3 Understand the Whole

Solve & Shar
Mrs. Garcia’s third-grade class is planting a flower garden and a vegetable garden.
Draw a picture of the whole flower garden and the whole vegetable garden based on the parts shown. How did you decide what the whole of each garden looked like?
I can … identify the whole by seeing a part.

Look Back! What do the fractions and tell you about the number of equal parts in the whole?
Answer:
A basic way to interpret a fraction is by dividing a whole object into several equal parts.
The denominator tells how many equal parts the whole is subdivided into.
The numerator tells the number of those parts that are under consideration.

Essential Question
How Can You Use a Fractional Part to Find the Whole?
Answer:
For finding a fraction of a whole number, we multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction.

Visual Learning Bridge
Anya and Novi are running in different races. The diagrams below show how much of their races each runner has completed.
Draw a picture of the whole of each track. Write a fraction to represent the whole.

You can look at the fraction to find how many parts will make up the whole.

You know Anya and Novi have each completed \(\frac{1}{6}\) of their races.
Six lengths of \(\frac{1}{6}\) make \(\frac{6}{6}\), or 1 whole.

Convince Me! Reasoning Why is Novi’s track longer than Anya’s track?
Answer:
Novi’s track is longer than Anya’s track because 1/6th of the track were of different size.

Another Example! The part of a race Rob completed is shown at the right. You can use fractional parts like this to identify the whole.
\(\frac{2}{3}\) is 2 copies of \(\frac{1}{3}\). Divide Rob’s track into 2 equal parts.

Three copies of \(\frac{1}{3}\) make \(\frac{3}{3}\), or 1 whole. Draw one more third.
1 = \(\frac{3}{3}\).

Guided Practice

Do You Understand?
Question 1.
If the distance Anya ran was of the length of the track, what fraction would you use to represent the whole track?
Answer:
The fraction of whole track = 6/6
Explanation:
Six lengths of 1/6 make 6/6 or whole.

Question 2.
What is true about the numerator and denominator of each fraction that represents one whole?
Answer:
A fraction represents a part of a whole.
Explanation:
The numerator represents how many parts of that whole are being considered,
while the denominator represents the total number of parts created from the whole.

Do You Know How?
3. Draw a picture of the whole and write a fraction to represent the whole.

Answer:

Independent Practice

In 4-7, draw a picture of the whole and write a fraction to represent the whole.
Question 4.

Answer:

1 = 3/3

Question 5.

Answer:

1 = 2/2

Question 6.

Answer:
1 = 4/4

Question 7.

Answer:

1 = 6/6

Problem Solving

Question 8.
Ronnie and Gina were shown \(\frac{1}{2}\) of a table. They each drew a picture of the whole table. Whose drawing could be correct? Explain.

Answer:
Gina’s drawing of the whole table is correct
Explanation:
Both Ronnie and Gina were correct.
but tables are generally square , rectangle or circle in shape so Gina’s table is correct

Question 9.
Higher Order Thinking If the part shown in Exercise 8 is \(\frac{1}{4}\) of a table, what could the whole table look like? Draw a picture and write a fraction to represent the whole.
Answer:

One whole

Question 10.
The Florida panther is endangered. In 1970, the population was estimated at 20 panthers. In 2017, the population was estimated at 230 panthers. About how many more panthers were there in 2017 than in 1970?

Answer:
About 210 more panthers were there in 2017 than in 1970.
Explanation:
In 1970, the population was 20 panthers.
In 2017, the population was estimated at 230 panthers.
So 230 – 20 = 210.
Question 11.
Construct Arguments Jenna and Jamal are making rugs. They have finished the parts shown. Draw pictures to show each whole rug. Whose rug will be longer when it is finished? Explain.

Answer:
Jenna: I have finished 1/3 of my rug.
Jamal: I have finished 1/3 of my rug.
Jamal: My rug is bigger than you.
Jenna: How is your rug bigger than mine. Explain?
Jamal: My 1/3 of the rug is bigger than your 1/3 of the rug
Explanation:
Jamal’s 1/3 rd of the rug is bigger than Jenna’s 1/3 of the rug

So Jamal’s rug is longer than Jenna.
Assessment Practice

Question 12.
The picture shows \(\frac{2}{3}\) of a granola bar. Which shows the whole granola bar?

Answer:
Option B

Question 13.
Each part below is \(\frac{1}{2}\) of a different whole. Which is part of the largest whole?

Answer:
Option A

Lesson 12.4 Number Line: Fractions Less Than 1

Solve & Share
At a state park, there is a 1-mile hiking path between the park entrance and the beach. Scenic lookouts are located at points and of the distance from the park entrance to the beach. Show about where the lookout points are located on the line below.
I can… represent fractions on a number line.

Look Back! If you know about where the point for \(\frac{1}{3}\) is located, how can you find about where the point for \(\frac{2}{3}\) is located?
Answer:
The line is divided into 3 parts,
We know 1/3 location on number line.
The point next to 1/3is 2/3, so we know where 2/3 point is located.

Essential Question
How Can You Record Fractions on a Number Line?
Answer:
Fractions expand our number system beyond whole numbers and integers.
Explanation:
Fractions help us to denote any decimal number with higher precision.
Representation of Fractions on the number line is important to understand how fractions represent part of a whole.

Visual Learning Bridge
Mr. Singer is picking up his daughter, Greta, from school to go to soccer practice. Greta’s school is located at \(\frac{3}{4}\) of the distance from the Singers’ house to the soccer field. How can you represent \(\frac{3}{4}\) on a number line?
Every number on a number line represents a distance from 0.

Convince Me! Critique Reasoning Jenna and Benito each marked \(\frac{1}{4}\) on a number line. The length of the part from 0 to \(\frac{1}{4}\) on Jenna’s number line is shorter than on Benito at Benito’s. Did someone make a mistake? Explain your thinking.

Jenna did a mistake by marking unit fraction on a small number line, compared with Benito number line. 
Guided Practice

Do You Understand?
Question 1.
Maliya divides a number line from 0 to 1 into 6 equal lengths. What unit fraction represents each equal length? What should Maliya label the tick mark just to the left of 1? Explain.
Answer:
5/6 unit fraction
Explanation:
0 to 1 is divided in to 6 fractions
Each 1/6 unit fraction

Question 2.
Josh divides a number line from 0 to 1 into 8 equal lengths. What should he label the first tick mark just to the right of 0? Explain.
Answer:
1/8 unit fraction.
Explanation:

Do You Know How?
In 3 and 4, divide the number line into the given number of equal lengths. Then mark and label the given fraction on the number line.
Question 3.
2 equal lengths; \(\frac{1}{2}\)

Answer:

Question 4.
4 equal lengths; \(\frac{2}{4}\)

Answer:

Explanation :
Draw a line and make 3 equal parts on number line and then mark 1/4, 2/4 and 3/4unit fraction.

Leveled Practice In 5 and 6, divide the number line into the given number of equal lengths. Then mark and label the given fraction on the number line.
Question 5.
3 equal lengths; \(\frac{2}{3}\)

Answer:
2/3 unit fraction.

Explanation : Draw a line and make 3 equal parts on number line and then mark 1/3, 2/3 and 3/3 units

Question 6.
6 equal lengths; \(\frac{2}{6}\)

Answer: 2/6

Explanation :
Draw a line and make 6 equal parts on number line and then mark 1/6, 2/6,3/6,4/6,5/6 and 6/6units

In 7 and 8, draw a number line from 0 to 1. Divide the number line into equal lengths for the given fraction. Then mark and label the given fraction on the number line.
Question 7.
\(\frac{4}{6}\)
Answer: 4/6

Explanation :
Draw a line and make 6 equal parts on number line and then mark 1/6, 2/6,3/6,4/6,5/6 and 6/6units

Question 8.
\(\frac{5}{8}\)
Answer: 5/8

Explanation :
Draw a line and make 8 equal parts on number line and then mark 1/8 , 2/8 , 3/8 , 4/8 , 5/8 , 6/8 , 7/8 and 8/8units

Problem Solving

Question 9.
Construct Arguments Terrance and Dana each drew a number line and marked \(\frac{3}{4}\). Did each person represent \(\frac{3}{4}\) in the correct place on his or her line? Explain.

Answer:
yes
Explanation:
Terrance number line is a bit smaller that Dana’s but both the number lines are divided into equal parts.

Question 10.
A gymnast starts at the left end of the balance beam and does some handsprings. When she is finished, she is at the point shown on the diagram. What fraction represents how far she went on the balance beam?

Answer:
6/8 unit fraction.
Explanation :
The balance beam is divided in to 8 equal parts of same unit lengths
the point is market at 6/8 on the balance beam.

Question 11.
Mark draws a number line and labels the points for 0 and 1. He divides the distance from 0 to 1 into 2 equal lengths and labels the fraction \(\frac{1}{2}\). If Mark divides each half into 2 equal lengths, what fractions can Mark label on his number line?
Answer:

Explanation:
Mark draws a number line and labels the points for 0 and 1 of two equal lengths and labels the fraction and label 0 , 1/2 and 1.
Mark divides each half into 2 equal lengths, each fractions is marked labels on his number line as 1/4, 2/4, 3/4 and 4/4
as shown in the above figure.

Question 12.
Higher Order Thinking Show 3 ways you can represent three eighths.
Answer:

The number ABOVE the line tells HOW MANY PARTS
we have (the colored parts).The number BELOW the line tells how many EQUAL parts
the whole is divided into. To find 3/8 of a number, we multiply the numerator 3 by the given whole number and then divide the product by the denominator 8.

Assessment Practice

Question 13.
What fraction does the red point on this number line represent?

Answer:
Option  C
Explanation:
The above line is of 6 equal parts of each label 1/6, 2/6, 3/6, 4/6, 5/6 and 6/6

Question 14.
Which number line has a red point at \(\frac{1}{3}\)?

Answer:
Option A
Explanation :
In the number line has a red point at \(\frac{1}{3}\)

Lesson 12.5 Number Line: Fractions Greater Than 1

Solve & Share
The length of one strip of paper is 1 whole unit. Fold two strips of paper in half. Open the two strips and place them end to end.
How many halves do you have? Use fractions to name each fold line. Tell how you decided. Draw a picture to show your work.
Answer:
2 halves

strip of paper is 1 whole unit. Fold two strips of paper in half,
two halves for two strips of papers , if it unfolded and kept end to end open

I can … represent fractions equal to or greater than 1 on a number line

Look Back! If you added a third strip of paper folded in half, how could you use halves to name the fold lines? Explain.
Answer:
If you add a third strip of paper folded in half, as 5/4 and 6/4.
Explanation:
One can represent fractions equal to or greater than 1 on a number line.

Essential Question
How Can You Use a Number Line to Represent Fractions Greater Than 1?
Answer:
Fractions greater than 1 have numerators larger than their denominators, those that are less than 1 have numerators smaller than their denominators; the rest are equal to 1.

Visual Learning Bridge
A marsh rabbit hopped \(\frac{7}{4}\) the length of a rabbit trail. How can you show this on a number line?
Number lines can represent fractions that are greater than 1 whole \(\frac{7}{4}\). 5 is greater than 1 whole, but less than 2 wholes. The whole is the distance between 0 and 1.

Divide each whole into 4 equal lengths.
Each length is \(\frac{1}{4}\) of the whole.
\(\frac{4}{4}\) is the same as 1 whole.

The marsh rabbit hopped 7 lengths of the unit fraction \(\frac{1}{4}\).
The point showing 7 lengths of \(\frac{1}{4}\) can be labeled as \(\frac{7}{4}\)

Answer: 7/4
Explanation:
Marsh rabbit hopped shown in the number line.

Convince Me! Be Precise One tick mark on the number line below has been named with the fraction \(\frac{2}{3}\). On the number line the lengths marked are equal. Write fractions for the other tick marks shown.

Answer:

Explanation:
Divided a number line from 0 to 1 into 3 equal lengths. Each unit fraction represents 1/3 of equal length.

Guided Practice

Do You Understand?
Question 1.
Name a fraction that is to the right of the tick mark for 2 on a number line.
Answer: 7/3
Explanation :

Question 2.
Quinn says that \(\frac{10}{8}\) comes to the right of \(\frac{9}{8}\) on a number line. Do you agree? Why or why not?
Answer: YES
Explanation:

Do You Know How?
In 3 and 4, each number line has equal lengths marked. Write the missing fractions.
Question 3.

Answer:
1/3 and 4/3 of unit fraction.
Explanation:
Marked on number line.

Question 4.

Answer:
1/4,  4/4,  5/4 and 7/4 are marked on number line.
Explanation:

Independent Practice

Leveled Practice In 5-7, each number line has equal lengths marked. Write the missing fractions.
Question 5.

Answer:
1/2 and 3/2 are missing marked on number line.
Explanation:

Question 6.

Answer:
1/4 and 4/4 or 1 are marked on number line.

Explanation:

Question 7.

Answer:
2/6,  4/6 and 5/6 are missing marked on number line.
Explanation:

In 8 and 9, divide the number lines into equal lengths. Write the missing fractions.

Question 8.

Answer:
1/3, 4/3, 5/3 7/3 and 8/3 are marked on number line.

Explanation:

Question 9.

Answer:
2/8, 3/8, 5/8 and 6/8 are missing numbers marked on number line.
Explanation:

Problem Solving

In 10 and 11, use the number line below.

Question 10.
What fraction tells how far the swimming pool is from the school? Explain how you know.
Answer:
1⅓ mile from school.
Explanation :

Question 11.
Higher Order Thinking The hospital is halfway between the grocery store and the post office. What fraction tells how far the hospital is from the school? Explain.
Answer:
4/6 unit fraction.
Explanation :
The hospital is 4/6 mile distance from the school, it is located at 4/6 on number line.

Question 12.
Tim has 78 board games. He has 10 boxes. Each box holds 9 games. If Tim puts all the games he has into the boxes, how many more games can he fit? Complete the bar diagram and solve the problem.

Answer:
12 more games.
Explanation:

Tim has 10 Boxes, each box holds 9 games.
Total boxes can hold 90 games, but the Tim has 78 games.
Required games = 90-78 = 12 games.

Question 13.
Critique Reasoning Rachel says that she can find (7 × 5) × 2 by calculating (7 × 2) + (5 × 2) = 14 + 10. Then add to get 24. Does Rachel’s reasoning make sense? Use properties of operations to explain.
Answer:
Rachel’s reasoning doesn’t make any sense.
Explanation:
Commutative Property      x + y = y+ x
Associative Property          x + (y + z) = (x + y) + z
According to the above two properties (7×5)x2=70 and
(7 × 2) + (5 × 2) = 14 + 10 =24.

Assessment Practice

Question 14.
What fraction is represented by the total length marked on the number line? Select the correct fraction from the box.

Answer:
4/3 fraction on number length.
Explanation:

Lesson 12.6 Line Plots and Length

Solve & Share
Jamie measured the lengths of 6 beetles. She measured each beetle’s length to the nearest inch and to the nearest half inch. She recorded the lengths in the two line plots below. Measure the length of each beetle below to the nearest inch and to the nearest half inch. Record your measurements in Jamie’s line plots.
I can … measure to the nearest half inch and show the data on a line plot.

Look Back! What tool did you use to measure the length of each beetle? How did you use this tool?
Answer :
I used a scale to measure the beetle.
We have to place the beetle beside the scale and then we have to mark the length of the beetle on a piece of paper.

Essential Question
How Can You Measure Lengths and Use Line Plots to Show the Data?
Answer:
Line plots, are particularly useful for showing measurement data.
Explanation:
If a class of students all measured the length of their pencils, a line plot would highlight the range and frequency of the measurements.

Visual Learning Bridge
Julio is measuring some lengths of yarn in inches. How can he use a ruler to measure to the nearest half inch?
Line up one end of the object with 0.

The fifth \(\frac{1}{2}\)-inch tick mark is closest to the end of the length of yarn.
So, to the nearest half inch, the yarn measures \(\frac{5}{2}\) inches.
This length is two whole inches and one \(\frac{1}{2}\) inch. You can write this length as 2\(\frac{1}{2}\) inches.
Answer:
Julio measured 9 other lengths of yarn in inches:

Explanation:
One can use number lines to show fractions.
A line plot is a way to organize data on a number line.

Steps to Make a Line Plot

• Draw a number line. Show a scale based on the data.
• Write a title for the line plot.
• Mark a dot for each data value.
  Answer:
  

Convince Me! Reasoning Suppose you measured a length of yarn that was about 4\(\frac{1}{2}\) inches. How would you need to change the line plot above to record this length?
Answer:
It has to extend up to 9/2.
Explanation:
The line is extended to right side and the values are increases as shown in the above line plot,
values on line is extended up to 9/2 for 4½.

Guided Practice

Do You Understand?
Question 1.
Draw a line that is 1½ inches long.
Answer:

Question 2.
If a line measures halfway between 3 and 3\(\frac{1}{2}\) inches and you need to measure to the nearest \(\frac{1}{2}\) inch, what length will you record? Why?
Answer:
3 inches is the nearest inch.

Explanation:
The line is nearer to 3 inch mark.

Do You Know How?
Question 3.
Measure the length of each of your fingers. List the measurements to the nearest half inch.
Answer:
1 Index or Point Finger of Length 3 inches
2 Middle Finger of Length 3½ inches
3 Ring Finger of Length 3 inches
4 Little Finger of Length 2½ inches
5 Thumb Finger of Length  2½ inches
Explanation:
Answers may vary from hand to hand.

Question 4.
Make a line plot to show the measurements of your fingers.
Answer:
Inches of fingers may vary from person to person.
Explanation:

Question 5.
Measure the lengths of the pieces of yarn at the right to the nearest half inch. Write the length for each piece.

Answer:
First      – 3 inches
Second – 2½ inches
Third     – 3 inches
Forth     – 2 inches
Fifth      – 2 inches
Explanation:
Length of yarn may vary.

Question 6.
Draw a line to represent another length of yarn. Measure your line to the nearest half inch.
Answer:
3½ inches length yarn.

Question 7.
Make a line plot to show the measurements of the yarn.

Answer:
3½ inches length yarn.

Problem Solving

Question 8.
Measure the lengths of 10 classroom objects to the nearest half inch. Choose objects that are between 1 and 6 inches long. Record your measurements.
Answer:

Question 9.
On grid paper, draw a line plot to show your data from Exercise 8.
Answer:

Question 10.
Make Sense and Persevere Raymond weighed his three dogs. The oldest dog weighs 74 pounds. The other two dogs each weigh 34 pounds. How many more pounds does the oldest dog weigh than the other two dogs combined?
Answer:
The oldest dog weighs 6 more ponds than the other two dogs.
Explanation:
Weight of oldest dog is 74
Weight of other two dogs (34+34) is 68
So the oldest dog weighs 6 ponds more
74 – 68 = 6

Question 11.
Draw a number line from 0 to 2. Label the wholes. Divide each whole into thirds. Label each fraction.
Answer:

In 12 and 13, use the table at the right.

Question 12.
How many more of the shortest paper chains does Rico have than the longest paper chains? Explain.
Answer:
Shortest paper chain length 6½
Rico has 3 shortest paper chains each of length 6½
Explanation :
In the table the shortest length of the paper chain is 6½
There are 3 shortest 6½

Question 13.
Higher Order Thinking Look at Rico’s measurements. Can you tell if he measured the paper chains to the nearest half inch or to the nearest inch? Explain.
Answer:
Rico’s measurements are to the nearest half inch
Explanation:
If we look at Rico’s measurements all of the measurements are in inches and nearest half inches,
there are no one fourth inches.
So Rico’s measurements are in nearest half inches.

Assessment Practice

Question 14.
Jessica used 4 of Nail A, 2 of Nail B, and 3 of Nail C to build a birdhouse. Measure each nail to the nearest half inch. Then complete the line plot.

Answer:

Lesson 12.7 More Line Plots and Length

Solve & Share
Monica and her friends measured the lengths of their shoes. Show this data by marking a dot for each length on the line plot below.
Measure the length of three classmates’ shoes. Add a dot to represent each length on the line plot. What length was the most common?
I can … measure to the nearest fourth inch and show the data on a line plot.

Look Back! Are there different ways to record the results of a data collection? Explain.
Answer:
Yes, there are different ways to record the results of a data collection.
Explanation:
We can use a scale, measuring tape, and so on to measure the data.

Essentials Question
How Can You Make and Use Line Plots?
Answer:
A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer than 25 numbers. It is a quick, simple way to organize data.

Visual Learning Bridge
Anna is measuring the length of her crayons. How can she use a ruler to measure to the nearest fourth inch?
Line up one end of the object with 0.

The tenth \(\frac{1}{4}\)-inch tick mark is closest to the end of the length of the crayon.
So, to the nearest fourth inch, the crayon measures \(\frac{10}{4}\) inches.
This length is two whole inches and two \(\frac{1}{4}\) inches. You can write this length as 2\(\frac{2}{4}\) inches.

Anna measured her other crayons.
She then recorded the data in a line plot.

Convince Me! Make Sense and Persevere Nathan also made a line plot to show the lengths of his crayons. Tell three things you know about the lengths of Nathan’s crayons.

Answer:
Nathan’s measured his crayons nearest ¼th
Most of Nathan’s crayons are 2¼ inches
The smallest crayon Nathan’s has 1 inch.

Guided Practice

Do You Understand?
Question 1.
Measure the length of this line to the nearest fourth inch.

Answer:
Length = 3¾ inches
Explanation:

Question 2.
Describe how you would show this measurement on a line plot.
Answer:

Do You Know How?
Question 3.
Draw a line plot to show the data.

Answer:

Question 4.
Measure your pencil to the nearest fourth inch. Show the length on your line plot.
Answer:
length of pencil : 3 \(\frac{3}{4}\)

Independent Practice

Question 5.
Daisy measured the lengths of her toy dinosaurs to the nearest fourth inch. She listed the lengths. Make a line plot to show the data.
1\(\frac{2}{4}\) in., 2\(\frac{1}{4}\) in., 1 in., 1\(\frac{2}{4}\) in., 1\(\frac{3}{4}\) in.
Answer:

Question 6.
Measure the lengths of the toy dinosaurs at the right to the nearest fourth inch. Write the length for each toy. Show the lengths on your line plot.
Answer:
length of toy 1 : 1\(\frac{2}{4}\) in.
length of toy 2 : 2\(\frac{1}{4}\) in.
length of toy 3 : 1 in.
length of toy 4 : 1\(\frac{2}{4}\) in.
length of toy 5 : 1\(\frac{3}{4}\) in.

Problem Solving

In 7 and 8, use the line plot at the right.

Question 7.
Arty made a line plot to show the number of inches that different snails crawled in a 5-minute race. What was the most common distance that the snails crawled?
Answer:
the most common distance that the snails crawled is 9 \(\frac{1}{4}\) inches

Question 8.
Higher Order Thinking How many more snails crawled a length more than 8\(\frac{3}{4}\) inches than a length less than 8\(\frac{3}{4}\) inches?
Answer:
snails that crawled length less than 8\(\frac{3}{4}\) inches are : 6
snails that crawled length more than 8\(\frac{3}{4}\) inches are : 19
difference : 19 – 6 = 13 snails
13 more snails crawled a length more than 8\(\frac{3}{4}\) inches than a length less than 8\(\frac{3}{4}\) inches

Question 9.
Measure the lengths of 10 classroom objects to the nearest fourth inch. Choose objects that are between 1 and 5 inches long. Record your measurements.
Answer:

Question 10.
On grid paper, draw a line plot to show your data from Exercise 9.
Answer:

Question 11.
Jackson bought 5 books that cost $7 each. How much change did he get from $40?
Answer:
Jackson got $5 change.
Explanation:
Cost of each book = $7
Cost of 5 books = 5×7
Total cost of 5 books =$35
Total amount paid = $40
Total change he received = 40-35
= $5.

Question 12.
Use Structure Use the digits 2, 6, and 8 to make as many 3-digit numbers as you can. Use place value to arrange the numbers in order from least to greatest.
Answer:
H     T     U
2     6      8
2     8      6
6     2      8
6     8      2
8     2      6
8     6      2
Assessment Practice

Question 13.
Tonya is making headbands. She recorded the lengths of all the blue bows she purchased for the headbands. Tonya also purchased 4 red bows with lengths of 1 inch, 1\(\frac{1}{4}\) inches, 1\(\frac{2}{4}\) inches, and 1\(\frac{2}{4}\) inches. Record the lengths of Tonya’s red bows in the line plot.

Answer:
Red bows are : 1 inch , 1\(\frac{1}{4}\) inches, 1\(\frac{2}{4}\) inches, and 1\(\frac{2}{4}\) inches.
so there are 4 red bows.

Lesson 12.8 Problem Solving

Make Sense and Persevere
Solve & Share
Marcus, Mariah, and Tony painted a mural. They divided it into equal parts. Marcus painted 2 parts, Mariah painted 3 parts, and Tony painted the rest. What fraction of the mural did each student paint?
This problem may have missing or extra information. If information you need is missing, make up some reasonable information and then solve the problem.
I can … make sense of problems and keep working if I get stuck.

Thinking Habits
Be a good thinker! These questions can help you.

• What do I need to find?
• What do I know?
• What’s my plan for solving the problem?
• What else can I try if I get stuck?
• How can I check that my solution makes sense?
  

Look Back! Make Sense and Persevere What information was not given in the problem? How did you still solve the problem?
Answer:
The number of parts the mural is divided into was not given
Additional information:
Marcus, Mariah, and Tony painted a mural. They divided it into 8 equal parts. Marcus painted 2 parts, Mariah painted 3 parts, and Tony painted the rest. What fraction of the mural did each student paint?
Answer:
Marcus painted 2 parts
Mariah painted 3 parts
and Tony painted the rest
= 8 – ( 2 + 3 )
= 8 – 5
= 3 parts
Tony painted 3 parts
Marcus painted  :  \(\frac{2}{8}\)
Mariah painted  :  \(\frac{3}{8}\)
Tony painted      :  \(\frac{3}{8}\)

Essential Question
How Can You Make Sense of a Problem and Persevere in Solving It?
Answer:
The meaning of a problem and looking for entry points to its solution. Helps to analyze givens, constraints, relationships, and goals.

Suki divides her garden into 6 equal parts. She plants daisies, roses, and violets. It takes Suki 1 hour to plant the flowers. She plants daisies in 1 part, roses in 2 parts, and violets in the rest of the garden.
In what fraction of the garden does Suki plant violets?

What is a good plan for solving the problem?
I need to make sense of the given information. I need to think about what I can use to help me solve the problem.

How can I make sense of and solve this problem?
Answer:
I can…..

• identify the quantities given.
• understand which quantities are needed to solve the problem.
• choose and implement an appropriate strategy.
• check to be sure my work and answer make sense.
  Explanation:

The information about 1 hour to plant the flowers is not needed to solve the problem.
I can use a picture to help make sense.
1 equal part for daisies is \(\frac{1}{6}\) of the whole.
2 equal parts for roses is \(\frac{2}{6}\) of the whole.
There are 3 equal parts left for violets.

3 copies of \(\frac{1}{6}\) is \(\frac{3}{6}\).
So, Suki plants violets in \(\frac{3}{6}\) of the garden.

Convince Me! Make Sense and Persevere How can you check to make sure the work and answer given above make sense?
Answer:
Total number of parts garden is divided into is: 6 parts
Daisies are planted in 1 part [ 1/6 fraction]
Roses are planted in 2 parts [ 2/6 fraction]
So Suki plants violets in 3 parts as :
1 + 2 = 3
6 – 3  = 3 parts
3/6 unit fraction.

Guided Practice

Make Sense and Persevere Keira and Matt cut a sandwich into 4 equal parts. They each ate 1 part. Keira is 9 years old. Matt is the same age as Keira. What fraction of the sandwich is not eaten?

Question 1.
Is there any missing or extra information? Explain.
Answer:
Missing information : none
Extra information : the ages of Keira and Matt are given [we don’t need their ages to determine the parts of the sandwich left]

Question 2.
What do you need to find before you can determine how much of the sandwich is left?
Answer:
We don’t need to find the any other information as all the needed information is given in the question

Question 3.
Solve the problem. If information you need is missing, make up some reasonable information for the problem.
Answer:
The sandwich is divided into 4 equal parts
Keira and Matt each ate one part so total parts eaten : 2 parts
number of parts left is : 4- 2 = 2 parts

Independent Practice

Make Sense and Persevere Marni planted a vegetable garden. She put lettuce in 1 part, carrots in 4 parts, and broccoli in the rest of her garden. In what fraction of the garden did Marni plant broccoli?
Question 4.
Is there any missing or extra information?
Answer:
Missing information : the question did not specify the number of the parts Marni’s garden is divided into
Extra information : none

Question 5.
Solve the problem. If information you need is missing, make up some reasonable information for the problem.
Answer:
Additional information : Marni’s garden is divided into 8 parts. She put lettuce in 1 part, carrots in 4 parts, and broccoli in the rest of her garden. In what fraction of the garden did Marni plant broccoli?
Answer:
fraction in which broccoli is planted : 3/8
Explanation:
Total number of parts Marni’s garden is divided into is 8 parts
lettuce : 1 part
carrots : 4 parts
broccoli : 8 – (1 + 4)
.             : 8 – 5 = 3
fraction in which broccoli is planted : 3/8

Question 6.
Can you use a different number of parts and still solve the problem? Explain.
Answer:
yes
Explanation :
If Total number of parts Marni’s garden is divided into is 6 parts
lettuce : 1 part
carrots : 4 parts
broccoli : 6 – (1 + 4)
.             : 6 – 5 = 1
fraction in which broccoli is planted : 1/8

Problem Solving

Performance Task
Sports Day
Green School divides its school gym into 8 equal parts for a sports day. Basketball is in 2 parts, soccer is in 1 part, and volleyball and tennis are in the rest.

Question 7.
Make Sense and Persevere The gym teacher wants to know what fraction of the gym is used for tennis. What missing information do you need to solve the problem?
Answer:
School gym is divides into 8 equal parts.
Tennis and Volleyball not clearly mentioned, these two are missing information do you need to solve the problem.

In 8 and 9, draw a picture to represent the number of parts in each plan.
Question 8.
Reasoning What fraction of the gym would be used for tennis if 2 parts were for volleyball?

Answer: 3 parts

Explanation:
if 2 parts were used for volleyball , three parts used for tennis

Question 9.
Reasoning What fraction of the gym would be used for tennis if 3 parts were used for volleyball?
Answer: 2 PARTS

Explanation : if 3 parts were used for volleyball , two parts used for tennis as shown in that above picture

Question 10.
Construct Arguments To have the same fraction for tennis as for basketball, which plan, Exercise 8 or 9, should be used? Justify your answer.
Answer:
plan 9 should be used
Explanation:
for tennis and basket ball to be equal we need to have equal number of parts for tennis and basket ball
in question 9 plan tennis and basket ball both are takin a space of 2 parts
whereas in question 8 plan tennis is taking up more space than that of basket ball
so,
for tennis and basket ball to be equal we need to have equal number of parts for tennis and basket ball

Topic 12 Fluency Practice Activity

Follow the path
Shade a path from START to FINISH. Follow the sums and differences where the digit in the hundreds place is greater than the digit in the tens place. You can only move up, down, right, or left.
I can … add and subtract within 1,000.

Answer :

Topic 12 Vocabulary Review

Understand Vocabulary
Word List

• denominator
• fraction
• line plot
• nearest fourth inch
• nearest half inch
• numerator
• unit fraction

Question 1.
Circle each unit fraction.
\(\frac{1}{4}\)
\(\frac{3}{8}\)
\(\frac{1}{6}\)
\(\frac{1}{8}\)
\(\frac{2}{3}\)
Answer:

Question 2.
Circle each fraction where 6 is the denominator.
\(\frac{3}{6}\)
\(\frac{6}{8}\)
\(\frac{1}{6}\)
\(\frac{5}{6}\)
\(\frac{4}{8}\)
Answer:

Question 3.
Circle each fraction where 4 is the numerator.
\(\frac{2}{4}\)
\(\frac{4}{8}\)
\(\frac{1}{4}\)
\(\frac{3}{4}\)
\(\frac{4}{6}\)
Answer:

Question 4.
Circle the lengths that could be measurements to the nearest half inch.
2\(\frac{1}{2}\) in.
4 in.
3\(\frac{3}{4}\) in.
7\(\frac{1}{4}\) in.
6 in.
Answer:

Question 5.
Circle the lengths that could be measurements to the nearest fourth inch.
8\(\frac{3}{4}\) in.
1\(\frac{1}{4}\) in.
11 in.
7\(\frac{1}{4}\) in.
6 in.
Answer:

Write always, sometimes, or never.
Question 6.
The numerator in a fraction is _?_ greater than the denominator. _________
Answer:
Some times
Explanation:
In a proper fraction, the numerator is sometimes more than the denominator.
Question 7.
A fraction ? _ has a numerator and denominator. __________
Answer:
Always
Explanation:
A fraction represents a part of a whole or any number of equal parts.
For example, one-half, eight-fifths, three-quarters.
Question 8
A line plot_?_ shows measurements of lengths. _________
Answer:
Never
Explanation:
A Line plot can be defined as a graph that displays data as points or check marks above a number line, showing the frequency of each value.

Question 9.
Use at least 2 terms from the Word List to explain how to find the unit fraction of the shape shown below.

Answer:
1/6
Explanation:
A unit fraction is any fraction with 1 as its numerator (top number), and a whole number for the denominator (bottom number).
If we divide the hexagon into 6 equal parts
then each part will be one part of the six parts
that is 1/6

Topic 12 Reteaching

Set A pages 437-440

This is one way to divide a whole into fourths.

Because each of the 4 parts has the same area, each part is one fourth of the whole.
You can write this fraction as \(\frac{1}{4}\)
A unit fraction represents one of the equal parts \(\frac{1}{4}\) is a unit fraction.

Remember that fractions can name equal parts of a whole.

In 1 and 2, draw lines to divide the shape into the given number of equal parts. Then write the fraction that represents 1 part.
Question 1.
6 equal parts

Answer:

Explanation:
total area of the figure : 12
12 divided into 6 parts is 12 ÷ 6 = 2

Question 2.
2 equal parts

Answer:

Explanation:
total area of the figure : 12
12 divided into 2 parts is 12 ÷ 2 = 6

Question 3.
Martin divides a shape into 3 equal parts. What unit fraction can he write to represent 1 part?
Answer:

Set B pages 441-444

What fraction of this rectangle is shaded?

The rectangle is divided into 8 equal parts. So, the unit fraction of the rectangle is \(\frac{1}{8}\).
In the whole rectangle, there are 8 parts of \(\frac{1}{8}\).
8 copies of \(\frac{1}{8}\) is \(\frac{8}{8}\)
For the shaded part there are 6 parts of \(\frac{1}{8}\).

6 copies of \(\frac{1}{8}\) is \(\frac{6}{8}\)
So, \(\frac{6}{8}\) of the rectangle is shaded.

Remember that you need to think about how many parts there are in all and how many parts are shaded.

In 1-4, write the unit fraction that represents each part of the whole. Next, write the number of shaded parts. Last, write the fraction of the whole that is shaded.
Question 1.

Answer:
Unit fraction = 1/3
Number of shaded part is one.
Fraction of whole that is shaded = 1/3
Question 2.

Answer:
Unit fraction = 5/6
Number of shaded parts are 5
Fraction of whole that is shaded = 5/6
Question 3.

Answer:
Unit fraction = 3/4
Number of shaded parts are 3
Fraction of whole that is shaded = 3/4

Question 4.

Answer:
Unit fraction = 2/4
Number of shaded parts are 2
Fraction of whole that is shaded = 2/4

Set C pages 445-448

This shape is \(\frac{2}{4}\) of a piece of fabric Tina used in a quilt. You can draw a picture and write a fraction to represent the whole piece of fabric.

\(\frac{2}{4}\) is 2 copies of \(\frac{1}{4}\)
Divide the piece of fabric into 2 equal parts.
4 copies of \(\frac{1}{4}\) makes \(\frac{4}{4}\). or 1 whole.

Remember that the denominator shows the total number of equal parts in a whole.

In 1 and 2, draw a picture and write a fraction to represent the whole.
Question 1.

Answer:

1 = 4/4

Question 2.

Answer:

1 = 8/8

Set D pages 449-452

You can show fractions on a number line.
The fraction \(\frac{5}{6}\) is labeled. What are the missing fractions?

First, find the unit fraction. The line is divided into six equal lengths. So, the number line shows sixths.
Each jump represents \(\frac{1}{6}\). So, the first tick mark is labeled \(\frac{1}{6}\). The second tick mark is labeled \(\frac{2}{6}\), and so on.
The missing fractions on the number line are \(\frac{1}{6}, \frac{2}{6}, \frac{3}{6}\), and \(\frac{4}{6}\)

Remember to first decide what unit fraction is shown on each number line.

In 1 and 2, write the missing fractions on each number line.
Question 1.

Answer:
1/4 and 3/4

Question 2.

Answer:
1/8 , 2/8 , 4/8 , 5/8 , 7/8

Question 3.
Divide the number line below into 3 equal parts and mark \(\frac{2}{3}\) on the line.

Answer:

Set E pages 453-456

Number lines can have fractions greater than 1.
The number line below is divided into thirds.
The denominator is 3 because the unit fraction is \(\frac{1}{3}\). The numerator shows how many copies of the unit fraction each point represents.

Remember that the numerator increases by 1 because each part of the number line is 1 more copy of the unit fraction.

Question 1.
The number line has equal lengths marked. Write the missing fractions.

Answer:
1/6 , 4/6 , 5/6 , 7/6 , 8/6

Question 2.
Divide the number line into fourths. Label each point.

Answer:

Set F pages 457-460

You can use a line plot to show data, such as lengths measured to the nearest half inch.
Steps to make a line plot:

• Draw a number line and choose a scale.
• The scale should show data values from the least to the greatest.
• Write a title for the line plot.
• Mark a dot for each value.
  

Remember to mark a dot for each length. Check your completed line plot against the data in the chart.

Question 1.
Draw a line plot to show the data.
Answer:

Question 2.
How many strings does Carl have in all?
Answer:
10 strings
Explanation:
2½ inch strings – 04
3 inch    strings – 03
3½ inch strings – 02
4 inch    strings – 01

Question 3.
Draw a line that is the same length as the most common string length.
Answer:
Most common string is 2½ inch

Set G pages 461-464

You can measure to different lengths, such as to the nearest fourth inch.
The closest fourth-inch mark to the end of the length of the rectangle is the 2\(\frac{1}{4}\)-inch mark.

The lengths can be shown on a line plot.

Remember to think about the scale of the line plot. It needs to include the least and greatest values.

Question 1.
Measure and record the lengths of 5 classroom objects to the nearest fourth inch. Use objects that are between 1 and 3 inches long.
Answer:
Eraser : 1.5 inches
Pencil :  2.7 inches
Pen Cap : 2.3 inches
Chalk : 2.3 inches
Sticker : 1 inch

Question 2.
Draw a line plot to show your data.
Answer:

Set H pages 465-468

Think about these questions to help you make sense and persevere in solving problems.
Thinking Habits

• What do I need to find?
• What do I know?
• What’s my plan for solving the problem?
• What else can I try if I get stuck?
• How can I check that my solution makes sense?
  

Remember to make sense of the problem by identifying the quantities. Then use what you know to solve.

Gavin divided his notebook into 8 equal parts. He plans to use 3 parts to take notes for math and 2 parts for reading. He has school from 8:30 A.M. to 3:30 P.M. What fraction of his notebook does he have left?
Question 1.
Is there any missing or extra information? Explain.
Answer:
Gavin divided his book into 8 equal parts
3 parts are used for math 3/8
2 parts are used for reading 2/8
The fraction of notebook he has left is :
3 + 2 = 5
8 – 5 = 3
The fraction of notebook he has left is 3/5

Question 2.
Solve the problem. If information you need is missing, make up some reasonable information for the problem. You can draw a picture to help.
Answer:
The missing information is:
3/8 part of the book was used for science

Topic 12 Assessment Practice

Question 1.
What fraction of the whole is colored green? What fraction of the whole is colored yellow?

Answer:
3/6 fraction of the whole is colored green.
3/6 fraction of the whole is colored yellow.

Question 2.
Write a fraction to name the equal parts of the whole pizza. How many parts would you need to make two whole pizzas? Explain.

Answer:
Fraction name : 1/8
we need 16 parts to make 2 whole pizzas
Explanation:
1 pizza needs 8 parts to make 1 whole so we need 16 parts [8 + 8 = 16] to make 2 wholes

Question 3.
This line segment represents \(\frac{1}{3}\) of the distance from Mal’s house to the library. Which represents the whole distance and has an accurate explanation?

A. The line segment represents \(\frac{1}{3}\) the distance from Mal’s house to the library. So, the whole distance is 3 times as long.
B. The line segment represents \(\frac{1}{3}\) the distance from Mal’s house to the library. So, the whole distance is 2 times as long.
C. The line segment represents \(\frac{1}{3}\) the distance from Mal’s house to the library. So, the whole distance is 4 times as long.
D. The line segment represents the distance from Mal’s house to the library. So, the whole distance is the identical line segment.
Answer:
Option A
Explanation:
The line segment represents 1/3 the distance from Mal’s house to the library. So, the whole distance is 3 times as long.

Question 4.
Which point is at \(\frac{3}{6}\) on the number line?

A. Point A
B. Point B
C. Point C
D. Point D
Answer:
Point B

Question 5.
Which of the fractions would be to the right of 1 on a number line? Select all that apply.

Answer:
5/4

Question 6.
A. Draw a picture to show \(\frac{2}{4}\).
Answer:

B. Explain how you knew you had shaded the correct amount of your picture.
Answer:
Divide the circle into fourths and then shade 2 of the 4 parts blue

Question 7.
Jeremy put pepperoni on \(\frac{1}{2}\) of a pizza. He put olives on \(\frac{1}{3}\) of the pizza. What fraction of the pizza did NOT have pepperoni? What fraction of the pizza did NOT have olives?
Answer:
1/2 of the fraction did not have pepperoni.
2/3 of the fraction did not have olives.

Question 8.
One point on the number line below has been named with the fraction \(\frac{2}{4}\). Write a fraction for each of the other points shown.

Answer:

Question 9.
Explain how you know \(\frac{3}{3}\) represents a whole.
Answer:
Fraction 3/3 means 3 parts of 3 parts
Dividing 3 with 3 we get 1
So the fraction 3/3 is a whole 1

Question 10.
Jared folded a piece of paper 9 inches by 12 inches into sections as shown below. What fraction of the total area is in each section? Explain.

Answer:
Fraction of total Area is 36
Explanation:
Area of total paper = 9 x 12 = 108 sq.inches
The paper is divided into 3 equal part
Area of each part = 108 ÷ 3 = 36 sq.inches

Question 11.
How many \(\frac{2}{8}\)s do you need to get \(\frac{8}{8}\)?
Answer:
Four
Explanation:
we need four 2/8 fractions to get 8/8
2/8 + 2/8 + 2/8 + 2/8 = 8/8

Question 12.
Lane’s class is painting a mural with 6 equal parts. They spent 45 minutes painting on each of 2 days. On the first day, the class painted \(\frac{1}{6}\) of the mural. The next day, the class painted another \(\frac{1}{6}\) of the mural. How many \(\frac{1}{6}\) parts did the class paint in the two days?
A. 1
B. 2
C. 3
D. 4
Answer:
Option B
Explanation:
The class paints 1/6 part each day in d days the class paints 2/6 parts
1/6 – day 1
1/6 – day 2
By day 2 no of parts painted are 1/6 + 1/6 = 2/6

Question 13.
How many \(\frac{1}{8}\) s do you need to get \(\frac{5}{8}\)? Use the number line below for help.
A. 1
B. 3
C. 5
D. 8

Answer:
Option C
Explanation:
You need 5 yards to make 1/8 as 5/8

Question 14.
Which point represents 6 lengths of \(\frac{1}{8}\) on the number line? Explain.

Answer:
Point D

Question 15.
Divide the circle into 8 equal parts. What fraction does each part represent?

Answer:

Each part represent1/8 fraction.

Question 16.
Seth drew \(\frac{2}{4}\) of a shape below. Draw a picture to show the whole shape and write a fraction to represent the whole.

Answer:

Explanation:
One whole is 4/4 that means to get 4/4 we need to have 2 parts of 2/4
As 2/4 + 2/4 = 4/4

Question 17.
Mara believes the point marked on the number line is \(\frac{2}{3}\). Is she correct? Explain.

Answer:
Mara is wrong
Explanation:
the markings of the fractions on the number line are not correct
[the markings are not even there is a lot of gap between 1/3 and 3/3]

Question 18.
Select all the sentences that describe this shape.

Answer:

Question 19.
Divide the number line into equal lengths. Then mark and label the given fraction.
6 equal lengths; \(\frac{5}{6}\)

Answer:

Explanation:
First divide the number line into 6 equal parts like in the picture below

Then mark the 5/6th point

Question 20.
Tony collects colored strings. The table shows the lengths of some of his strings.

A. Measure the lengths of Tony’s red and brown strings shown below to the nearest fourth inch.

Answer:
Red string     : 3     inches
Brown string : 2¾ inches

B. Draw a line plot to show the lengths of Tony’s 7 strings to the nearest fourth inch.
Answer:

Topic 12 Performance Task

Art Display
Three students, Zach, Allie, and Paige, are making an art display.

Use the Paint Colors list and the design at the right to answer Questions 1-4.
Question 1.
The display will be divided into 8 equal parts. Paint Colors Draw lines to show one way to do this. Then write the fraction that describes the the total shape that is represented by 1 equal part.
Paint Colors

• Allie is painting the blue parts.
• Paige is painting the red parts.
• Zach is painting the yellow parts.
•  Each student will paint at least 2 parts.
  

Answer:

1/8 part

Question 2.
Shade the parts blue, yellow, or red to show how many parts each student could paint. Write fractions to show how much of the total display Allie and Paige painted.
Answer:

• Allie is painting the 3 blue parts.      3/8
• Paige is painting the 3 red parts.      3/8
• Zach is painting the 2 yellow parts.

Question 3.
Divide the number line into the number of equal parts of the display. Then mark a dot to show the fraction of the display that Zach painted on the number line.

Answer:

Question 4.
Which fraction represents the whole display? Explain. Then mark a dot to show where this fraction is located on the number line above.
Answer:
8/8 is the whole fraction

Use the Ribbon Lengths diagram on the right and the Number of Ribbons table below to answer Question 5.

Question 5.
The students will use the ribbon lengths at the right in their display
Part A
Measure and record the lengths of each of these ribbons to the nearest fourth inch.
Answer:
RED Ribbon : 3¾
BLUE Ribbon : 3 2/4  [3½]
GREEN Ribbon : 3¼

Part B
The Number of Ribbons table shows how many of each color ribbon will be used. Draw a line plot to show this data.

Answer:

Question 6.
In order to complete the display, the students recorded the number of half-hour sessions they spent working together. The number line below is divided into equal parts. Each part represents half an hour. Write the missing fractions on the number line.

Answer:

Go through the enVision Math Common Core Grade 2 Answer Key Topic 9 Numbers to 1,000 regularly and improve your accuracy in solving questions.

enVision Math Common Core 2nd Grade Answers Key Topic 9 Numbers to 1,000

enVision STEM Project: Breaking Apart and Putting Together

Find Out Collect sets of building blocks. Take turns and work together. Use the blocks to build a model. Then take that model apart and use the same blocks to build a different model.

Journal: Make a Book Show your models in a book.
In your book, also:

• Tell how many pieces you used to build your models.
• Show how to use place-value blocks to model different names for the same number.

Answer:
Building the Blocks:

• Tell how many pieces you used to build your models.

1. I have used 20 blocks to create the above model.
2. I have used 13 plain blocks and 7 wheel blocks.

• Show how to use place-value blocks to model different names for the same number.

Review What You Know

Vocabulary

Question 1.
Circle the coin with the least value. Put a square around the coin with the greatest value.

Answer:

Question 2.
Circle the number that has 5 ones and 4 tens.
54
45
40
5
Answer:

Question 3.
Tom is having breakfast. The minute hand on the clock shows half past 7 o’clock. Circle the time on the clock.
7:15 a.m.
7:30 a.m.
7:15 p.m.
7:30 p.m.
Answer:

Counting Money

Question 4.
Circle coins that total 37¢.

Answer:

Breaking Apart Numbers

Question 5.
Break apart each number into tens and ones.
23 = ___ + ___
47 = ___ + ___
96 = ___ + ___
Answer:
23 = 2 tens + 3 ones
47 = 4 tens + 7 ones
96 = 9 tens + 6 ones

Math Story

Question 6.
Howie has $13. A. backpack costs $30. How much more money does Howie need to buy the backpack?
$ ____
Answer:
Howie has $13. A. backpack costs $30. He already has $13 so we have to subtract $30 – $13 = $17. Howie needs $17 more to buy a backpack.

Pick a Project

PROJECT 9A
Which are the hottest planets in our solar system?
Project: Make a Planets Poster

Answer:
Sun is the Hottest planet in out solar system but sun doesn’t be called as Planet it is called as Star. When according to planets the hottest planet in our solar system is Venus with 464 temperature
Drawing a Poster for Planets:

PROJECT 9B
What is the height of the tallest waterfall in the world?
Project: Design a Waterfall Guide

Answer:-
The height of the tallest waterfall in the world is Denmark Strait cataract with 3,505 m of height.

PROJECT 9C
How much do large animals weigh?
Project: Create an Animal Riddle Booklet

Answer:
The Antarctic blue whale (Balaenoptera musculus ssp. Intermedia) is the biggest animal on the planet, weighing up to 400,000 pounds (approximately 33 elephants) and reaching up to 98 feet in length.
Task
Kids love jokes and riddles! Your class will create a series of riddles that other students can use to learn about animals.
Engage
In this lesson, students will complete research about an animal and demonstrate their knowledge about the animal by creating a riddle they present to challenge other student’s knowledge.

Introduce your students to animal riddles by reading ABC Animal Riddles (rhyming verse) by Susan Joyce or If Not for the Cat (haiku) by Jack Prelutsky. These books will engage your students in the process and demonstrate various ways that riddles can be written.

Discuss the riddles you have read with your students. You might ask:

• What was your favorite riddle? Why?
• What clues helped you figure out the answer?
• What types of words did the author use?
• What makes a good riddle?

Let your students know that they will be creating their own animal riddles. Each student will choose an animal and create two pages in Wixxie for the riddle.

Page 1 will be the riddle. An example might look like this:

• I have beautiful black spots. I am a carnivore. I live on the savanna. I am the fastest land animal on the planet.

Page 2 will be an illustration of the animal.

Brainstorm a list of different animals with the entire class. Depending on your current science focus, you may want to narrow your brainstorm to types of animals, such as mammals, or animals that live in a particular habitat like the desert.

Students should choose one animal from the list and write down what they already know about the animal using a cluster, character trait map, or other graphic organizer.

In order to formulate the riddle, students will write clues based on the following questions:

• What does this animal look like?
• Where does it live?
• What does it eat?
• What makes it unique?

Give students time in the library or online to research the answers to these questions. Students should add their research notes to their existing cluster organizer.
Create
When their research is complete, students should write a draft of the riddle. Students can write their riddle a number of ways. For example, the riddle could contain four sentences that explain:

• Sentence 1: how the animal looks
• Sentence 2: what the animal eats
• Sentence 3: where the animal can be found
• Sentence 4: a unique fact or distinguishing characteristic

The riddle could also take the form of a haiku!

Students can use a tool like Wixie to create their riddle pages. Use the Text tool to add the text of the riddle to page 1. Use the paint tools or image button to illustrate the animal.

3-ACT MATH PREVIEW

Math Modeling

Makes Cents

Before watching the video, think: How can you save money you earn or find? What are some good places to put your money? What are some good ways to sort your money?

Lesson 9.1 Understand Hundreds

Activity

Solve & Share

What is another way to show 100? Draw a picture and explain.

Answer:-

Visual Learning Bridge

Convince Me!
10 ones make ten. 10 tens make I hundred. 10 hundreds make I thousand. Do you see a pattern? Explain.

Guided Practice
Complete each sentence. Use place-value blocks and your workmat to help.

Question 1.

Answer:

Question 2.

Answer:

Independent Practice

Complete each sentence. Use models if needed.

Question 3.

___ equals ___ hundreds, ___ tens, and __ ones.
Answer:

Question 4.

___ equals ___ hundreds, ___ tens, and __ ones.
Answer:

Question 5.

___ equals ___ hundreds, ___ tens, and __ ones.
Answer:

Question 6.

___ equals ___ hundreds, ___ tens, and __ ones.
Answer:

Question 7.
Number Sense Complete the pattern.

Answer:

Problem Solving

Solve each problem. Use models if needed.

Question 8.
Use Tools Lucy picked a number. She says her number has 8 hundreds, 0 tens, and o ones.
What is Lucy’s number?
____
Answer:

Question 9.
Vocabulary Complete the sentences using the words below.

There are 100 ___ in one hundred.
There are 10 ___ in one ___.
Answer:
There are 100  ones  in one hundred.
There are 10 tens in one hundred.

Higher Order Thinking
Farrah and Cory are playing beanbag toss. Circle the two other numbers they each must get to score 1,000 points.

Question 10.
Farrah has 300 points.
200 500 600 300
Answer:

Explanation: Farrah and Cory need 1000 points and Farrah already have 300 points and Cory needs 700 points to make 1000 points.

Question 11.
Cory has 500 points.
100 200 400 700
Answer:

Explanation: Farrah and Cory need 1000 points and Cory already have 500 points and Farrah needs 500 points to make 1000 points.

Question 12.
Assessment Practice Each box has 100 pencils. Count by hundreds to find the total. Which number tells how many pencils are in the boxes?

A. 170
B. 700
C. 800
D. 900
Answer:
700
Explanation: Each box has 100 pencils. We have 7 boxes of crayons so 100 + 100 + 100 + 100 + 100 + 100 + 100 = 700

Lesson 9.2 Models and 3-Digit Numbers

Activity

Solve & Share

How can you use place-value blocks to show 125? Explain.
Draw your blocks to show what you did.

;

Answer:

Visual Learning Bridge

Convince Me!
How many hundreds are in 395? How many tens? How many ones?
Answer: There are 3  hundreds, 9 tens, and 5 ones in 395

Guided Practice

Write the numbers shown. Use place-value blocks and your workmat if needed.

Question 1.

Answer:

Question 2.

Answer:

Independent Practice

Write the numbers shown. Use models and your workmat if needed.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.
Higher Order Thinking Find the number. It has 5 hundreds. The digit in the tens place is between 5 and 7. The number of ones is 2 less than 4. ___
Answer: The number is 562 because there are  5 hundreds and the tens is between 5 and 7 and that is 6 and the one 2 less than 4

Problem Solving

Solve the problems below.