Category: Envision Math

Go through the enVision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 15 Equal Shares of Circles and Rectangles

Essential Question:
What are some different names for equal shares?

Find Out Talk to friends and relatives about different objects that have wheels. Ask them how they use wheels in their everyday lives.
Journal: Make a Book Show what you found out. In your book, also:

• Draw pictures of different objects that have wheels. Describe the shapes you see. How could you divide the shapes into equal shares?
• Tell how wheels are used to move people or things.

Review What You Know

Vocabulary
Question 1.
Put an X on the circle.

Answer:

Question 2.
Draw a rectangle.
Answer:

Explanation:
Draw a rectangle using a scale and pencil.

Question 3.
Draw the hands on the clock to show a time to the half hour.

Answer:

Different kinds of Rectangles
Question 4.
Color all the rectangles.
Then draw an X on the rectangle that is a square.

Answer:

Explanation:
Color all the rectangles
Then put X on the rectangle that is square

Question 5.
How many rectangles do you see?

____________ rectangles
Answer:
2 rectangles
Explanation:
A rectangle has four sides
The envelope has 4 sides
The unicorn puzzle has 4 sides
So there are 2 rectangles

What’s the Time?
Question 6.
Cody gets home at 4:30. Draw the hour and minute hands on the clock to show at what time Cody gets home.

Answer:

Explanation:
Draw the minutes hand at 6 [30 minutes]
Draw the hours hand between 4 and 5

Pick a Project

PROJECT 15A
What games do you play at recess? Project: Design and Play a Game

PROJECT 15A
Answer:

PROJECT 15B
Do you have a favorite dance? Project: Create Your Own Square Dance

Answer:

PROJECT 15C
Is every game fair? Project: Make a Pair of Spinners

3-ACT MATH PREVIEW

Math Modeling Pieced Out
Before watching the video, think: What shapes can you use to make a square? Can you find another way to use shapes to make a square? What kind of designs can you make?

I can … model with math to solve a problem that involves making a design with 2-D shapes
Answer:

Explanation:
We can create a square using equal shares of triangles and one fourths of a square
the first 2 squares are patterns using triangles
the last square are patterns using rectangles and squares

Lesson 15.1 Make Equal Shares

Solve & Share
Draw a line inside the blue circle to show 2 parts that are the same size.

Draw a line inside the yellow circle to show 2 parts that are NOT the same size.

How do you know the 2 parts you made in the blue circle are the same size?

I can … determine if shapes are divided into equal shares.
Answer:

Explanation:
In the blue circle the line is drawn exactly in the middle dividing the circle into 2 equal shares.

Visual Learning Bridge

Convince Me! Is this shape divided into equal shares? Explain how you know.
Answer:
In the second picture the rectangle is divided into 2 equal shares
In the third picture the rectangle is divided into 4 equal share.

Guided Practice

Decide if each picture shows equal shares. Then circle Yes or No.
Question 1.

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Independent Practice

Write the number of equal shares in each shape. Practice If the shares are NOT equal, write 0.
Question 7.

__________ equal shares
Answer:
0 equal shares
Explanation:
The shares are not equal.

Question 8.

________ equal shares
Answer:
2 equal shares
Explanation:
The shares are equal.

Question 9.

________ equal shares
Answer:
2 equal shares
Explanation:
The shares are equal.

Question 10.

_________ equal shares
Answer:
4 equal shares
Explanation:
The shares are equal.

Question 11.

________ equal shares
Answer:
4 equal shares
Explanation:
The shares are equal.

Question 12.

_________ equal shares
Answer:
2 equal shares
Explanation:
The shares are equal.

Question 13.

_________ equal shares
Answer:
0 equal shares
Explanation:
The shares are not equal.

Question 14.

_________ equal shares
Answer:
4 equal shares
Explanation:
The shares are equal.

Question 15.
Higher Order Thinking
Draw a square, a circle, or a rectangle. Divide your shape into equal shares. Then write the number of equal shares in your shape.
_________ equal shares
Answer:

4 equal shares.

Problem Solving

Solve each problem below.
Question 16.
Be Precise Matt makes a flag with 4 equal shares. Which flag did he make? Circle the correct flag.

Answer:

Explanation:
The red flag has equal shares

Question 17.
Be Precise Ruth picks a flag with equal shares. Which flag did she pick? Circle the correct flag.

Answer:

Explanation:
The yellow flag has equal shares

Question 18.
Higher Order Thinking Mr. Kelly made 2 pizzas. He sliced each one into 4 slices. Each slice is the same size piece. How many slices are there? Draw a picture. Then write an equation.
Answer:

Explanation:
8 slices
1 pizza is divided into 4 slices
4 + 4 = 8 slices

Question 19.
Assessment Practice Which square does NOT show 4 equal shares?

Answer:
D
Explanation:
In all the options the square is divided into 4 equal shares, But in option D the square is divided into 3 shares.

Lesson 15.2 Make Halves and Fourths of Rectangles and Circles

Solve & Share
Draw a line inside the circle to show 2 equal shares. Color 1 of the shares. Then write numbers to tell how many shares you colored.

Draw lines inside the rectangle to show 4 equal shares. Color 2 of the shares. Then write numbers to tell how many shares you colored.

I can … divide shapes into 2 and 4 equal shares and use words to describe those shares.
Answer:

I colored 2 out of 4 equal shares.

Visual Learning Bridge

Convince Me! What share of the rectangle is green?

Answer:
The 3rd share of the rectangle is Green.

Guided Practice

Circle the correct shapes for each problem.
Question 1.
One quarter blue

Explanation:
one quarter blue means we have to color one fourth blue.

Question 2.
One half yellow

Answer:

Independent Practice

Color the shapes for each problem.
Question 3.
One half red

Answer:

Explanation:
We have to color one half of the figure red.

Question 4.
One fourth orange

Answer:

Explanation:
one fourth means we have to color one of the Orange.

Question 5.
One quarter green

Answer:

Explanation:
one fourth means we have to color one of the Green.

Question 6.
One half blue

Answer:

Explanation:
one half blue means we have to color one of the halves blue.

Question 7.
Higher Order Thinking
Alex has one half of an oatmeal bar. Jen has one quarter of a different oatmeal bar. Jen’s piece is bigger. How could Jen’s piece be bigger? Use words or pictures to solve.

Answer:
Alex has one half of an oatmeal bar. Jen has one quarter of a different oatmeal bar. Both oatmeal bars are of different size, as shown in the picture, hence Jen’s piece is bigger

Jens oat meal bar is bigger.

Question 8.
Explain Sam says the rectangle is divided into halves. Is he correct? Circle Yes or No. Then explain how you know.

Answer:
Yes
Explanation:
The rectangle is divided in to two equal parts or two halves by the diagonal.

Question 9.
Explain Mia says the circle is divided into fourths. Lucy says it is divided into quarters. Who is correct? Explain how you know.

Answer:
Lucy is correct
Explanation:
The difference between Fourth and Quarter. When used as nouns, fourth means the person or thing in the fourth position, whereas quarter meaning in math is 1/4 . When used as adjectives, fourth means the ordinal form of the number four, whereas quarter means pertaining to an aspect of a quarter.

Question 10.
Higher Order Thinking Dana draws a rectangle divided into fourths. She colors one half of the rectangle blue and one quarter of the rectangle green. Draw a rectangle to match the one Dana drew.
Answer:

Question 11.
Assessment Practice Yao colors a circle. One half of the circle is blue. The other half is NOT blue. Which shows the shape Yao could have colored? Choose two that apply.

Answer:

Lesson 15.3 Understand Halves and Fourths

Which is larger: one half or one fourth of the same sandwich?
Divide the sandwiches. Then circle the sandwich that has larger equal shares.

I can … tell that more equal shares of the same whole creates smaller shares.

Answer:

Visual Learning Bridge

Convince Me! David has a sandwich. Is half of the sandwich more or less food than one fourth of the sandwich? Explain.
Answer:
The half sandwich is more than the one fourth of the sandwich
Explanation:
One fourths means the sandwich is divided into 4 parts
whereas the half of sandwich means the sandwich is divided into 2 parts
half = 1 fourth + 1 fourth
so half of sandwich is more than one fourth of a sandwich

Guided Practice

Circle the shape that has more equal shares. Put an X on the shape that has larger equal shares.

Question 1.

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Independent Practice

Solve each Problem
Question 5.
Draw a line to divide this shape in half.

Answer:

Explanation:
If we draw a line exactly in the middle of the rectangle the rectangle will be divided into 2 equal halves

Question 6.
Shade one quarter of this shape.

Answer:

Explanation:
Shade 1 quarter of the circle.

Question 7.
Draw lines in the orange square to make smaller equal shares than are in the blue square.

Answer:

Explanation:
Draw a line dividing the orange square into 2 equal shares like in the blue squares

Question 8.
Higher Order Thinking Joan cuts a rectangle into 2 equal shares. Then she cuts each share in half. How many equal shares are there now? What are these shares called? Use words or pictures to explain.

Answer:
The rectangle is divided into 2 equal shares
The 2 equal shares are then divided into 2 equal share. which means
1 rectangle into 2 parts 2 parts into 2 parts each = 4 shares
These shares are called one fourth or quarters

Problem Solving

Solve each problem.
Question 9.
Reasoning Steve cuts one pan of cornbread into halves. He cuts another pan of cornbread into fourths. Each pan is the same size.

How many pieces did Steve cut in all? Which pieces are larger, the halves or the fourths? Use the picture to help you solve.
_______ pieces in all
The _______ are larger.
Answer:
6 pieces in all
The halves are larger.
Explanation:
1st pan is cut into 2 shares
And the 2nd pan is cut into 4 shares
2 + 4 = 6 pieces in all.
So the half pieces are larger.

Question 10.
Higher Order Thinking Burke and Alisha each have a sheet of paper. Both sheets are the same size. Burke uses one half of his sheet. Alisha uses two fourths of her sheet. Alisha says that they used equal amounts of paper.
Is she correct? Explain your answer. You can draw a picture to help.
Answer:
Yes. Alisha is correct
Explanation:
Bruke uses one half of the sheet
Alisha uses 2 fourths of the sheet

1 half = 1 fourth + 1 fourth
1 half = 2 fourth
So Alisha is correct
They used equal amounts of paper.

Question 11.
Assessment Practice Joey has two circles of the same size. He cuts one into halves and the other into fourths. Which words describe how the halves compare to the fourths?
A. smaller, more
B. smaller, fewer
C. larger, more
D. larger, fewer
Answer:
D
Explanation:
The halves are larger and fewer than the fourths.

Lesson 15.4 Problem Solving

Model with Math

Mary’s blanket is divided into 2 equal shares. One share of the blanket is yellow and the other is orange. How can you describe the share of the blanket that is yellow? Draw and color the blanket to show your work.

I can … make a drawing or diagram to show a problem about equal shares.
Answer:

Thinking Habits Can I use a drawing, diagram, table, graph, or objects to show the problem?

Visual Learning Bridge

Convince Me! Amy buys a green and blue rug. It is divided into 4 equal shares. Half of the rug is green. The rest is blue. How many shares are blue? How do you know?
Answer:
Amy buys a green and blue rug
She divides the rug into 4 equal shares

half of the rug is green = 2 fourths
that means the other half is colored blue = 2 fourths
that means 2 shares are blue

Guided Practice

Draw a picture to solve the problem. Then complete the sentence.
Question 1.
Pete makes a purple and yellow flag. The flag is divided into fourths. 2 shares are yellow. The rest of the flag is purple. How many of the shares are purple?
2 out of 1 equal shares are purple.
Answer:

2 out of 1 equal shares are purple.
2 out of 1 equal shares are yellow
there are 2 purple shares

Independent Practice

Draw a picture to solve each problem. Then complete the sentence.
Question 2.
Tracy’s pizza is cut into halves. She eats 1 of the shares. How many shares of the pizza does she eat?
Tracy eats _________ out of _________ equal shares.
Answer:
Tracy eats 1 out of 2 equal shares.
Explanation:
The pizza is cut into 2 equal shares
She eats 1 of the shares
2 halves – 1 halves = 1half
she eats 1 share of the pizza

Question 3.
Mia cut her sandwich into quarters. 2 of the shares have cheese. What share of the sandwich does NOT have cheese?
_________ out of _________ shares do NOT have cheese.
Answer:
2 out of 4 shares do NOT have cheese.

Question 4.
Algebra Color the correct number of shares to continue the pattern.

Answer:

Problem Solving

Performance Task
Question 5.
Pizza Shares
Kim cuts a pizza into 4 equal shares. She gives half of the pizza to Stephen.
Model Draw a picture to show the shares of the pizza that Stephen has.
Answer:

Question 6.
Reasoning How many shares of the pizza are left after Kim gives half to Stephen? Write the missing numbers.
_________ out of _________ shares are left.
Answer:
2 out of 4 shares are left.

Question 7.
Explain What if kim gives Stephen only I share of the pizza?
Explain how you can find the number of shares that Kim has left.
Answer:
Kim gave Stephen 1 share
no of shares Kim has now : 4 – 1 = 3 shares

Topic 15 Fluency Practice Activity

Find a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box next to the match. Find a match for every clue.

I can … add and subtract within 10.

Clues
A. 4 + 2 + 1
B. 4 – 1
C. 5 – 3
D. 2 + 2 + 2
E. 5 – 1
F. 1 + 3 + 1
G. 4 + 4
H. 1 + 3 + 6

Vocabulary Review
Understand Vocabulary

Word List
• Equal shares
• Fourths
• Halves
• Quarters

Question 1.
Fill in the blank.
I can cut my sandwich into two equal parts called _______.
Answer:
Halves
Explanation:
I can cut my sandwich into two equal parts called halves.

Question 2.
Fill in the blank.
When you share a sandwich equally with three other people, you cut it into _______.
Answer:
Equal shares
Explanation:
When you share a sandwich equally with three other people, you cut it into equal shares.

Question 3.
Fill in the blank.
If you want everyone to get the same amount of a sandwich, you need to cut it into _______.
Answer:
Quarters
If you want everyone to get the same amount of a sandwich, you need to cut it into quarters.

Question 4.
Fill in the blank.
Four people share one whole carton of juice and each person gets the same amount. The whole carton is divided into _______.
Answer:
Fourths
Explanation:
Four people share one whole carton of juice and each person gets the same amount. The whole carton is divided into fourths.

Use Vocabulary in Writing
Question 5.
Explain one way you could share a snack with one or more friends. Use at least one term from the Word List.
Answer:
I could share a snack with one or more friend by dividing it into equal shares among the friends.

Topic 15 Reteaching

Set A
You can divide a whole into shares.

4 equal shares

0 equal shares

Write the number of equal shares in each shape. If the shares are NOT equal, write 0.
Question 1.

_______ equal shares
Answer:
2 equal shares

Question 2.

_______ equal shares
Answer:
0 equal shares

Set B

You can divide shapes into equal shares. You can describe the shares using the words half or fourth.

Divide and color the shapes for each problem.
Question 3.
one half green

Answer:

Explanation:
Divide the circle into halves and color one half of the circle green.

Question 4.
One fourth orange

Answer:

Explanation:
Divide the square into one fourths and color one fourth of the square orange

Set C

You can compare shares of the same shape that are different sizes.
These circles are the same size, but they are divided differently.

The red circle has larger equal shares.
The yellow circle has more equal shares.

Divide the shapes. Then circle the words that complete the sentences.

Answer picture:

Question 5.
The blue square has smaller / larger equal shares than the green square.
Answer:
Smaller
Explanation:
The blue square has smaller equal shares than the green square.

Question 6.
The green square has more / fewer equal shares than the blue square.
Answer:
Fewer
Explanation:
The green square has fewer equal shares than the blue square.

Set D

Thinking Habits
Model with Math
How can I use math words I know to help solve the problem?
Can I use a drawing, diagram, table, graph, or objects to show the problem?

Draw a picture to solve the problem.
Question 7.
Maya’s scarf is divided into 4 equal shares. 1 share is green. 2 shares are yellow. The rest is blue. What share of the scarf is blue?
_______ out of _______ equal shares is blue.
Answer:
1 out of 4 equal shares is blue.

Topic 15 Assessment Practice

Question 1.
A. Which shape shows 2 equal shares?

Answer:
C

B. Describe the shares in your answer to A.
Answer:
C
Explanation:
If we cut the circle along the line the two pieces overlap each other,
that means the 2 halves are equal

Question 2.
A. Which shape does NOT show one fourth colored blue?

Answer:
D

B. How do you know your answer to A is correct?
Answer:
The answer to A is correct as D is not divided into 4 equal parts so it does not have one fourth of the figure colored blue.

Question 3.
Divide the rectangle into halves. Then color half of the rectangle.
Explain how you know that you colored the right amount.

Answer:

Explanation:
First draw a line to divide the rectangle into 2 equal shares
Color 1 half of the rectangle

Question 4.
Compare the two shapes. Circle two ways to describe the equal shares in each.

Answer:

Question 5.
Ron draws a flag divided into 4 equal shares. 2 shares are purple and the rest are blue. How many shares of the flag are blue?
Draw a picture to solve the problem. Then complete the sentence.
_______ out of _______ equal shares are blue.
Answer:
2 out of 4 equal shares are blue.
Explanation:
Total shares : 4
Purple shares : 2
Blue share :4 – 2 = 2 shares

Topic 15 Performance Task

Kerry’s Kitchen Kerry loves to cook! She makes many different foods.
Question 1.
Kerry bakes a loaf of bread. She cuts it into equal shares. How many equal shares are there?

Answer:
4 equal shares.
Explanation:
Count the number of shares of the bread

There are 4 equal shares.

Question 2.
Kerry makes a pizza.
She cuts it so that she and her sister each get an equal share. What are the shares called? _______
Show two ways that Kerry could divide the pizza.

Answer:
One fourths

Explanation:
Kerry divided the pizza into 4 equal shares
So she and her sister gets equal amount of shares

Question 3.
Kerry makes a sandwich. She eats one half of it. Color to show how much she ate.

How many halves make the whole sandwich?
_______ halves

Answer:
2 halves

Explanation:
Half means 2 equal shares
If we divide the sandwich into 2 equal shares
There will be 2 halves
Kerry eats 1 half
so there is 1 more half of the sandwich left
Draw a line in the middle of the sandwich
Color one of the halves of the sandwich like in the picture below

Question 4.
Kerry makes a pan of oatmeal bars. She cuts up the bars.
Kerry says that she divided the bars into fourths.

Is she correct? Circle Yes or No.
Explain your answer.
Answer:

Explanation:
Dividing into fourths means every bar is the same size
Kerry divided incorrectly
Kerry must divide it like in the picture below:

Question 5.
Kerry makes a salad.
She cuts a tomato into four equal shares. She puts I equal share of the tomato in the salad.
Part A
Draw a picture to show the share of the tomato that is in the salad.

Part B
The equal shares that Kerry cut are called fourths.
What is another name for these shares?
Answer:
Quarters

Part C
How many fourths are in the whole tomato?
There are _______ fourths in the whole tomato.
Answer:
There are 4 fourths in the whole tomato.

Go through the enVision Math Common Core Grade 3 Answer Key Topic 14 Solve Time, Capacity, and Mass Problems regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 14 Solve Time, Capacity, and Mass Problems

Essential Question:
How can time, capacity, and mass be measured and found?

Answer:
The time is measured in hours.
the capacity is measured in liters.
the mass is measured in grams.

Explanation:
In the above-given question,
given that,
1 hour = 60 min.
1000 ml = 1 liter.
1000 g = 1 kg.
The time is measured in hours.
the capacity is measured in liters.
the mass is measured in grams.

enVision STEM Project: Forces and Interactions
Do Research Use the Internet or other sources to find information about magnets. How are magnets used? What types of magnets are there? Attach different amounts of paper together using a metal paper clip. How can you lift the paper using the magnet? How much mass can the magnet lift?

Answer:
There are three types of magnets are there.

Explanation:
In the above-given question,
given that,
there are three types of magnets are there.
they are permanent magnets, temporary magnets, and electromagnets.
Magnet is defined as a material that can produce its own magnetic field.
permanent magnets are magnets that are used permanently.
temporary magnets are used as per the situation.
electro magnets are used due to the support of an electric field.

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

• Give examples of magnetic and non-magnetic materials.
• Find the masses of the paper clip and of the paper.
• Write an equation to show how much mass you can lift using the magnet.

Review What You Know

Vocabulary

• denominator
• numerator
• number line
• unit fraction

Choose the best term from the box. Write it on the blank.
Question 1.
The _________ tells the number of repetitions of the unit fraction.

Answer:
The numerator tells the number of repetitions of the unit fraction.

Explanation:
In the above-given question,
given that,
the numerator tells the number of repetitions of the unit fraction.
for example:
the numerator is 1.
the denominator tells how many equal parts are there.
examples of the unit fractions are 1/2, 1/3, 1/4, and 1/8.
so the numerator tells the number of repetitions of the unit fraction.

Question 2.
The ________ tells what fractional part is being counted.

Answer:
The denominator tells what fractional part is being counted.

Explanation:
In the above-given question,
given that,
the denominator tells what fractional part is being counted.
for example:
2/8 = 1/4.
so the denominator tells what fractional part is being counted.

Question 3.
One equal part of a whole can be represented using a _________

Answer:
One equal part of a whole can be represented using a number line.

Explanation:
In the above-given question,
given that,
one equal part of a whole can be represented using a number line.
for example:
if the number line is divided into 4 parts.
the fractions can be written as 1/4, 2/4, 3/4, and 4/4.
one equal part of a whole can be represented using a number line.

Solving 2-Step Problems
Question 4.
Mr. Vernon rides a train for 188 miles. Then he rides a subway for 9 stops. Each stop is 2 miles apart. How far does he travel?

Answer:
The number of miles Mr. Vernon rides = 206 miles.

Explanation:
In the above-given question,
given that,
Mr. Vernon rides a train for 188 miles.
then he rides a subway for 9 stops.
each stop is 2 miles apart.
9 x 2 = 18.
188 + 18 = 206.
so the number of miles Mr.Vernon rides = 206 miles.

Question 5.
Ms. Slate has a box of 320 new light bulbs. She replaces the light bulbs in 50 lamps. Each lamp has 5 sockets. How many new light bulbs does Ms. Slate have left?

Answer:
The number of light bulbs does Ms. Slate has left = 70 bulbs.

Explanation:
In the above-given question,
given that,
Ms. Slate has a box of 320 new light bulbs.
She replaces the light bulbs in 50 lams.
each lamp has 5 sockets.
50 x 5 = 250.
320 – 250 = 70.
so the number of light bubls does Ms. Slate has left = 70 bulbs.

Number Lines

Label the missing numbers on the number lines.
Question 6.

Answer:
The missing numbers on the number line are 2/6, 4/6, 5/6, 6/6, 7/6, and 1.

Explanation:
In the above-given question,
given that,
label the missing numbers on the number lines.
the number line is divided into 6 parts.
the missing numbers are 2/6, 4/6, 5/6, 6/6, 7/6, and 1.
so the missing number is 2/6, 4/6, 5/6, 7/6, and 1.

Question 7.

Answer:
The missing numbers are 50, 100, 150, 200, 350, and 400.

Explanation:
In the above-given question,
given that,
label the missing numbers on the number line.
the distance between each point is 50.
so the starting point is 50.
50 + 50 = 100, 100 + 50 = 150, 150 + 50 = 200, 200 + 50 = 250, 250 + 50 = 300.
so the missing numbers are 50, 100, 150, 200, 350, and 400.

Fractions

Question 8.
Rena divides a square into 8 equal parts. What unit fraction should she write as a label for each of the parts?
A. \(\frac{0}{8}\)
B. \(\frac{1}{8}\)
C. \(\frac{8}{8}\)
D. \(\frac{8}{1}\)

Answer:
Option B is the correct answer.

Explanation:
In the above-given question,
given that,
Rena divides a square into 8 equal parts.
1/8 is the correct fraction.
so option B is the correct answer.

Question 9.
Write two fractions that are equal to 1.

Answer:
The two fractions are 5/5 and 1/1.

Explanation:
In the above-given question,
given that,
the two fractions that are equal to 1 are,
5/5 = 1.
1/1 = 1.
so the two fractions are 5/5 and 1/1.

Pick a Project

PROJECT 14A
How do you show elapsed time on a clock?
Project: Write and Tell a Story About Time

Answer:
The time is 11:55.

Explanation:
In the above-given question,
given that,
the minute hand is on the 11.
the hour hand is on the 12.
so the time is 11:55.
5 x 11 = 55.
so the time is 11:55.

PROJECT 14B
What is the best way to plan for a full day?
Project: Create and Play a Matching Game

Answer:
The numbers 12 and 29 comes on Saturday and Tuesday.

Explanation:
In the above-given question,
given that,
the numbers on the calendar are:
1, 2, 3, 4, 5, 6, …..and 31.
the numbers are 12 and 29 comes on Saturday and Tuesday.

PROJECT 14C
How did people tell time before clocks?
Project: Design and Make a Sundial

PROJECT 14D
What is your favorite recipe?
Project: Perform a Song About the Masses of Objects

Lesson 14.1 Time to the Minute

Solve & Share
Xander and his mother are visiting a store. In the store, there are many clocks on the shelves. The clocks show different times. Tell the times shown on each of the clocks below.
I can … show and tell time to the minute using clocks.

Answer:
The times are 1’o clock, 5’30, and 5:55.

Explanation:
In the above-given question,
given that,
in the 1st watch, the minute hand is on the 12 and the hour hand on the 1.
so the time is 1:00.
in the 2nd watch, the minute hand is on the 6 and the hour hand on the 5.
so the time is 5:30.
in the 3rd watch, the minute hand is on the 11 and the hour hand on the 6.
so the time is 5:55.

Look Back! Xander and his mother leave the store at 8:47. How can you use the clock to show this time?

Answer:
The minute hand is on the 9 and the hour hand is on the 8.

Explanation:
In the above-given question,
given that,
Xander and his mother leave the store at 8:47.
the minute hand is on the 9.
the hour hand is on the 8.
so the time is 8:47.

Essential Question
How Do You Tell Time to on the Nearest Minute?

Visual Learning Bridge
The clock shows the time a train from Memphis is scheduled to arrive at Central Station. What time is the train scheduled to arrive? Write the time in digital form and in two other ways.

Convince Me! Model with Math A train arrives from Atlanta one hour after the Memphis train. Write the arrival time of the Atlanta train in digital form and two other ways. Use a clock face to help.

Guided Practice

Do You Understand?
Question 1.
In the Memphis train example, why is 42 minutes after 12 o’clock the same as 18 minutes before 1 o’clock? Explain.

Answer:
The 42 minutes after 12 o’clock is the same as 18 minutes before 1 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 8 after two small points.
5 x 8 = 40.
40 + 2 = 42.
the hour hand is in between 12 and 1.
the time is 12:42.
so the 42 minutes after 12 o’clock is the same as 18 minutes before 1 o’clock.

Question 2.
An airplane landed at 3:55. Does the clock show the time the airplane landed? Explain.

Answer:
Yes, the time is correct.

Explanation:
In the above-given question,
given that,
the minute hand is on the 11.
the hour hand is on the 3.
5 x 11 = 55.
so the time is 3:55.
the time is correct.

Do You Know How?
In 3 and 4, write the time shown on each clock in two ways.
Question 3.

Answer:
The time is 3:12 and 12 minutes after 3 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 2.
the hour hand is on the 3.
the time is 12 minutes after 3 o’clock.
5 x 2 = 10.
10 + 2 = 12.
so the time is 3:12.

Question 4.

Answer:
The time is 5:43 and 43 minutes after 5 o’clock .

Explanation:
In the above-given question,
given that,
the minute hand is on the 5.
the hour hand is on the 8.
5 x 8 = 40.
40 + 3 = 43.
so the time is 5:43.
the time is 43 minutes after 5 o’clock.

Independent Practice

In 5-7, write the time shown on each clock in two ways.
Question 5.

Answer:
The time is 11:20 and 20 minutes after 11 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 4.
the hour hand is on the 11.
the time is 20 minutes after 11 o’clock.
5 x 4 = 20.
so the time is 11:20.

Question 6.

Answer:
The time is 7:39 and 21 minutes before 8 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 7.
the hour hand is on the 7.
the time is 21 minutes before 8 o’clock.
5 x 7 = 35.
35 + 2 = 37.
so the time is 7:39.

Question 7.

Answer:
The time is 8:44.

Explanation:
In the above-given question,
given that,
the minute hand is on the 2.
the hour hand is on the 3.
5 x 2 = 10.
10 + 2 = 12.
so the time is 3:12.

Problem Solving

In 8 and 9, use the table.

Question 8.
Roy says that the scarf and the hat together cost about the same amount as a blanket and a hat. Is this a reasonable estimate? Explain.

Answer:
No, it is not reasonable.

Explanation:
In the above-given question,
given that,
Roy says that the scarf and the hat together cost about the same amount as a blanket and a hat.
the scarf cost $18.
the hat cost $12.
blanket cost $19.
18 + 12 = 30.
19 + 12 = 31.
so both are not same.

Question 9.
What did Jorge buy at the sale if $19 + $19+ $19+ $18 stands for the total cost of his purchase?

Answer:
The total cost is $75.

Explanation:
In the above-given question,
given that,
Jorge buy at the sale $19 + $19 + $19 + $18.
19 + 19 = 38.
19 + 18 = 37.
37 + 38 = 75.
so the total cost is $75.

Question 10.
Be Precise Mia left her house at 25 minutes before 3 o’clock. Draw hands on the clock to show when she left.

Answer:
The time is 2:35.

Explanation:
In the above-given question,
given that,
Mia left her house 25 minutes before 3 o’clock.
the minute hand is on the 7.
the hour hand is on the 2.
5 x 7 = 35.
so the time is 2:35.

Question 11.
Higher Order Thinking Sandra’s party started at 7:00. Her friends Theo and Lily arrive at 10 minutes after 7 o’clock. Her friend Marcus arrives 35 minutes after Theo and Lily. What time did Marcus arrive? Write this time in two other ways.

Answer:
The time did Marcus arrive = 7:45.

Explanation:
In the above-given question,
given that,
Sandra’s party started at 7:00.
Theo and Lily arrive 10 minutes after 7 o’clock.
Her friend Marcus arrives 35 minutes after Theo and Lily.
7:10 + 35 = 7:45.
so the time Marcus arrive = 7:45.

Assessment Practice

Question 12.
Clay and his family sit down to eat dinner at the time shown on the clock. Which of the following are other ways to write that time? Select all that apply.

☐ 3 : 25
☐ 5 : 16
☐ 16 minutes after 5 o’clock
☐ 44 minutes before 5 o’clock
☐ 16 minutes before 5 o’clock

Answer:
The time is 5:16 and 16 minutes after 5 o’clock.

Explanation:
In the above-given question,
given that,
the minute hand is on the 3 after 1 point.
the hour hand is on the 5.
5 x 3 = 15.
15 + 1 = 16.
so the time is 5:16 and 16 minutes after 5 o’clock.

Question 13.
Mary Ann called her grandmother. She ended the call at the time shown on the clock. Which of the following are NOT other ways to write this time? Select all that apply.

☐ 14 minutes before 9 o’clock
☐ 3 : 46
☐ 46 minutes after 3 o’clock
☐ 9 : 19
☐ 14 minutes before 4 o’clock

Answer:
The wrong options are 3:46 and 14 minutes before 9 o’clock.

Explanation:
In the above-given question,
given that,
Mary Ann called her grandmother.
She ended the call at the time shown on the clock.
so the minute hand is on the 9.
the hour hand is in between 3 and 4.
5 x 9 = 45.
45 + 1 = 46.
so the time is 3:46.

Lesson 14.2 Units of Time: Measure Elapsed Time

Solve & Share
Denise went to see a movie. The movie started at 1:05 P.M. It ended at 2:35 P.M. How long did the movie last? Explain your reasoning.
I can… measure intervals of time in hours and minutes.

Look Back! Without counting hours and minutes, how do you know the movie Denise went to see was less than 2 hours long?

Answer:
The number of minutes the movie lasts = 1 hour 30 minutes.

Explanation:
In the above-given question,
given that,
Denise went to see a movie. The movie started at 1:05 P.M.
It ended at 2:35 P.M.
2:35 – 1:05 = 1:30.
so the number of minutes the movie lasts = 1 hour 30 minutes.

Essential Question
How Can You Find Elapsed Time?

Visual Learning Bridge
Janey took part in a charity walk. The walk started at 7:10 A.M. It ended at 11:20 A.M. How long did the walk last?

Convince Me! Make Sense and Persevere After the charity walk, Janey talked with friends from 11:25 A.M. to 11:40 A.M. Then lunch was served from 11:45 A.M. until 2:10 P.M. How long did lunch last?

Another Example!
You can also use a number line to measure elapsed time.
Janey’s charity walk lasted 4 hours, 10 minutes.
The number line shows the number of hours and minutes that elapsed during the walk.

Guided Practice

Do You Understand?
Question 1.
If a start time is 7:15 A.M. and an end time is 7:45 A.M., why do you not have to count hours to find the elapsed time?

Answer:
The elapsed time is 7:30 A.M.

Explanation:
In the above-given question,
given that,
If a start time is 7:15 A.M. and an end time is 7:45 A.M.
7:45 – 7:15 = 7:30.
so the elapsed time is 7 hours 30 minutes.

Question 2.
A movie started at 2:30 P.M. and ran for 2 hours, 15 minutes. What time did the movie end?

Answer:
The time did the movie end = 4:45 P.M.

Explanation:
In the above-given question,
given that,
The movie started at 2:30 P.M and ran for 2 hours, 15 minutes.
30 + 15 = 45.
2 + 2 = 4.
so the time did movie end = 4:45 P.M.

Do You Know How?
Question 3.
Draw a number line to count the hours from 11:00 A.M. to 5:00 P.M. What is the elapsed time?

Answer:
The elapsed time = 6 hours.

Explanation:
In the above-given question,
given that,
hours from 11 to 5 is 6 hours.
the time is 11:A.M to 5:00 P.M.
11 + 1 = 12.
1 + 5 = 6.
so the elapsed time is 6 hours.

Independent Practice

Leveled Practice In 4-7, use clocks or number lines to find the elapsed or end time.

Question 4.
Hours from 6:30 P.M. to 9:30 P.M. ___________
Minutes from 9:30 P.M. to 9:50 P.M. ___________
The elapsed time is ___________ hours, ___________ minutes.

Answer:
3 hours.
20 minutes.
the elapsed time is 3 hours and 20 minutes.

Explanation:
In the above-given question,
given that,
the hours from 6:30 P.M to 9:30 P.M is 6 + 3 = 9.
the minutes from 9:30 P.M to 9:50 P.M is 30 + 20 = 50.
9 – 6 = 3.
50 – 20 = 30.
so the elapsed time is 3 hours and 20 minutes.

Question 5.
Start Time: 10:00 A.M.
End Time: 3:00 P.M.
Elapsed Time: ___________

Answer:
The elapsed time = 5 hours.

Explanation:
In the above-given question,
given that,
Start Time: 10:00 A.M.
End Time: 3:00 P.M.
10 A.M + 1 = 11 + 1 = 12.
12 + 1 = 1.
1 + 2 = 3.
3  + 2 = 5 hours.

Question 6.
Start Time: 9:15 A.M.
End Time: 10:45 A.M.
Elapsed Time: ___________

Answer:
The elapsed time = 1 hour 30 minutes.

Explanation:
In the above-given question,
given that,
Start Time: 9:15 A.M.
End Time: 10:45 A.M.
45 – 15 = 30.
10 – 1 = 9.
so the elapsed time is 1 hour 30 minutes.

Question 7.
Start Time: 11:30 A.M.
Elapsed Time: 5 hours, 25 minutes
End Time: ___________

Answer:
The End time = 4:55 P.M.

Explanation:
In the above-given question,
given that,
Start Time: 11:30 A.M.
Elapsed Time: 5 hours, 25 minutes
11:30 + 5 = 4:30.
30 + 25 = 55.
so the End Time = 4:55 P.M.

Problem Solving

In 8 and 9, use the list at the right.

Question 8.
Reasoning Mr. Flores made a list of the times it takes for different items to bake. Which items will take less than \(\frac{1}{2}\) hour to bake?

Answer:
The items that take half an hour to bake are bread, granola bars, vegetables.

Explanation:
In the above-given question,
given that,
Mr. Flores made a list of the times it takes for different items to bake.
1/2 hour = 30 minutes.
bread will bake in 27 minutes.
granola bars bake in 21 minutes.
vegetables bake in 24 minutes.
The pasta dish bakes in 48 minutes.
so the items that take half an hour to bake are bread, granola bars, vegetables.

Question 9.
Which two items, when you add their baking time together, take less time to bake than the pasta dish?

Answer:
The two items that take less time to bake are granola bars and vegetables.

Explanation:
In the above-given question,
given that,
Mr. Flores made a list of the times it takes for different items to bake.
1/2 hour = 30 minutes.
bread will bake in 27 minutes.
granola bars bake in 21 minutes.
vegetables bake in 24 minutes.
The pasta dish bakes in 48 minutes.
21 + 24 = 45.
so the two items that take less time to bake are granola bars and vegetables.

Question 10.
Sally finds elapsed time using these clock faces. She counts the hours by 1s, but counts the minutes by 5s. Why does she count the minutes by 5s instead of by 1s?

Answer:
The elapsed time = 5 hours 15 minutes.

Explanation:
In the above-given question,
given that,
Sally finds elapsed time using these clock faces.
She counts the hours by 1s but counts the minutes by 5s.
minutes hand is between 5 seconds.
hours hand is between 5 minutes.
the start time = 3 :30.
the end time = 8:45.
45 – 30 = 15.
8 – 3 = 5.
so the elapsed time = 5 hours 15 minutes.

Question 11.
Higher Order Thinking A basketball tournament started at 12:15 P.M. and ended at 4:00 P.M. Did the tournament last more than 4 hours? Explain.

Answer:
No, the tournament did not last more than 4 hours.

Explanation:
In the above-given question,
given that,
A basketball tournament started at 12:15 P.M. and ended at 4:00 P.M.
12:15 + 1 hour = 1:15.
1 :15 + 2 hours = 3:15.
3 :15 + 1 hour = 4:15.
so the tournament last for 3 hours 15 minutes.

Question 12.
Algebra A farmer is selling 744 pieces of produce. He has 162 watermelons, 345 ears of sweet corn, and some avocados. Write and solve an equation to find how many avocados the farmer is selling. Let x stand for the unknown quantity of avocados.

Answer:
The number of avocados = 237.

Explanation:
In the above-given question,
given that,
A farmer is selling 744 pieces of produce.
He has 162 watermelons, 345 ears of sweet corn, and some avocados.
345 + 162 = 507.
744 – 507 = 237.
so the number of avocados = 237.

Assessment Practice

Question 13.
Geo is taking a train from Carlton to Elgin. The train leaves Carlton at 9:25 A.M. and reaches Elgin 9:25 A.M. at 10:55 A.M. How long does the ride last? Use the leave number line to help.

A. 30 minutes
B. 1 hour
C. 1 hour, 30 minutes
D. 2 hours

Answer:
Option C is the correct answer.
The long does the ride last = 1 hour 30 minutes.

Explanation:
In the above-given question,
given that,
Geo is taking a train from Carlton to Elgin.
The train leaves Carlton at 9:25 A.M. and reaches Elgin at 9:25 A.M. at 10:55 A.M.
9 + 1 = 10.
25 + 30 = 55.
so the time is 10:55.
option c is the correct answer.

Lesson 14.3 Units of Time: Solve Word Problems

Solve & Share
Madison wants to exercise 30 minutes every day. Before school, she only has enough time to exercise for 10 minutes or less. One day, she exercised for 8 minutes before school and 22 minutes after school. This is one way she can exercise for 30 minutes. Find two other ways she can exercise before school and after school to reach her goal of exercising for 30 minutes each day.
I can … use representations to solve word problems about time.

Look Back! Do you think there are more than two ways to solve the problem above? Explain.

Answer:
She exercised for 4 minutes before school and 26 minutes after school.
the other way is 5 minutes before school and 25 minutes after school.

Explanation:
In the above-given question,
given that,
Madison wants to exercise 30 minutes every day.
4 + 26 = 30.
5 + 25 = 30.
so she exercised for 4 minutes before school and 26 minutes after school.
the other way is 5 minutes before school and 25 minutes after school.

Essential Question
How Can You Add or Subtract on Time Intervals?

Visual Learning Bridge
Joaquin made a list of the time he should spend on different activities. Joaquin has practiced playing the piano 35 minutes so far. How much longer does he need to practice?

One Way
You can use a bar diagram to represent the problem and show time intervals.

Another Way
You can use a number line to represent the problem and show time intervals.

Convince Me! Model with Math How much longer will it take Joaquin to finish all of his after-school activities? Show one way to represent and solve.

Answer:
The longer will it take Joaquin to finish all of his after-school activities = 155 minutes.

Explanation:
In the above-given question,
given that,
play with Ron for 50 minutes.
practice piano for 45 minutes.
homework 60 minutes.
50 + 45 + 60 = 155.
so the longer will it take Joaquin to finish all of his after-sccool activities = 155 minutes.

Guided Practice

Do You Understand?
In 1 and 2, complete the bar diagram or number line to solve.
Question 1.
Rhody plans to ride his bicycle for 55 minutes. So far, he has ridden for 29 minutes. How many more minutes does he have to ride?

Answer:
The more minutes he wants to ride = 26 minutes.

Explanation:
In the above-given question,
given that,
Rhody plans to ride his bicycle for 55 minutes.
So far, he has ridden for 29 minutes.
55 – 29 = 26.
so the more minutes he wants to ride = 26 minutes.

Do You Know How?
Question 2.
Ms. Darren spends the reading period working with two different reading groups. She meets with the first group for 23 minutes and meets with the second group for 17 minutes. How long is the reading period?

Answer:
The long is the reading period = 40 minutes.

Explanation:
In the above-given question,
given that,
Ms. Darren spends the reading period working with two different reading groups.
She meets with the first group for 23 minutes and meets with the second group for 17 minutes.
23 + 17 = 40.
so the long is the reading period = 40 minutes.

Independent Practice

Leveled Practice In 3-6, complete or draw a bar diagram or number line to solve.
Question 3.
Claire and Owen played video games. The first game lasted 24 minutes. After the first game, Claire and Owen had lunch for 30 minutes. The second game lasted 36 minutes. How many minutes did they play the games?

Answer:
The number of minutes did they play the games = 60.

Explanation:
In the above-given question,
given that,
Claire and Owen played video games.
The first game lasted 24 minutes.
After the first game, Claire and Owen had lunch for 30 minutes.
The second game lasted 36 minutes.
24 + 36 = 60.
so the number of minutes did they play the games = 60.

Question 4.
Yan jogged for 60 minutes on Friday. Dino jogged 12 fewer minutes than Yan. Both friends swim for 40 minutes each week. How many minutes did Dino jog on Friday?

Answer:
The number of minutes did Dino jog on Friday = 48 minutes.

Explanation:
In the above-given question,
given that,
Yan jogged for 60 minutes on Friday.
Dino jogged 12 fewer minutes than Yan.
Both friends swim for 40 minutes each week.
60 -12 = 48.
so the number of minutes did Dino jog on Friday = 48 minutes.

Question 5.
Mr. Hart’s class is putting on a play. The play is divided into two acts. Each act lasts 27 minutes. How many minutes long is the play?

Answer:
The number of minutes that long the play = 54 minutes.

Explanation:
In the above-given question,
given that,
Mr. Hart’s class is putting on a play.
The play is divided into two acts.
Each act lasts 27 minutes.
27 + 27 = 54.
so the number of minutes that long the play = 54 minutes.

Question 6.
A chef wants to bake a dish for 30 minutes. So far, the dish has been baking for 12 minutes. How many more minutes does the dish need to bake?

Answer:
The more minutes the dish needs to bake = 18 minutes.

Explanation:
In the above-given question,
given that,
A chef wants to bake a dish for 30 minutes.
So far, the dish has been baking for 12 minutes.
30 – 12 = 18.
so the more minutes the dish needs to bake = 18 minutes.

Problem Solving

Question 7.
Reasoning Ms. Merrill spends 55 minutes washing all the windows in her two-story house. How much time could she have spent on each floor? Complete the chart to show three different ways.

Answer:
25 + 30 = 55.
30 + 25 = 55.
20 + 35 = 55.

Explanation:
In the above-given question,
given that,
Ms. Merrill spends 55 minutes washing all the windows in her two-story house.
On the 1st floor, he spends 25 minutes, and 2nd floor he spends 30 minutes.
30 + 25 = 55.
20 + 35 = 55.
so that are the three ways to wash all the windows.

Question 8.
Number Sense Harry measures a sticker that is \(\frac{4}{2}\) inches. Rhea’s sticker is \(\frac{6}{2}\) inches. Whose sticker is longer? Explain.

Answer:
Rhea’s sticker was long.

Explanation:
In the above-given question,
given that,
Harry measures a sticker that is \(\frac{4}{2}\) inches.
Rhea’s sticker is \(\frac{6}{2}\) inches.
4/2 = 2.
6/2 = 3.
so Rhea’s sticker was long.

Question 9.
Higher Order Thinking Mr. Collins is learning to drive a truck. He drives 22 minutes on Monday and 14 minutes on Tuesday. Finally, he drives 6 more minutes on Wednesday than he did on Tuesday. How many total minutes does he practice driving a truck?

Answer:
The total number of minutes does he practice driving a truck = 56 minutes.

Explanation:
In the above-given question,
given that,
Mr. Collins is learning to drive a truck.
He drives 22 minutes on Monday and 14 minutes on Tuesday.
he drives 6 more minutes on Wednesday than he did on Tuesday.
22 + 14 + 20 = 56.
so the total number of minutes does he practice driving a truck = 56 minutes.

Assessment Practice

Question 10.
Sonya hikes up a mountain. It takes her 25 minutes to hike to a cliff that is partway up the mountain. After that, she hikes for 17 more minutes to the summit. Use the number line and complete the table to show how many total minutes Sonya spends hiking.

Answer:
The total number of minutes Sonya spends hiking = 42.

Explanation:
In the above-given question,
given that,
Sonya hikes up a mountain.
It takes her 25 minutes to hike to a cliff that is partway up the mountain.
After that, she hikes for 17 more minutes to the summit.
25 + 17 = 42.
so the total number of minutes Sonya spends hiking = 42.

Question 11.
Meg walks a dog named Shep for 12 minutes. Then she walks Sparky. Finally, she walks Brownie for 18 minutes. Meg spends 52 minutes walking all three dogs. Use the number line and complete the table to show how many minutes Meg spends walking each dog.

Answer:
The number of minutes Meg spends walking each dog = 22 minutes.

Explanation:
In the above-given question,
given that,
Meg walks a dog named Shep for 12 minutes.
Then she walks Sparky.
Finally, she walks Brownie for 18 minutes.
Meg spends 52 minutes walking all three dogs.
18 + 12 = 30.
52 – 30 = 22.
so the number of minutes Meg spends walking each dog = 22 minutes.

Lesson 14.4 Estimate Liquid Volume

Solve & Share
The water bottle below has a capacity of 1 liter. Estimate the capacity of a small bowl, a large bowl, and a pitcher to the nearest half liter. Use an actual 1-liter water bottle, small and large bowls, and a pitcher to solve this problem.
I can … use a standard unit to estimate liquid volume.

Look Back! After you estimate the capacity of the containers, how can you use a 1-liter water bottle to check that your estimate for each container is reasonable? Check your estimates.

Essential Question
Do You Estimate Capacity?

Visual Learning Bridge
What is the capacity of the pail?

Compare the capacity of the water bottle to the capacity of the pail.

The pail appears to be large enough to hold several liters.
Count how many times you can fill a liter container and empty it into the pail.
This pail holds about 8 liters.

Convince Me! Be Precise Suppose you want to estimate the capacity of the pail to the nearest half liter. How can you check that your estimate is reasonable?

Guided Practice

Do You Understand?
Question 1.
Susie estimates the capacity of a water glass as 3 liters. Hakim estimates the capacity as á liter. Is Susie’s or Hakim’s estimate more reasonable? Explain.

Answer:
Hakim estimates the capacity as a liter was more reasonable.

Explanation:
In the above-given question,
given that,
Susie estimates the capacity of a water glass as 3 liters.
Hakim estimates the capacity as a liter.
so Hakim’s estimation was correct.

Question 2.
Find a container that you predict will hold more than a liter and another that you predict will hold less than a liter. Use a liter container to check your predictions by finding the actual capacity of each container.

Answer:
The containers are a small bowl and a large bowl.

Explanation:
In the above-given question,
given that,
container that you predict will hold more than a liter and another that you predict will hold less than a liter.
container hold exactly 1 liter.
a small bowl holds less than a liter.
A large bowl holds more than a liter.
so the containers are a small bowl and a large bowl.

Do You Know How?
In 3-6, circle the better estimate for each.
Question 3.

\(\frac{1}{4}\) L or 2 L

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 2 liters.
the glass holds 1/4 liter.
so the better estimate is 1/4 liters.

Question 4.

100 L or 1 L

Answer:
The better estimate is 100 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1 liter and 100 liters.
the bucket holds 100 liters.
so the better estimate is 100 liters.

Question 5.
Bottle of juice
3 L or 1L

Answer:
The better estimate is 1 liter.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1 liter and 3 liters.
the bottle holds 1 liter.
so the better estimate is 1 liter.

Question 6.
Cereal bowl
\(\frac{1}{4}\) L or 3 L

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 3 liters.
the cereal bowl holds 1/4 liter.
so the better estimate is 1/4 liters.

Independent Practice

In 7-14, circle the better estimate for each.
Question 7.

\(\frac{1}{4}\) L or 40 L

Answer:
The better estimate is 40 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 40 liters.
the glass aquarium holds 40 liters.
so the better estimate is 40 liters.

Question 8.

\(\frac{1}{8}\) L or 1 L

Answer:
The better estimate is 1/8 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/8 liter and 1 liter.
the spoon holds 1/8 liter.
so the better estimate is 1/8 liters.

Question 9.

\(\frac{1}{2}\) L or 14 L

Answer:
The better estimate is 1/2 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/2 liter and 14 liters.
the glass holds 1/2 liter.
so the better estimate is 1/2 liters.

Question 10

\(\frac{1}{4}\) L or 250 L

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 250 liters.
the juice holds 1/4 liter.
so the better estimate is 1/4 liters.

Question 11.
Teacup
\(\frac{1}{4}\) L or 15 L

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 15 liters.
the teacup holds 1/4 liter.
so the better estimate is 1/4 liters.

Question 12.
Bathtub
15 L or 115 L

Answer:
The better estimate is 115 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
15 liter and 115 liters.
the bathtub holds 115 liters.
so the better estimate is 115 liters.

Question 13.
Soup bowl
\(\frac{1}{2}\) L or 3 L

Answer:
The better estimate is 1/2 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/2 liter and 3 liters.
the soup bowl holds 1/2 liter.
so the better estimate is 1/2 liters.

Question 14.
Teapot
1 L or 10 L

Answer:
The better estimate is 1 liter.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1 liter and 10 liters.
the teapot holds 1/4 liter.
so the better estimate is 1 liters.

Question 15.
Write an estimate for the capacity of a dog bowl. _________

Answer:
The better estimate is 1/4 liters.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1/4 liter and 2 liters.
the dogbowl holds 1/4 liter.
so the better estimate is 1/4 liters.

Question 16.
Write an estimate for the capacity of a flower vase. __________

Answer:
The better estimate is 1 liter.

Explanation:
In the above-given question,
given that,
circle the better estimates for each.
1 liter and 2 liters.
the flower vase holds 1 liter.
so the better estimate is 1 liter.

Problem Solving

Question 17.
Generalize Which cooler has the greater capacity? Explain your thinking

Answer:
Cooler B has the greatest capacity.

Explanation:
In the above-given question,
given that,
the two coolers with different capacities.
cooler A has a small capacity.
cooler B has a larger capacity.

Question 18.
List these containers in order from least capacity to greatest capacity.
Washing machine
Large pot
Soup spoon
Travel mug

Answer:
The containers from least to greatest = soup spoon, travel mug, large pot, and washing machine.

Explanation:
In the above-given question,
given that,
there are 4 containers.
they are a washing machine, large pot, soup spoon, travel mug.
soup spoon, travel mug, large pot, and washing machine.
so the containers from least to greatest = soup spoon, travel mug, large pot, and washing machine.

Question 19.
A basketball team scores 27 points in its first game and 41 points in its second game. After three games, it scores 100 points in all. How many points does the team score in its third game?

Answer:
The number of points does the team score in its third game = 32 points.

Explanation:
In the above-given question,
given that,
A basketball team scores 27 points in its first game and 41 points in its second game.
After three games, it scores 100 points in all.
27 + 41 = 68.
100 – 68 = 32.
so the number of points does the team score in its third game = 32 points.

Question 20.
Higher Order Thinking Becky wants to measure the capacity of her brother’s baby pool. She has a 1-liter container and a 10-liter container. Which should she use? Explain your reasoning.

Answer:
The capacity of her brother’s baby pool is a 10-liter container.

Explanation:
In the above-given question,
given that,
Becky wants to measure the capacity of her brother’s baby pool.
She has a 1-liter container and a 10-liter container.
so a 10-liter container is the capacity of her brother’s pool.

Question 21.
A sandgrouse can soak up water in its fluffy feathers. It can carry the water a long way to its chicks. Does a sandgrouse carry \(\frac{1}{10}\) liter of water or 2 liters of water?

Answer:
Sandgrouse carries 1/10 liter of water.

Explanation:
In the above-given question,
given that,
A sandgrouse can soak up water in its fluffy feathers.
It can carry the water a long way to its chicks.
sandgrouse can carry 1/10 liter of water.

Assessment Practice

Question 22.
Gary is painting a small storage shed. He estimates that he can do the job with one can of paint. Which of the following is the best estimate of the total liquid volume of a can of paint?

A. \(\frac{1}{4}\) liter
B. 4 liter
C. 40 liters
D. 400 liters

Answer:
The best estimate of the total liquid volume of a can of paint = 4 liters.

Explanation:
In the above-given question,
given that,
Gary is painting a small storage shed.
He estimates that he can do the job with one can of paint.
the best estimate of the total liquid volume of a can of paint = 4 liters.

Lesson 14.5 Measure Liquid Volume

Solve & Share
Select six different containers. Estimate the capacity of each container. Record your estimates in the table, and arrange the containers in order from least to greatest liquid volume. Then use a marked liter beaker to measure the capacity of each container. Record your measurements in the table. Compare your estimates to your measures. Using your measures, rearrange the containers in order from least to greatest liquid volume.
I can … use a standard unit to measure liquid volume.

Answer:
The containers in order from least to greatest are teacup, glass, mug, bottle, tea jar, kettle, and bucket.

Explanation:
In the above-given question,
given that,
they have given 7 containers.
they are teacup, glass, mug, bottle, tea jar, kettle, and bucket.
teacup = 1/4 liter.
glass = 1/3 liter.
mug = 1/8 liter.
bottle = 1 liter.
tea jar = 1/2 liter.
kettle = 3/4 liter.
bucket = 10 liters.

Look Back! How did you measure the capacity of containers that are less than 1 liter? Is there another way to measure?

Essential Question
How Do You Measure Capacity?

Visual Learning Bridge
Eric is cleaning his fishbowl and wants to know how much water he needs to refill the fishbowl. How can he find the capacity of the fishbowl?

Pour from the filled fishbowl into the 1-liter container. Empty the container and repeat until the fishbowl is empty.

It is helpful to keep a record of measurements made.
The 1-liter container was filled 5 times.
So, the capacity of the fishbowl is 5 liters.

Convince Me! Critique Reasoning Jason says, “I think it is better to find the measurement of the fishbowl by filling the fishbowl with liters of water instead of emptying the fishbowl into liter beakers.” Is Jason correct?

Another Example!
When only part of the 1-liter container is filled, use fractions of liters.

The capacity of the pot is 2\(\frac{1}{2}\) liters.

Guided Practice

Do You Understand?
Question 1.
What is the capacity of 2 pots like the one shown in the Another Example! above?

Answer:
The capacity of the 2 pots like the one shown is 5 liters.

Explanation:
In the above-given question,
given that,
the capacity of one pot is 2 and 1/2 liters.
2 + 2 + 1 = 5.
so the capacity of the 2 pots like the one shown is 5 liters.

Question 2.
Find a container that you think holds less than a liter. Estimate, and then check your estimate for the capacity of the container.

Answer:
The container that holds less than a liter = teacup.

Explanation:
In the above-given question,
given that,
the container is a teacup.
teacup holds 1/8 of a liter.
so the container that holds less than a liter = teacup.

Do You Know How?
In 3 and 4, find the total capacity represented in each picture.
Question 3.

Answer:
The total capacity represented in each picture = 2 liters.

Explanation:
In the above-given question,
given that,
there are 4 containers.
the containers each weight is 1/2 liter.
1/2 + 1/2 + 1/2 + 1/2 = 2 liters.
so the total capacity represented in each picture = 2 liters.

Question 4.

Answer:
The total capacity represented is 1 and 1/2 liter.

Explanation:
In the above-given question,
given that,
there are 2 containers.
they are 1 is totally filled and the other one is half-filled.
1 + 1/2 = 1.5 liters.
so the total capacity represented is 1 and 1/2 liter.

Independent Practice

In 5-7, find the total capacity represented in each picture.
Question 5.

Answer:
The total capacity represented is 18 liters.

Explanation:
In the above-given question,
given that,
there are 2 containers.
they are 1 is totally filled and the other one is 8 liters filled.
10 + 8 = 18 liters.
so the total capacity represented is 18 liters.

Question 6.

Answer:
The total capacity represented is 20 liter.

Explanation:
In the above-given question,
given that,
there are 2 containers.
they are totally filled.
10 + 10 + 10 + 10 = 20 liters.
so the total capacity represented is 20 liters.

Question 7.

Answer:
The total capacity represented is 24 liters.

Explanation:
In the above-given question,
given that,
there are 3 containers.
they are 2 is totally filled and the other one is half-filled.
10 + 10 + 4 = 24 liters.
so the total capacity represented is 24 liters.

Problem Solving

Question 8.
Lawrence manufactures jam. He makes 200 liters of grape jam and 350 liters of strawberry jam. He then sells 135 liters of the grape jam. How much jam does Lawrence have left?

Answer:
The quantity of jam does Lawrence has left = 415 liters.

Explanation:
In the above-given question,
given that,
Lawrence manufactures jam.
He makes 200 liters of grape jam and 350 liters of strawberry jam.
He then sells 135 liters of grape jam.
200 – 135 = 65.
350 + 65 = 415.
so the quantity of jam does Lawrence have left = 415 liters.

Question 9.
Use Appropriate Tools Find a container that you think holds more than a liter. Estimate, and then check your estimate for the capacity of the container.

Answer:
The capacity of the container is more than 2 liters and it is a kettle.

Explanation:
In the above-given question,
given that,
the container is a kettle.
the kettle holds 2 liters.

Question 10.
How many 2-liter cartons can be filled with 18 liters of juice?

Answer:
The number of 2-liter cartons can be filled with 18 liters of juice = 9 liters.

Explanation:
In the above-given question,
given that,
2 x 9 = 18.
so the number of 2-liter cartons can be filled = 9.

Question 11.
Which of the following measurements is NOT reasonable for the capacity of a full bathroom sink: 15 liters, \(\frac{1}{2}\) liter, 10 liters, 9 liters, or 12 liters? Explain.

Answer:
The 1/2 liter is not reasonable for the capacity of a full bathroom sink.

Explanation:
In the above-given question,
given that,
the capacity of a full bathroom sink is 15 liters, 1/2 liter, 10 liters, 9 liters, 12 liters.
so I am thinking that the capacity of a full bathroom sink is 12 liters.
so half-liter is not reasonable.

Question 12.
Higher Order Thinking Emma prepares 72 liters of punch for an event. She pours all of the punch equally into the pitchers on 9 different tables. If there are 4 pitchers on each table, how many liters of punch are in each pitcher?

Answer:
The number of liters of punch is in each pitcher = 32.

Explanation:
In the above-given question,
given that,
Emma prepares 72 liters of punch for an event.
She pours all of the punch equally into the pitchers on 9 different tables.
9 x 8 = 72.
8 x 4 = 32.
so the number of liters of punch are in each pitcher = 32.

Assessment Practice

Question 13.
Use the picture of the water jugs to find the amount of water the team drank during soccer practice.

A. 6 liters
B. 7 liters
C. 8 liters
D. 23 liters

Answer:
Option B is the correct answer.

Explanation:
In the above-given question,
given that,
the amount of water before soccer practice is 15 liters.
15 – 8 = 7liters.
so the amount of water before soccer is 15 liters.
option B is the correct answer.

Lesson 14.6 Estimate Mass

Solve & Share
Look at the measurements for the mass of the book and the mass of the olive. List 4 items that should be measured using kilograms and 4 items that should be measured using grams. Explain your reasoning.
I can … use standard units to estimate the masses of solid objects.

Look Back! How could you use tools to check that the items in part of your list are reasonable choices for measuring mass with grams? Explain.

Answer:
The weight of the cup = 250 grams.

Explanation:
In the above-given question,
given that,
1kilo gram = 1000 grams.
so the weight of the cup = 250 grams.
the weight of the bottle is 1000 grams.

Essential Question
How Can You Use Reasoning to Estimate Mass?

Visual Learning Bridge
Stephen and Marissa estimated the mass of an apple. Stephen’s estimate is 250 grams. Marissa’s estimate is 2 kilograms. Which is the better estimate of the mass of an apple?

Step 1
Use known masses and the table to compare grams to kilograms. Select the unit that will give a better estimate.

The apple is smaller than the cantaloupe. A kilogram is too large of a unit to estimate the mass of the apple.
The grape is smaller than the apple. Grams are smaller units that can be used to estimate the mass of the apple.

Step 2
Use a pan balance to find the mass of the apple. Then evaluate Stephen’s estimate.

The apple has a mass of 262 grams.
250 grams is close to 262 grams. Stephen’s estimate is reasonable.
250 grams is a better estimate than 2 kilograms.

Convince Me! Critique Reasoning Zoe says two apples would have a mass greater than a kilogram. Do you agree? Explain.

Answer:
No, i do not agree with it.

Explanation:
In the above-given question,
given that,
Zoe says two apples would have a mass greater than a kilogram.
one apple = 250 grams.
250 x 2 = 500.
250 + 250 = 500 grams.
so zeo says wrong.

Guided Practice

Do You Understand?
Question 1.
In Step 2 on the previous page, why do you need to find the actual mass of the apple?

Answer:
The actual mass of the object is 262 grams.

Explanation:
In the above-given question,
given that,
the actual mass of the object is 262 grams.
262 grams is approximately equal to 250 grams.
262 + 262 = 524.
so the actual mass of the object is 262 grams.

Question 2.
Find an object that you think has a mass more than a kilogram and another that has a mass less than a kilogram. Then determine what tools to use to check your estimate.

Answer:
The tools are apple and jaggery.

Explanation:
In the above-given question,
given that,
the object that you think has a mass more than a kilogram and has a mass less than a kilogram.
the weight of the apple is 250 grams.
the weight of the jaggery is 1200 grams.
so the tools are apple and jaggery.

Do You Know How?
In 3-6, circle the better estimate for each
Question 3.

5 g or 5 kg

Answer:
The better estimation of the coin is 5 g.

Explanation:
In the above-given question,
given that,
the measurements are 5 g and 5 kg.
the weight of the coin is 5 g.
so the better estimation of the coin is 5 g.

Question 4.

40 g or 4 kg

Answer:
The better estimation of the dog is  4 kg.

Explanation:
In the above-given question,
given that,
the measurements are 40 g and 4 kg.
the weight of the dog is 4 kg.
so the better estimation of the dog is 4 kg.

Question 5.
Sunglasses
16 g or 1 kg

Answer:
The better estimation of the sunglasses is 16 g.

Explanation:
In the above-given question,
given that,
the measurements are 16 g and 1 kg.
the weight of the sunglasses is 16 g.
so the better estimation of the sunglasses is 16 g.

Question 6.
Envelope
1 g or 70 g

Answer:
The better estimation of the Envelope is 1 g.

Explanation:
In the above-given question,
given that,
the measurements are 1 g and 70 g.
the weight of the Envelope is 1 g.
so the better estimation of the Envelope is 1 g.

Independent Practice

Leveled Practice In 7-18, circle the better estimate for each.
Question 7.

100 g or 10 kg

Answer:
The better estimation of the blanket is 10 kg.

Explanation:
In the above-given question,
given that,
the measurements are 100 g and 10 kg.
the weight of the blanket is 10 kg.
so the better estimation of the coin is 10 kg.

Question 8.

15 g or 15 kg

Answer:
The better estimation of the monitor is 15 kg.

Explanation:
In the above-given question,
given that,
the measurements are 15 g and 15 kg.
the weight of the monitor is 15 kg.
so the better estimation of the monitor is 15 kg.

Question 9.

4g or 400 g

Answer:
The better estimation of the spectacles box is 400 g.

Explanation:
In the above-given question,
given that,
the measurements are 4 g and 400 g.
the weight of the spectacles box is 400 g.
so the better estimation of the spectacles box is 400 g.

Question 10.

200 g or 2 kg

Answer:
The better estimation of the net bag is 2 kg.

Explanation:
In the above-given question,
given that,
the measurements are 200 g and 2 kg.
the weight of the bag is 2 kg.
so the better estimation of the net bag is 2 kg.

Question 11.
Bicycles
2 kg or 12 kg

Answer:
The better estimation of the bicycles is 12 kg.

Explanation:
In the above-given question,
given that,
the measurements are 2 kg and 12 kg.
the weight of the bicycles is 12 kg.
so the better estimation of the bicycles is 12 kg.

Question 12.
Feather
1 g or 1 kg

Answer:
The better estimation of the feather is 1 g.

Explanation:
In the above-given question,
given that,
the measurements are 1 g and 1 kg.
the weight of the feather is 1 g.
so the better estimation of the feather is 1 g.

Question 13.
Horse
5 kg or 550 kg

Answer:
The better estimation of the horse is 550 kg.

Explanation:
In the above-given question,
given that,
the measurements are 5 kg and 550 kg.
the weight of the horse is 550 kg.
so the better estimation of the horse is 550 kg.

Question 14.
Penny
3 g or 300 g

Answer:
The better estimation of the penny is 3 g.

Explanation:
In the above-given question,
given that,
the measurements are 3 g and 300 g.
the weight of the penny is 3 g.
so the better estimation of the penny is 3 g.

Question 15.
Dining table
350 g or 35 kg

Answer:
The better estimation of the dining table is 35 kg.

Explanation:
In the above-given question,
given that,
the measurements are 350 g and 35 kg.
the weight of the dining table is 35 kg.
so the better estimation of the dining is 35 kg.

Question 16.
Microwave oven
1,500 g or 15 kg

Answer:
The better estimation of the microwave oven is 15 kg.

Explanation:
In the above-given question,
given that,
the measurements are 1500 g and 15 kg.
the weight of the microwave oven is 15 kg.
so the better estimation of the microwave oven is 15 kg.

Question 17.
Kitten
2 kg or 20 kg

Answer:
The better estimation of the kitten is 2 kg.

Explanation:
In the above-given question,
given that,
the measurements are 2 kg and 20 kg.
the weight of the kitten is 2 kg.
so the better estimation of the kitten is 2 kg.

Question 18.
Crayon
20 g or 200 g

Answer:
The better estimation of the crayon is 20 g.

Explanation:
In the above-given question,
given that,
the measurements are 20 g and 200 g.
the weight of the crayon is 20 g.
so the better estimation of the crayon is 20 g.

Problem Solving

Question 19.
Use Appropriate Tools Choose the best tool to measure each item described. Write the correct letter of the tool on the blank.

The capacity of a mug _______
The temperature of water _______
The length of a box _______
The mass of a pear _______
The time you finish lunch _______

Answer:
The capacity of a mug is 1 liter.
the temperature of the water is 1000 degrees celsius.
the length of a box is 1 cm.
the mass of a pear is 100 g.
the time you finish lunch is 12:15.

Explanation:
In the above-given question,
given that,
the items are mug, pear, temperature, and box.
The capacity of a mug is 1 liter.
the temperature of the water is 1000 degrees celsius.
the length of a box is 1 cm.
the mass of a pear is 100 g.
the time you finish lunch is 12:15.

Question 20.
Number Sense Ethan will subtract a 3-digit number from 920. He says the difference could be a 1-digit number, a 2-digit number, or a 3-digit number. Write three subtraction equations that show each difference. Be sure you start with 920 and subtract a 3-digit number each time.
You can use place value and mental math to solve this problem.

Answer:
The three subtraction equations are 917, 10, and 3.

Explanation:
In the above-given question,
given that,
Ethan will subtract a 3-digit number from 920.
He says the difference could be a 1-digit number, a 2-digit number, or a 3-digit number.
920 – 3 = 917.
920 – 10 = 920.
920 – 917 = 3.
so the three subtraction equations are 917, 10, and 3.

Question 21.
en Vision® STEM Clay learned that solids have a definite shape. Now he wants to measure some solids, so he measures the mass of a bead. The bead has a mass of 10 grams. He estimates that 10 beads will have a mass of 1 kilogram. Is he correct? Explain.

Answer:
No, he was not correct.

Explanation:
In the above-given question,
given that,
Clay learned that solids have a definite shape.
the bead has a mass of 10 grams.
10 beads will have a mass of 1 kilogram.
1000 grams = 1 kilogram.
so he was not correct.

Question 22.
Higher Order Thinking Correct the mistakes in the shopping list below.
Shopping List
2 L of apples
3 kg of milk
5 cm of flour

Answer:
The shopping list contains 2 liters of milk, 3 kg of apples, and 5 cm of flour.

Explanation:
In the above-given question,
given that,
2 l of apples, 3 kg of milk, 5 cm of flour.
the mistakes in the shopping list are apples, milk, and flour.
so the shopping list contains 2 liters of milk, 3 kg of apples, and 5 cm of flour.

Assessment Practice

Question 23.
Todd is thinking of an animal with a mass greater than 1 kilogram, but less than 20 kilograms. Which animal could Todd be thinking of?
A. Horse
B. Cat
C. Elephant
D. Rhinoceros

Answer:
Option A is correct.

Explanation:
In the above-given question,
given that,
the animal with a mass greater than 1 kilogram, but less than 20 kilograms.
the animals are horse, cat, elephant, and rhinoceros.
the weight of the horse is more than 1 kilogram and less than 20 kilograms.
so option A is correct.

Question 24.
Anna has a bar of soap. She estimates its mass before measuring to find the actual mass. Which units should Anna use for her measure?
A. Grams
B. Kilograms
C. Liters
D. Inches

Answer:
The actual mass of the soap is grams.

Explanation:
In the above-given question,
given that,
the measurements are grams, kilograms, liters, and inches.
so the mass of the soap will be in grams.

Lesson 14.7 Measure Mass

Solve & Share
Work with a group to choose 6 objects whose masses can be measured using a pan balance. Estimate the mass of each object. Then use metric weights to find the actual mass for each in grams (g) or kilograms (kg). Use the table and explain your reasoning.
I can … use grams and kilograms to measure the mass of objects.

Look Back! How did you decide which metric unit(s) to use when making your estimates? Explain.

Essential Question
How Do You Measure Mass?

Visual Learning Bridge
A pan balance with gram and kilogram weights can be used to find the mass of an object. What is the mass of a box of chalk?

Place the box on one pan. Place enough gram and kilogram weights on the other pan so the pans balance.

The box balances with one 1-kilogram weight, two 100-gram weights, and four 10-gram weights.
So, the mass of the box is 1 kilogram 240 grams or 1,240 grams.
Write the larger unit before the smaller unit when recording measurements.

Convince Me! Be Precise What metric units would you use to estimate the mass of half of a box of chalk? Explain.

Answer:
The mass of the half of the box of chalk = 620 grams.

Explanation:
In the above-given question,
given that,
the mass of the box is 1 kilogram 240 grams or 1,240 grams.
1kg = 1000 g.
1240 / 2 = 620.
so the mass of the half of box of chalk = 620 grams.

Guided Practice

Do You Understand?
Question 1.
Find an object that you think has a mass greater than a kilogram. Find another object that has a mass less than a kilogram. Use a pan balance with gram and kilogram weights to measure the mass of each object.

Answer:
The weight of Malachi is 1 g and the mass of the cat is 1200 g.

Explanation:
In the above-given question,
given that,
the object that has a mass greater than a kilogram and has a mass less than a kilogram.
the mass of Malachi is 1 g.
the mass of the cat is 1200g.
the mass of Malachi is less than a kilogram.
the mass of the cat is greater than a kilogram.
so the weight of Malachi is 1 g and the mass of the cat is 1200 g.

Question 2.
If you use a pan balance to measure the mass of a pen, would you use any kilogram weights? Explain.

Answer:
We will use one gram weight.

Explanation:
In the above-given question,
given that,
the mass of a pen is 2 grams.
so we will use the gram weights.

Do You Know How?
In 3 and 4, write the total mass represented in each picture.
Question 3.

Answer:
The total mass is 3500 g.

Explanation:
In the above-given question,
given that,
there are 3 1 kg and 1 500 g.
1 kg = 1000 g.
1000 + 1000 + 1000 + 500 = 3500 g.
so the total mass is 3500 g.

Question 4.

Answer:
The total mass is 245 g.

Explanation:
In the above-given question,
given that,
there are 2 100 g objects, 4 10 g, and 5 1 g objects.
100 + 100 = 200.
10 + 10 + 10 + 10 = 40.
1 + 1 + 1 + 1 + 1 = 5.
200 + 40 + 5 = 245g.
so the total mass is 245 g.

Independent Practice

In 5-7, write the total mass represented in each picture.
Question 5.

Answer:
The total mass is 931 g.

Explanation:
In the above-given question,
given that,
there are 1 500 g.
4 100 g and 3 10 g and 1 g.
500 + 100 + 100 + 100 + 100 = 900.
3 x 10 = 30.
30 + 1 = 31.
900 + 30 + 1 = 931.
so the total mass is 931 g.

Question 6.

Answer:
The total mass is 6 kg.

Explanation:
In the above-given question,
given that,
there are 6 1 kg objects.
1 + 1 + 1 + 1 + 1 + 1 = 6.
so the total mass is 6 kg.

Question 7.

Answer:
The total mass is 2106 g.

Explanation:
In the above-given question,
given that,
there are 2-1 kg objects.
2 x 1000 = 2000.
1 x 100 = 100.
6 x 1 = 6.
2000 + 100 + 6 = 2016 g.

Problem Solving

Question 8.
Algebra Olivia put 220 grams of nuts in a bag. Then she added more nuts to the bag. The total mass of Olivia’s bag of nuts was 850 grams. Use the equation 220 + a = 850 to find the mass in grams of the nuts Olivia added to her bag.

Answer:
The mass of the grams she added = 630 g.

Explanation:
In the above-given question,
given that,
Algebra Olivia put 220 grams of nuts in a bag.
Then she added more nuts to the bag.
The total mass of Olivia’s bag of nuts was 850 grams.
220 + a = 850.
a = 850 – 220.
a = 630.
so she added the 630 grams into the bag.

Question 9.
An adult manatee has a mass of about 450 kilograms. What is the mass of 2 adult manatees?

Answer:
The mass of 2 adult manatees = 900 kg.

Explanation:
In the above-given question,
given that,
An adult manatee has a mass of about 450 kilograms.
450 + 450 = 900.
so the mass of 2 adult manatees = 900 kg.

Question 10.
Reasoning Sophie used a pan balance to measure the mass of a pineapple. The pans balanced when she used one 500-gram weight and three 100-gram weights. Zach measured the same pineapple but used eight 100-gram weights. Did someone make a mistake? Explain.

Answer:
No one makes a mistake.

Explanation:
In the above-given question,
given that,
The pans balanced when she used one 500-gram weight and three 100-gram weights.
Zach measured the same pineapple but used eight 100-gram weights.
500 + 100 + 100 + 100 = 800 gram.
100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 = 800 gram.
so no one makes a mistake.

Question 11.
Higher Order Thinking Lawrence bought some red potatoes with a mass of 410 grams. He also bought white potatoes with a mass of 655 grams. Did he buy more or less than 1 kilogram of potatoes? Explain how you know.

Answer:
He buys more than 1 kilogram of potatoes.

Explanation:
In the above-given question,
given that,
Lawrence bought some red potatoes with a mass of 410 grams.
He also bought white potatoes with a mass of 655 grams.
410 + 655 = 1065.
so he buys more than 1 kilogram of potatoes.

Question 12.
Meg uses 16 kilograms of butter to make 8 large batches of cookies. She uses an equal amount of butter for each batch. How many kilograms of butter are used for each batch?

Answer:
The number of kilograms of butter is used for each batch = 2 kg.

Explanation:
In the above-given question,
given that,
Meg uses 16 kilograms of butter to make 8 large batches of cookies.
She uses an equal amount of butter for each batch.
16 / 8 = 2.
he uses 2 kilograms of butter for each batch.
so the number of kilograms of butter is used for each batch = 2 kg.

Question 13.
Kalista has 154 grams of glitter. She uses 97 grams to sprinkle the tops of the tables. How many grams of glitter remain?

Answer:
The number of grams of glitter remains = 57.

Explanation:
In the above-given question,
given that,
Kalista has 154 grams of glitter.
She uses 97 grams to sprinkle the tops of the tables.
154 – 97 = 57.
so the number of grams of glitter remains = 57.

Assessment Practice

Question 14.
Evan used a pan balance and metric weights to measure the total mass of 3 bricks. What is the mass of the 3 bricks?

A. 6 kilograms
B. 5 kilograms
C. 4 kilograms
D. 3 kilograms

Answer:
The mass of the 3 bricks = 3 kg.

Explanation:
In the above-given question,
given that,
Evan used a pan balance and metric weights to measure the total mass of 3 bricks.
3 x 1000 = 3000.
so the mass of the 3 bricks = 3 kg.

Lesson 14.8 Solve Word Problems Involving Mass and Liquid Volume

Solve & Share
The animals at a pet store eat 80 kilograms of vegetables each day. How many kilograms of vegetables do they eat in one week?
I can … solve problems about mass and liquid volume.

Look Back! Describe the plan you used to solve the problem.

Answer:
The number of vegetables does they eat in 1 week = 560 kg.

Explanation:
In the above-given question,
given that,
The animals at a pet store eat 80 kilograms of vegetables each day.
1 week = 7 days.
80 x 7 = 560.
so the number of vegetables do they eat in 1 week = 560 kg.

Essential Question
How Can You Solve Problems Involving Mass and Liquid Volume?

Visual Learning Bridge
In a juice factory, one 50-liter container had 28 liters of juice in it. An hour later, it had 45 liters of juice. How many liters of juice were added?

Convince Me! Make Sense and Persevere In the example above, another beaker had 33 liters of juice. How many total liters of juice were there in all? How can you solve this problem?

Answer:
The liters of juice that were added = 5 liters.

Explanation:
In the above-given question,
given that,
another beaker had 33 liters of juice.
one 50-liter container had 28 liters of juice.
33 – 28 = 5.
so the number of liters that were added = 5 liters.

Guided Practice

Do You Understand?
Question 1.
Suppose 42 liters of juice were evenly divided into 6 batches. How many liters of juice are in each batch? Write and solve an equation.

Answer:
The number of liters is in each batch = liters.

Explanation:
In the above-given question,
given that,
Suppose 42 liters of juice were evenly divided into 6 batches.
42 /6 = 7.
6 x 7 = 42.
so the number of liters are in each batch = 7 liters.

Do You Know How?
Question 2.
Alex buys a box of pudding mix and a box of cocoa. The mass of the box of pudding mix is 100 grams. The total mass of the 2 boxes is 550 grams. What is the mass of the box of cocoa?

Answer:
The mass of the box of cocoa is 450 g.

Explanation:
In the above-given question,
given that,
Alex buys a box of pudding mix and a box of cocoa.
The mass of the box of pudding mix is 100 grams.
The total mass of the 2 boxes is 550 grams.
550 – 100 = 450.
so the mass of the box of cocoa is 450 g.

Independent Practice

Leveled Practice In 3-6, use bar diagrams or equations to help solve.
Question 3.
Peter divided 120 liters of water equally into 3 containers. How many liters did Peter pour into each container?

Answer:
The number of liters did peter pour into each container = 40 liters.

Explanation:
In the above-given question,
given that,
peter divided 120 liters of water equally into 3 containers.
c + c + c = 120.
3c = 120.
c = 120/3.
c = 40.
so the number of liters did peter pour into each container = 40 liters.

Question 4.
Adeela pours 235 liters of milk into a blue vat and 497 liters of milk into a red vat. How many liters of milk does she pour in all? Write and solve an equation.

Answer:
The quantity of milk she pours in all = liters.

Explanation:
In the above-given question,
Adeela pours 235 liters of milk into a blue vat and 497 liters of milk into a red vet.
235 + 497 = 732.
so the quantity of milk she pours in all = 732 liters.

Question 5.
Samantha bought 523 grams of grapes. After eating some grapes, she had 458 grams. How many grams did she eat?

Answer:
The number of grams did she eat = 65 g.

Explanation:
In the above-given question,
given that,
Samantha bought 523 grams of grapes.
After eating some grapes, she had 458 grams.
523 – 458 = 65.
so the number of grams did she eat = 65 g.

Question 6.
Omar is shipping 3 boxes. Each has a mass of 8 kilograms. What is the total mass of all of the boxes?

Answer:
The total mass of all the boxes = 24.

Explanation:
In the above-given question,
given that,
Omar is shipping 3 boxes.
each has a mass of 8 kilograms.
8 x 3 = 24.
so the total mass of all the boxes = 24.

Problem Solving

In 7 and 8, use the table. In 8, use the bar diagram.

Question 7.
Professor Newman has collected a soil sample from the forest preserve in her town. What is the total mass of the 3 minerals in the soil sample?

Answer:
The total mass of the 3 minerals in the soil sample is 279 g.

Explanation:
In the above-given question,
given that,
Professor Newman has collected a soil sample from the forest preserve in her town.
the sample of quartz is 141 g.
calcite is 96 g.
feldspar is 42 g.
141 + 96 + 42 = 279.
so the total mass of the 3 minerals in the soil sample is 279 g.

Question 8.
Higher Order Thinking The professor finds that there is the same amount of feldspar in each of the soil samples that she takes. If there are 210 grams of feldspar in all, how many soil samples does she collect?

Answer:
The number of soil samples does she collect = 447 g.

Explanation:
In the above-given question,
given that,
If there are 210 grams of feldspar in all.
141 + 96 + 210 = 447 g.
so the number of soil samples does she collect = 447 g.

Question 9.
Elijah has 2 hours before dinner. He spends the first 37 minutes practicing his guitar and the next 48 minutes doing his homework. How much time is left until dinner?

Answer:
The number of times is left until dinner is 35.

Explanation:
In the above-given question,
given that,
Elijah has 2 hours before dinner.
He spends the first 37 minutes practicing his guitar and the next 48 minutes doing his homework.
37 + 48 = 85.
1 hour = 60 minutes.
60 + 60 = 120.
120 – 85 = 35.
so the number of time is left unit dinner is 35.

Question 10.
Make Sense and Persevere Write and solve a word problem about the bar diagram.

Answer:
The mass of the a is 339 g.

Explanation:
In the above-given question,
given that,
the total mass of the object is 678 g.
678 – 239 = 339.
so the mass of the a is 339 g.

Assessment Practice

Question 11.
Eric filled a container to the 18-liter mark with juice an hour ago. The juice is now at the 15-liter mark. Mark the amount of juice Eric had on the beakers. Then find how many liters of juice have been poured out.

A. 3 liters
B. 4 liters
C. 5 liters
D. 6 liters

Answer:
The number of liters of juice that has been poured out = 3 liters.

Explanation:
In the above-given question,
given that,
Eric filled a container to the 18-liter mark with juice an hour ago.
The juice is now at the 15-liter mark.
18 – 15 = 3.
so the number of liters of juice has been poured out = 3 liters.

Lesson 14.9 Problem Solving

Reasoning
Solve & Share
Nina wants to arrive at the community center at 9:30 A.M. for an art class. It takes her 15 minutes to walk to the center, 30 minutes to make and eat breakfast, and 15 minutes to get ready after eating. What time should Nina start making breakfast? Use reasoning to decide.
I can … make sense of quantities and relationships in problem situations.

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

• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Look Back! Reasoning Does it make sense to use “minutes” as the unit for the answer to this problem? Explain.

Essential Question
How Can You Use Reasoning to Solve Problems?

Visual Learning Bridge
Eric’s family wants to arrive at a movie theater at 2:30 P.M. It takes them 30 minutes to eat lunch, 15 minutes to get ready after eating, and 30 minutes to travel to the theater.

What do I need to do to solve this problem?
I need to start with the end time. Then I need to use the time lengths given and work backward to find the starting time.

Answer:
The starting time is 1:15 P.M.

Explanation:
In the above-given question,
given that,
Eric’s family wants to arrive at a movie theater at 2:30 P.M.
It takes them 30 minutes to eat lunch.
15 minutes to get ready after eating, and 30 minutes to travel to the theater.
30 + 30 + 15 = 1 hour 15 minutes.
so the starting time is 1:15 P.M.

How can I use reasoning to solve this problem?
I can

• identify the quantities I know.
• draw a number line to show relationships.
• give the answer using the correct unit.

Here’s my thinking..
I used a number line to show the quantities and my reasoning.

30 minutes before 2:30 P.M. is 2:00 P.M.
15 minutes before 2:00 P.M. is 1:45 P.M.
30 minutes before 1:45 P.M. is 1:15 P.M.
Eric’s family should start eating lunch at 1:15 P.M.

Convince Me! Reasoning How can you check that the solution given above makes sense?

Guided Practice

Reasoning Kevin’s doctor appointment is at 10:30 A.M. It takes Kevin 30 minutes to clean his room, 20 minutes to get ready after he cleans, and 20 minutes to walk to the doctor’s office. What time should Kevin start cleaning his room? Use reasoning to decide.

Question 1.
Describe the quantities you know.

Answer:
The starting time is 9:20 A.M.

Explanation:
In the above-given question,
given that,
Kevin’s doctor appointment is at 10:30 A.M.
It takes Kevin 30 minutes to clean his room,
20 minutes to get ready after he cleans, and 20 minutes to walk to the doctor’s office.
10 : 30 – 30 = 10.
10 – 20 = 9:40.
9: 40 – 20 = 9:20.
so the starting time is 9:20 A.M.

Question 2.
Solve the problem and explain your reasoning. You can use a picture to help.

Answer:
The starting time is 9:20 A.M.

Explanation:
In the above-given question,
given that,
Kevin’s doctor appointment is at 10:30 A.M.
It takes Kevin 30 minutes to clean his room,
20 minutes to get ready after he cleans, and 20 minutes to walk to the doctor’s office.
10 : 30 – 30 = 10.
10 – 20 = 9:40.
9: 40 – 20 = 9:20.
so the starting time is 9:20 A.M.

Independent Practice

Reasoning Doreen’s favorite television show begins at 5:30 P.M. She will get her hair cut before the show. It takes Doreen 10 minutes to walk to the hair salon and 10 minutes to walk home. Her haircut takes 25 minutes. What time should Doreen leave home so that she will get back in time for her show? Use reasoning to decide.
Question 3.
Describe the quantities you know.

Answer:
The time should Doreen leave home so that she will get back in time for her show = 4: 45 P.M.

Explanation:
In the above-given question,
given that,
Doreen’s favorite television show begins at 5:30 P.M.
She will get her hair cut before the show.
It takes Doreen 10 minutes to walk to the hair salon and 10 minutes to walk home.
Her haircut takes 25 minutes.
10 + 10 + 25 = 45.
4 : 45 P.M + 45 = 5:30.
so the time should Doreen leave home so that she will get back in time for her show = 4:45 P.M.

Question 4.
Solve the problem and explain your reasoning. You can use a picture to help.

Answer:
The time should Doreen leave home so that she will get back in time for her show = 4 : 45 P.M.

Explanation:
In the above-given question,
given that,
Doreen’s favorite television show begins at 5:30 P.M.
She will get her hair cut before the show.
It takes Doreen 10 minutes to walk to the hair salon and 10 minutes to walk home.
Her haircut takes 25 minutes.
10 + 10 + 25 = 45.
4 : 45 P.M + 45 = 5:30.
so the time should Doreen leave home so that she will get back in time for her show = 4:45 P.M.

Question 5.
How did you know whether to use A.M. or P.M. in your answer to Exercise 4 above?

Answer:
We have to use P.M.

Explanation:
In the above-given question,
given that,
Doreen’s favorite television show begins at 5:30 P.M.
She will get her hair cut before the show.
It takes Doreen 10 minutes to walk to the hair salon and 10 minutes to walk home.
Her haircut takes 25 minutes.
10 + 10 + 25 = 45.
4 : 45 P.M + 45 = 5:30.
so the time should Doreen leave home so that she will get back in time for her show = 4:45.

Problem Solving

Performance Task
School Talent Show Karina is planning a talent show for 28 students. The table below tells how long each act lasts. Karina needs 5 minutes to introduce each act. She also needs to allow a 20-minute break. The break does not need to be introduced. The show must end at 9:00 P.M.

Question 6.
Be Precise What is the total time needed for all the acts before the break? Explain your thinking.

Answer:
The total time needed for all the acts before the break = 45 minutes.

Explanation:
In the above-given question,
given that,
the 3rd-grade dancers = 10 minutes.
the 3rd-grade singers = 10 minutes.
the 4th-grade singers = 10 minutes.
the 4th-grade magic act = 15 minutes.
10 + 10 + 10 + 15 = 45.
so the total time needed for all the acts before the break = 45 minutes.

Question 7.
Critique Reasoning Sachi says that the 5th grade singers should begin at 7:40 P.M. Phil says that the 5th grade singers should begin at 8:00 P.M. Who is correct?

Answer:
Phil says was correct.

Explanation:
In the above-given question,
given that,
Sachi says that the 5th-grade singers should begin at 7:40 P.M.
Phil says that the 5th-grade singers should begin at 8:00 P.M.
fifth-grade singers will sing in 10 minutes.
10 + 10 + 10 + 30 = 60.
so fifth grade singers will start at 8:00 P.M.
so Phil was correct.

Question 8.
Reasoning What time should the talent show begin? Explain your reasoning. You can draw a picture to help.

Answer:
The talent show begins at 7:15 P.M.

Explanation:
In the above-given question,
given that,
the 3rd-grade dancers = 10 min.
3rd-grade singers = 10 min.
4th-grade singers = 10 min.
4th-grade magic act = 15 min.
5th-grade singers = 10 min.
5th-grade magic act = 10 min.
5th grade dancers = 10 min.
finale = 30 min.
10 + 10 + 10 + 15 + 10 + 10 + 10 + 30 = 7:45 P.M.

Topic 14 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 1 and Partner 2 each point to a black number at the same time. Both partners subtract the lesser number from the greater number.
If the answer is on your color, you get a tally mark. Work until one partner has seven tally marks.
While playing the game, partners can use addition to check their subtraction.

I can… add and subtract within 1,000.

Topic 14 Vocabulary Review

Understand Vocabulary
Question 1.
Cross out any units below that are NOT measurement units of capacity.
gram
inch
kilogram
hour
liter

Answer:
The not measured units of capacity are gram and kilogram.

Explanation:
In the above-given question,
given that,
the units are gram, inch, kilogram, hour, and liter.
so the not measured units of capacity are gram and kilogram.

Question 2.
Cross out any units below that are NOT measurement units of mass.
kilogram
minute
hour
gram
liter

Answer:
The units that are not measured units of mass = gram and kilogram.

Explanation:
In the above-given question,
given that,
the units are kilogram, hour, gram, and liter.
mass is measured in weight.
so the units that are not measured units of mass = gram, and kilogram.

Question 3.
Cross out any amounts below that are shown in grams or kilograms.
5 kg
2L
80 in.
250 g
12 kg

Answer:
The amounts that are shown in grams or kilograms = 5 kg, 250 g, and 12 kg.

Explanation:
In the above-given question,
given that,
the units are 5 kg, 2 l, 80 in, 250 g, and 12 kg.
so the amounts that are shown in grams or kilograms = 5 kg, 250 g, and 12 kg.

Choose the right term from the box. Write it in the blank.
Word List

• A.M.
• capacity
• elapsed time
• gram
• hour
• kilogram
• liter
• mass
• minute
• P.M.
• time interval

Question 4.
The hours between midnight and noon are ________ hours.

Answer:
The hours between midnight and noon are A.M hours.

Explanation:
In the above-given question,
given that,
the words are P.M and A.M.
so the hours between midnight and noon are:
for example,
if it is the morning we will say it is 10:30 A.M.
if it is the evening we will say it is 4:00 P.M.

Question 5.
An amount of time is a __________.

Answer:
An amount of time is a time interval.

Explanation:
In the above-given question,
given that,
if we want to know the start time and end time we will use the time interval.
so an amount of time is a time interval.

Question 6.
The hours between noon and midnight are ________ hours.

Answer:
The hours between noon and midnight are P.M hours.

Explanation:
In the above-given question,
given that,
the words are P.M and A.M.
so the hours between midnight and noon are:
for example,
if it is the morning we will say it is 10:30 A.M.
if it is an evening we will say it is 4:00 P.M.

Question 7.
1 _________ equals 1,000 grams.

Answer:
1 kilogram equals 1000 grams.

Explanation:
In the above-given question,
given that,
the words are grams and kilograms.
1 kg = 1000 grams.

Question 8.
The total amount of time that passes from the beginning time to the ending time is called the _________.

Answer:
The time that passes from beginning to ending time is elapsed time.

Explanation:
In the above-given question,
given that,
the words are beginning time and elapsed time.
for example:
beginning time is 10:00 A.M.
ending time is 1: 00 P.M.
so the elapsed time is 3 hours.

Use Vocabulary in Writing
Question 9.
Maggie wants to measure this container. Use at least 3 terms from the Word List to explain how Maggie can measure the container in different ways.

Answer:
The container is 500 grams and half kg.

Explanation:
In the above-given question,
given that,
the container is a paint bucket.
so the container weight is 500 grams and half kg.

Topic 14 Reteaching

Set A pages 533-536

What is the time to the nearest minute?

The digital time is 10:27.
It is 27 minutes after 10 o’clock or 33 minutes before 11 o’clock.

Remember that, for minutes, count numbers on the clock by 5s, then count marks by 1.

Write the time shown on each clock in two ways.
Question 1.

Answer:
The time is 12:17.

Explanation:
In the above-given question,
given that,
the hour hand is between 12 and 1.
count by 5’s from 12 to 5.
that is 5, 10, 15.
count by 1’s from 15, 16, and 17.
so the time is 12:17.

Question 2.

Answer:
The time is 6:44.

Explanation:
In the above-given question,
given that,
the hour hand is between 6 and 7.
count by 5’s from 12 to 5.
that is 5, 10, 15, 20, 25, 30, 35, 40.
count by 1’s from 40, 41,42, 43, and 44.
so the time is 6:44.

Set B pages 537-540

Tomaz starts practicing his viola at 4:25 P.M. He practices until 5:05 P.M. How much time does he practice?

The amount of time is under 1 hour, so count the minutes from the start time to the end time, by 5s.

There are 40 minutes between 4:25 P.M. and 5:05 P.M. So, Tomaz practices for 40 minutes.

Remember that you can use a clock face to find elapsed time.

In 1-3, find the elapsed time.
Question 1.
Basketball practice begins at 6:30 P.M. and lasts until 8:15 P.M. How much time does practice last?

Answer:
The time does practice last = 1:45 min.

Explanation:
In the above-given question,
given that,
Basketball practice begins at 6:30 P.M.
lasts until 8:15 P.M.
6:30 + 1 hour = 7:30.
1 hour = 60 minutes.
7:30 + 45 min = 8:15.
so the time is 1:45 min.

Question 2.
Mr. Walters starts preparing breakfast at 6:45 A.M. He finishes at 7:50 A.M. How long does it take for him to prepare breakfast?

Answer:
The time it takes for him to prepare breakfast = 1 hour 5 min.

Explanation:
In the above-given question,
given that,
Mr. Wallets starts preparing breakfast at 6:45 A.M.
He finishes at 7:50 A.M.
7:50 – 6:45 = 1:05.
so the time it takes for him to prepare breakfast = 1 hour 5 min.

Question 3.
Jean goes for a horseback ride. She leaves the barn on her horse at 2:10 P.M., and comes back at 2:50 P.M. How long was her ride?

Answer:
The long was her ride = 40 min.

Explanation:
In the above-given question,
given that,
Jean goes for a horseback ride.
She leaves the barn on her horse at 2:10 P.M.
and comes back at 2:50 P.M.
2:50 – 2:10 = 40.
so the long was her ride = 40 min.

Set C pages 541-544

You can show addition and subtraction of time intervals on a number line.
In the morning, Xavier runs for 19 minutes. In the evening, he runs for 27 minutes. How much time does he spend running in all?

19 + 27 = ?
19 + 27 = 46
So, Xavier runs for 46 minutes.

Remember to decide whether you need to add or subtract.

In 1, solve by drawing a number line or a bar diagram.
Question 1.
It takes Don 52 minutes to drive to work. He has already driven for 16 minutes. How many more minutes will it take Don to drive to work?

Answer:
The more minutes will it take Don to drive to work = 36 minutes.

Explanation:
In the above-given question,
given that,
It takes Don 52 minutes to drive to work.
He has already driven for 16 minutes.
52 – 16 = 36.
so the more minutes will it take Don to drive to work = 36 minutes.

Set D pages 545-548

Estimate the capacity of a pitcher.

Think about what you already know. A liter is about the same size as a large water bottle. A pitcher usually holds more liquid than a water bottle. So, 2 liters seems like a good estimate.

Remember that capacity can be measured using liters.

In 1-4, circle the better estimate.

Question 1.

1 L or 10 L

Answer:
The better estimation of a bottle is 1 l.

Explanation:
In the above-given question,
given that,
the given measurements are 1 L or 10 L.
1000 ml = 1 liter.
500 ml = 1/2 liter.
so the better estimation of a bottle is 1 liter.

Question 2.

\(\frac{1}{4}\) L or 8 L

Answer:
The better estimation of a bucket is 8 l.

Explanation:
In the above-given question,
given that,
the given measurements are 1/4 L or 8 L.
1000 ml = 1 liter.
500 ml = 1/2 liter.
so the better estimation of a bucket is 8 liter.

Question 3.
Drinking glass
5 L or \(\frac{1}{2}\) L

Answer:
The better estimation of drinking glass is 1/2 l.

Explanation:
In the above-given question,
given that,
the given measurements are 5 L or 1/2 L.
1000 ml = 1 liter.
500 ml = 1/2 liter.
so the better estimation of a drinking bottle is 1/2 liter.

Question 4.
Washing machine
40 L or 4L

Answer:
The better estimation of a washing machine is 40 l.

Explanation:
In the above-given question,
given that,
the given measurements are 40 L or 4 L.
1000 ml = 1 liter.
500 ml = 1/2 liter.
so the better estimation of a washing machine is 40 liter.

Set E pages 549-552

How much water is in this beaker?
Use the scale to determine how full the beaker is. Think of the scale as a number line. Each mark represents 1 liter. The water is 3 marks : – 10 liters above 5 liters.

There are 8 liters in the beaker.

Remember to use the correct units when measuring capacity.

In 1 and 2, find the total capacity.
Question 1.

Answer:
The total capacity of two beakers = 3 liters.

Explanation:
In the above-given question,
given that,
the 1st beaker contains 1 n 1/2 liter.
the 2nd beaker contains 1 n 1/2 liter.
1.5 + 1.5 = 3 liters.
so the total capacity of two beakers = 3 liters.

Question 2.

Answer:
The total capacity of the beaker = 6 liters.

Explanation:
In the above-given question,
given that,
the 1st beaker contains 6 liters.
5 + 1 = 6 liters.
so the total capacity of beakers = 6 liters.

Set F pages 553-556

Estimate the mass of a battery.

A kilogram is too heavy, so estimate using grams.

Think about what you already know. A gram is about the same weight as a grape. A battery weighs about as much as a bunch of grapes. So 30 grams seems like a good estimate.

Remember that mass can be measured using grams and kilograms.

In 1-6, circle the better estimate for the mass.
Question 1.

15 g or 15 kg

Answer:
The better estimation of the pen is 15 g.

Explanation:
In the above-given question,
given that,
the given measurements are 15 g or 15 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a washing machine is 15 g.

Question 2.

500 g or 500 kg

Answer:
The better estimation of the pen is 500 g.

Explanation:
In the above-given question,
given that,
the given measurements are 500 g or 500 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a washing machine is 500 g.

Question 3.
One sheep
800 g or 80 kg

Answer:
The better estimation of sheep is 80 kg.

Explanation:
In the above-given question,
given that,
the given measurements are 800 g or 80 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a sheep is 80 kg.

Question 4.
Bag of flour
2 g or 2 kg

Answer:
The better estimation of the bag of flour is 2 kg.

Explanation:
In the above-given question,
given that,
the given measurements are 2 g or 2 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a bag of flour is 2 kg.

Question 5.
Notebook computer
3 g or 3 kg

Answer:
The better estimation of the Notebook computer is 3 kg.

Explanation:
In the above-given question,
given that,
the given measurements are 3 g or 3 kg.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a washing machine is 3 kg.

Question 6.
Quarter
5 g or 500 g

Answer:
The better estimation of the Quarter is 500 g.

Explanation:
In the above-given question,
given that,
the given measurements are 5 g or 5 00 g.
1000 g = 1 kg.
500 g = 1/2 kg.
so the better estimation of a quarter is 500 g.

Set G pages 557-560

What is the mass of this bar of soap?

When a pan balance is even, the mass on the left side equals the mass on the right side.
Find the total of the weights on the left side. Use mental math and place value to help add.
100 + 10 + 5 + 1 + 1 + 1 = 118
The bar of soap has a mass of 118 grams.

Remember to use the correct units when measuring mass.

In 1 and 2, find the total mass.
Question 1.

Answer:
The total mass is 701g.

Explanation:
In the above-given question,
given that,
they have given 1 500 g.
2 100 g.
1 hundred g.
500 + 200 + 1 = 701.
so the total mass is 701 g.

Question 2.

Answer:
The total mass is 2210 g.

Explanation:
In the above-given question,
given that,
they have given 1 100 kg.
2 100 g.
2 5 g.
1000 + 1000 + 200 +10 = 2210.
so the total mass is 2210 g.

Set H pages 561-564

There are 7 people bowling together. Each owns their own bowling ball. The mass of each bowling ball is 5 kilograms. What is the total mass of the team’s bowling balls?

Remember that you can use bar diagrams or equations to represent problems.

In 1 and 2, use bar diagrams or equations to help solve.
Question 1.
The water tank in Mary’s yard holds 60 liters of water. She used 13 liters to water her plants. How many liters of water remain in the water tank?

Answer:
The quantity of water that remains in the water tank = 47 liters.

Explanation:
In the above-given question,
given that,
the water tank in mary’s yard holds 60 liters of water.
she used 13 liters to water her plants.
60 – 13 = 47.
so the quantity of water remains in the water tank = 47 liters.

Question 2.
Eric has 3 dogs that each have a mass of 8 kilograms. What is the total mass of all of Eric’s dogs?

Answer:
The total mass of all of Eric’s dogs = 24 kg.

Explanation:
In the above-given question,
given that,
Eric has 3 dogs that each have a mass of 8 kilograms.
8 x 3 = 24.
24 /8 = 3.
so the total mass of all of Eric’s dogs = 24 kg.

Set I pages 565-568

Think about these questions to help you reason abstractly and quantitatively.
Thinking Habits

• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?
  

Remember to consider the units in the information you are given.

At 1:00 P.M., Ted will meet a friend in the park.. Ted needs 30 minutes to walk to the park. Ted needs 15 minutes to eat lunch and 10 minutes to prepare lunch. When must Ted start to prepare lunch?
Question 1.
Describe the quantities you know.

Answer:
Ted start to prepare lunch = 12:05 P.M.

Explanation:
In the above-given question,
given that,
Ted will meet a friend in the park.
Ted needs 30 minutes to walk to the park.
Ted needs 15 minutes to eat lunch and 10 minutes to prepare lunch.
30 + 15 + 10 = 55 minutes.
so ted start to prepare lunch = 12:05 P.M.

Question 2.
How can you show the relationships in this problem?

Answer:
Ted start to prepare lunch = 12:05 P.M.

Explanation:
In the above-given question,
given that,
Ted will meet a friend in the park.
Ted needs 30 minutes to walk to the park.
Ted needs 15 minutes to eat lunch and 10 minutes to prepare lunch.
30 + 15 + 10 = 55 minutes.
so ted start to prepare lunch = 12:05 P.M.

Question 3.
When must Ted start to prepare lunch?

Answer:
Ted start to prepare lunch = 12:05 P.M.

Explanation:
In the above-given question,
given that,
Ted will meet a friend in the park.
Ted needs 30 minutes to walk to the park.
Ted needs 15 minutes to eat lunch and 10 minutes to prepare lunch.
30 + 15 + 10 = 55 minutes.
so ted start to prepare lunch = 12:05 P.M.

Topic 14 Assessment Practice

Question 1.
Draw hands on the clock to show 8:36. What time will it be in 2 hours and 6 minutes?

Answer:
The time is 6:42.

Explanation:
In the above-given question,
given that,
the hour hand is on the 8.
the minute hand is on the 8.
the second’s hand is on the 42.
so the time is 6:42.

Question 2.
Jessica and Cody ran a long-distance race during an afternoon. The start times were different so that all the runners did not start at the same time. Who finished faster, and by how many minutes?

A. Jessica; 5 minutes faster than Cody
B. Cody; 5 minutes faster than Jessica
C. Jessica; 10 minutes faster than Cody
D. They finished in the same amount of time.

Answer:
Option D is the correct answer.

Explanation:
In the above-given question,
given that,
Jessica and Cody ran a long-distance race during the afternoon.
The start times were different so that all the runners did not start at the same time.
Jessica starts at 3:55 and ends at 4:40.
Cody starts at 4:15 and ends at 5:05.
5:05 – 4:15 = 90 min.
4:40 – 3:55 = 85 min.
so option D is the correct answer.

Question 3.
Two stores in a small town sell bags of apples. At Store A, each bag weighs 2 kilograms. At Store B, each bag weighs 4 kilograms. If you buy 6 bags at each store, how many more kilograms of apples will you buy from Store B?

Answer:
The kilograms of apples will you buy from store B = 24 kg.

Explanation:
In the above-given question,
given that,
Two stories in a small town sell bags of apples.
At Store A, each bag weighs 2 kilograms.
At Store B, each bag weighs 4 kilograms.
6 x 2 = 12 kg.
4 x 6 = 24 kg.
so the number of kilograms of apples will you buy from store B = 24 kg.

Question 4.
Name the metric unit that could be used to measure the capacity of a kitchen sink. Then, using that unit, write a reasonable estimate for the capacity of a kitchen sink.

Answer:
The reasonable estimate for the capacity of a kitchen sink = 30 kg.

Explanation:
In the above-given question,
given that,
the unit is kg.
the weight of the kitchen sink is 30 kg.
so the reasonable estimate for the capacity of a kitchen sink = 30 kg.

Question 5.
A. Mason is looking for a tool to measure the mass of an apple. Which tool should he use?
A. Pan balance
B. Ruler
C. 1-cup container
D. Clock

Answer:
Option A is correct.

Explanation:
In the above-given question,
given that,
the units are panned balance, ruler, 1-cup container, and clock.
pan balance is used to measure the mass of an apple.
so option A is correct.

B. Using the tool identified in Part A, what unit will Mason use to measure the mass of the apple?
A. Grams
B. Minutes
C. Cups
D. Inches

Answer:
Grams are the unit that measures the mass of the apple.

Explanation:
In the above-given question,
given that,
the units are grams, minutes, cups, and inches.
mass of the apple is measured in grams.
so grams is the unit that measures the mass of the apple.

Question 6.
Dale’s school bus picks him up at 7:45 A.M. To get ready for school, Dale needs 15 minutes to eat breakfast, 10 minutes to make lunch, and 10 minutes to get dressed. What time does Dale need to begin getting ready for school?
A. Describe the quantities you know.

Answer:
Dale needs to get ready for school = 7:10.

Explanation:
In the above-given question,
given that,
Dale’s school bus picks him up at 7:45 A.M.
To get ready for school, Dale needs 15 minutes to eat breakfast, 10 minutes to make lunch, and 10 minutes to get dressed.
15 + 10 + 10 = 35 min.
7:45 – 35 = 7:10.
so Dale needs to getting ready for school = 7:10

B. Solve the problem. Explain your reasoning. You can use a picture to help.

Answer:
Dale needs to get ready for school = 7:10.

Explanation:
In the above-given question,
given that,
Dale’s school bus picks him up at 7:45 A.M.
To get ready for school, Dale needs 15 minutes to eat breakfast, 10 minutes to make lunch, and 10 minutes to get dressed.
15 + 10 + 10 = 35 min.
7:45 – 35 = 7:10.
so Dale needs to getting ready for school = 7:10

Question 7.
Mary has a total of 18 liters of water in 6 bottles. Jess has a total of 15 liters in 3 bottles. If the bottles are equally filled, how much more water is in each of Jess’s bottles than in Mary’s bottles?

Answer:
One more bottle of water is filled in Jess.

Explanation:
In the above-given question,
given that,
Mary has a total of 18 liters of water in 6 bottles.
Jess has a total of 15 liters in 3 bottles.
18/6 = 3.
15/3 = 5.
15 + 3 = 18.
so one more bottle of water is filled in Jess.

Question 8.
Eric played the guitar for 33 minutes on Monday and 19 minutes on Tuesday. Write and solve an equation to find how many more minutes Eric played the guitar on Monday.

Answer:
The more minutes Eric played the guitar on Monday = 14 min.

Explanation:
In the above-given question,
given that,
Eric played the guitar for 33 minutes on Monday and 19 minutes on Tuesday.
33 – 19 = 14.
so the more minutes eric played the guitar on Monday = 14 min.

Question 9.
Mrs. Griggs writes a shopping list saying she needs to buy 1 gram of apples. Is this reasonable? Explain.

Answer:
No, it is not reasonable.

Explanation:
In the above-given question,
given that,
Mrs. Griggs writes a shopping list saying she needs to buy 1 gram of apples.
1000 grams = 1 kg.
the mass of the apple is 100 g.
so it is not reasonable.

Question 10.
Irene measured the mass of a bag of apples using kilograms. Forest measured the same bag using grams. How did the measurements compare? Select all the sentences that are true.
☐ There were more grams than kilograms.
☐ There were more kilograms than grams.
☐ There was an equal number of grams and kilograms.
☐ There were fewer grams than kilograms.
☐ There were fewer kilograms than grams.

Answer:
Options A, C, and E are correct.

Explanation:
In the above-given question,
given that,
Irene measured the mass of a bag of apples using kilograms.
Forest measured the same bag using grams.
there were more grams than kilograms.
there was an equal number of grams and kilograms.
there were fewer kilograms than grams.
so options A, C, and E are correct.

Question 11.
Jason said the mass of his book is about 1 kilogram. Julie said it is 1 liter. Who is correct? Select the best answer.
A. Jason is correct because kilograms are units of mass, and liters are units of capacity.
B. Julie is correct because liters are metric units.
C. They are both correct because kilograms and liters are units of mass.
D. Neither is correct because their estimates are not reasonable.

Answer:
The best answer is option A.

Explanation:
In the above-given question,
given that,
Jason said the mass of his book is about 1 kilogram.
Julie said it is 1 liter.
Jason is correct because kilograms are units of mass and liters are units of capacity.
so Option A is correct.

Question 12.
Explain why it would be better to use grams rather than kilograms to measure the mass of a crayon.

Answer:
It is better to use grams.

Explanation:
In the above-given question,
given that,
crayon is a very small object.
it is measured in grams.
so it is better to use grams for crayons.

Question 13.
It took Wallace 45 minutes to read part of a chapter of his science book. He finished reading the rest of the chapter in 17 minutes. Write and solve an equation to find how much time Wallace spent reading the chapter.

Answer:
The time he spent reading the chapter is 62 minutes.

Explanation:
In the above-given question,
given that,
It took Wallace 45 minutes to read part of a chapter of his science book.
He finished reading the rest of the chapter in 17 minutes.
45 + 17 = 62.
so the time he spent reading the chapter is 62 minutes.

Question 14.
Four brothers, Raphael, Don, Leo, and Mike, went to the gym to exercise. Don and Mike both started at 2:21 P.M. and exercised for 33 minutes. Raphael and Leo both started when Don and Mike finished and exercised until 3:36 P.M. For how many minutes did the brothers exercise in total?

Answer:
The number of minutes the brothers exercise in total = 75 minutes

Explanation:
In the above-given question,
given that,
Four brothers, Raphael, Don, Leo, and Mike, went to the gym to exercise.
Don and Mike both started at 2:21 P.M. and exercised for 33 minutes.
Raphael and Leo both started when Don and Mike finished and exercised until 3:36 P.M.
33 + 2:21 = 2:54.
3:36 – 2:54 = 82.
42 + 33 = 75.
so the number of minutes the brothers exercise in total = 75 minutes.

Question 15.
Mark used a pan balance to find the mass of his basketball. He said it was 580 kilograms. Is his answer reasonable? Explain.

Answer:
No, his answer was not reasonable.

Explanation:
In the above-given question,
given that,
Mark used a pan balance to find the mass of his basketball.
He said it was 580 kilograms.
the mass of the basketball is 5 kgs.
so the answer not reasonable.

Question 16.
Look at the time on the clock below.

A. Select all of the ways to write this time.
☐ 3 : 46
☐ 14 minutes before 4 o’clock
☐ 46 minutes after 3 o’clock
☐ 9 minutes before 4 o’clock
☐ 4 : 14

Answer:
Option A is the correct answer.

Explanation:
In the above-given question,
given that,
the hour hand is in between 3 and 4.
the minute’s hand is in between 9 and 10.
5 x 9 = 45.
45 + 1 = 46.
so Option A is the correct answer.

B. What time was it 2 hours, 45 minutes ago?

Answer:
The time was 1 hour 1 minute.

Explanation:
In the above-given question,
given that,
the time is 3:46.
3:46 – 2:45 = 1:01.
so the time is 1 hour 1 minute.

Question 17.
Maryann went to the grocery store at 3:10 P.M. She arrived home 1 hour, 15 minutes later.
A. What time did she arrive home?

Answer:
The time did she arrive = 4:25.

Explanation:
In the above-given question,
given that,
Maryann went to the grocery store at 3:10 P.M.
she arrived home 1 hour 15 minutes later.
3:10 + 1:15 = 4:25.
so the time did she arrive = 4:25.

B. Her neighbor Betty Sue got to the grocery store at the same time as Maryann and got home at 4:02 P.M. How much less time did Betty Sue spend shopping?

Answer:
The less time did Betty Sue spend shopping is 23 minutes.

Explanation:
In the above-given question,
given that,
Her neighbor Betty Sue got to the grocery store at the same time as Maryann and got home at 4:02 P.M.
4:25 – 4:02 = 23.
so the less time did Betty Sue spend shopping is 23 minutes.

Question 18.
Ricardo used 337 grams of flour to bake in the afternoon. He had already used 284 grams of flour to bake in the morning. Write and solve an equation to find how many grams of flour Ricardo used in all.

Answer:
The number of grams of flour Ricardo used in all = 53 g.

Explanation:
In the above-given question,
given that,
Ricardo used 337 grams of flour to bake in the afternoon.
He had already used 284 grams of flour to bake in the morning.
337 + a = 284.
a = 337 – 284.
a = 53.
so the number of grams of flour Ricardo used in all = 53 g.

Question 19.
A tank contained 750 liters of water. After some water drained out, the tank had 250 liters of water. Write and solve an equation to find how many liters of water drained out.

Answer:
The number of liters of water drained out = 500 liters.

Explanation:
In the above-given question,
given that,
A tank contained 750 liters of water.
After some water drained out, the tank had 250 liters of water.
750 + w = 250.
w = 750 – 250.
w = 500.
so the number of liters of water drained out = 500 liters.

Topic 14 Performance Task

Family Reunion
Anita and her brother Logan make plans for a family reunion.

Question 1.
Use the Fruit Bought table to answer the question. Logan estimated the mass of the fruit. He forgot to include the unit of mass. For each item, explain if he used a gram or kilogram.

Answer:
The missing values of mass are 4 kg, 90 g, and 3 kgs.

Explanation:
In the above-given question,
given that,
the estimated unit of the mass is grape is 4 kg.
one lemon has an estimated mass of 90 g.
the mass of the watermelon is 3 kgs.
so the missing values of mass are 4kg, 90 g, and 3 kgs.

Question 2.
Use the Mass of One Lime picture to answer the questions.

Part A
Each lime has the mass shown at the right. What is the mass of one lime?

Answer:
The mass of one lime is 30 g.

Explanation:
In the above-given question,
given that,
there is 3 mass of lime.
10 + 10 + 10 = 30.
3 x 10 = 30.
so the mass of one lime is 30 g.

Part B
Logan needs to buy at least 200 grams of limes. He plans to buy 7 limes. Will he buy enough? Use your response to Part A to explain.

Answer:
Yes, he will buy enough limes.

Explanation:
In the above-given question,
given that,
Logan needs to buy at least 200 grams of limes.
He plans to buy 7 limes.
7 x 30 = 210.
so he will buy enough limes.

Question 3.
Use the Liquids Needed table to answer the question.
Logan measures the liquids they need. Complete the table to show if the capacity of each container will likely be less than or greater than 1 liter.

Answer:
The container contains a spoon of vinegar, milk, and water.

Explanation:
In the above-given question,
given that,
the ingredients are vinegar, milk, and water.
the spoon of vinegar is measured in grams.
the measuring cup of milk is liters.
the large pot is measured in kilograms.

The Broth Used picture shows the amount of broth that Anita started with and the amount she had left after she poured some into two different soups.

Question 4.
Use the Broth Used picture to answer the questions.
Part A
How much broth did Anita use?

Answer:
The amount Anita used is 22 liters.

Explanation:
In the above-given question,
given that,
The Broth Used picture shows the amount of broth that Anita started with and the amount she had left.
20 + 2 = 22.
so the amount Anita used is 22 liters.

Part B
Anita poured an equal amount of broth into 2 pots. How much did she pour into 1 pot?

Answer:
The water she poured into 1 pot = 20 liters.

Explanation:
In the above-given question,
given that,
Anita poured an equal amount of broth into 2 pots.
Anita poured 20 liters in 1 both.
she poured 2 liters in 2nd both.
20 + 2 = 22.
so the water she poured into 1 pot = 20 liters.

Question 5.
Logan’s recipe says it takes 50 minutes to cook chicken. After 22 minutes pass, Logan flips the chicken. How many more minutes does the chicken have to bake after Logan flips it? Show your work on a number line.

Answer:
The many more minutes does the chicken have to bake after logan flips it = 28 minutes.

Explanation:
In the above-given question,
given that,
Logan’s recipe says it takes 50 minutes to cook chicken.
After 22 minutes pass, Logan flips the chicken.
50 – 22 = 28.
so the more minutes does the chicken have to bake after logan flips it = 28 minutes.

Question 6.
Use the Before Reunion table to answer the question.

Anita and Logan want to be at the reunion at 1:45 P.M. They need to clean, pack, and drive to the reunion. What time should they start? Explain.

Answer:
The time should they start = 12:15 P.M.

Explanation:
In the above-given question,
given that,
Anita and Logan want to be at the reunion at 1:45 P.M.
they have to clean for 20 min.
they have to pack for 15 min.
they have to drive for 55 min.
20 + 15 + 55 = 90.
1 hour = 60 min.
90 min = 1 and half hours.
1:45 – 12:15 = 1:30.
so the time should they start = 12:15 P.M.

Go through the enVision Math Common Core Grade 3 Answer Key Topic 9 Fluently Add and Subtract within 1,000 regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 9 Fluently Add and Subtract within 1,000

Essential Question: What are the procedures for adding and subtracting whole numbers?

enVision STEM Project: Changing Environments
Do Research Forest fires destroy, but they also make room for new growth. Use the Internet or other sources to find information about forest fires. Describe the effect of forest fires on plant and animal populations.
Journal: Write a Report Include data with numbers for the population you researched. Also in your report:

• Choose a kind of animal or plant. Tell how a change in the environment can affect the number of animals or plants.
• Write and solve an addition and a subtraction problem using your data.

Review What You Know

Vocabulary

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

• Associative Property of Addition
• Commutative Property of Addition
• compatible numbers
• inverse operations

Question 1.
___ are easy to add or subtract mentally.
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Thus, Compatible numbers are easy to add or subtract mentally.

Question 2.
According to the _______, the grouping of addends can be changed, and the sum will remain the same.
Answer:
The commutative property of addition says that changing the order of addends does not change the sum.
So, According to the commutative property of addition, the grouping of addends can be changed, and the sum will remain the same.

Question 3.
Addition and subtraction are ___
Answer:
Inverse operations are pairs of mathematical manipulations in which one operation undoes the action of the other.
Thus Addition and subtraction are inverse operations.

Rounding

Round each number to the nearest ten.

Question 4.
57
Answer:
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Here 7 is greater than 5.
So, 57 round to the nearest ten is 60.

Question 5.
241
Answer:
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
So, 241 round to the nearest ten is 240.

Question 6.
495
Answer:
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Thus 495 round to the nearest ten is 500.

Round each number to the nearest hundred.

Question 7.
732
Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 732 to the nearest hundred is 700.

Question 8.
81
Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 81 to the nearest hundred is 100.

Question 9.
553
Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 553 to the nearest hundred is 600.

Estimating Sums

Use compatible numbers to estimate each sum.

Question 10.
27 + 12
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Write 27 and 12 to the nearest ten.
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
27 to the nearest ten is 30.
12 to the nearest ten is 10.
30 + 10 = 40
Thus the estimated sum is 40.

Question 11.
133 + 102
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
133 to the nearest ten is 130.
102 to the nearest ten is 100.
130 + 100 = 230
Thus the estimated sum is 230.

Question 12.
504 + 345
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 504 to the nearest hundred is 500.
Thus the number 345 to the nearest hundred is 300.
500 + 300 = 800
Thus the estimated sum is 800.

Question 13.
52 + 870
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Thus the number 52 to the nearest ten is 50.
Thus the number 870 to the nearest hundred is 900.
900 + 50 = 950
Thus the estimated sum is 950.

Question 14.
293 + 278
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Thus the number 293 to the nearest hundred is 300.
Thus the number 278 to the nearest hundred is 300.
300 + 300 = 600
Thus the estimated sum is 600.

Question 15.
119 + 426
Answer:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Thus the number 119 to the nearest hundred is 100.
Thus the number 426 to the nearest hundred is 400.
100 + 400 = 500
Thus the estimated sum is 500.

Estimating Differences

Question 16.
Tony and Kim play a video game. Tony scores 512 points. Kim scores 768 points. About how many more points does Kim score than Tony? Which estimation method did you use?
Answer:
Given,
Tony and Kim play a video game. Tony scores 512 points. Kim scores 768 points.
768 – 512
Write the nearest hundred values for both the numbers to estimate the sum.
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Thus the number 512 to the nearest hundred is 500.
Thus the number 768 to the nearest hundred is 800.
800 – 500 = 300
Thus Kim scores nearly .00 points than Tony.

Question 17.
Which number sentence shows the most reasonable estimate for
A. 425 – 250 = 175
B. 500 – 200 = 300
C. 400 – 300 = 100
D. 470 – 230 = 240
Answer: 500 – 200 = 300

Pick a Project

PROJECT 9A

How do you know which is the tallest building?
Project: Research the Heights of Tall Buildings

PROJECT 9B
How can you record what you bought over time? Project: Create an Addition Skit

PROJECT 9C
How long before the space shuttle launches?
Project: Write a Report About Your Vacation

3-ACT MATH PREVIEW

Math Modeling
Fun Raiser

Before watching the video, think: When a school needs extra money for a field trip or a student club, it might hold a fundraiser to collect that money.
This check is SO BIG, we must have collected a ton of money!

Lesson 9.1 Use Partial Sums to Add

Activity

Solve & Share
There are 2 bins of oranges. One bin has 378 oranges. The other bin has 243 oranges. Find the sum of 378 + 243. Think about place value.

You can use structure. You can break apart the problem to show each of the addends in expanded form.

Look Back! Adam has 9 bags of oranges with 8 oranges in each. He also has a bin with 325 oranges. How many oranges does Adam have in all? Think about how you can use place value or other tools to help solve the problem. Explain your solution, what tool you used, and why.

Essential Question How Can You Break Apart Addition Problems to Solve?

Visual Learning Bridge

A.
Margot counted 243 manatees one year and 179 manatees the next. How many manatees did Margot count all together?

B.
You can estimate and then use place value to add the numbers.


The sum is about 400 manatees.

C.
One Way
Add each place value. Start with hundreds.

300, 110, and 12 are partial sums.
243 + 179 = 422 manatees

D.
Another Way
Add each place value. Start with ones.

When you add by place value, you add the hundreds, the tens, and the ones.

243 + 179 = 422 manatees
422 is close to the estimate of 400.
So, 422 is a reasonable sum.

Convince Me!
Critique Reasoning Lexi used partial sums to complete the problem. Critique Lexi’s reasoning. Is her work correct? Explain.

Guided Practices

Do You Understand?

Question 1.
Suppose you were adding 527 + 405. What numbers would you combine when adding the tens? Why?
Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
Add 3 to 527 = 530
530
410
940
Thus, It would be 3 because when you add it, it gets to be 932 and the tens place is 3.

Question 2.
Find the error. Show how to find the correct answer.

Answer:
First round the numbers to the nearest hundred.
237 to the nearest hundred is 200
285 to the nearest hundred is 300
200 + 300 = 500
So, the estimated answer is 500.

Do You Know How?

In 3, estimate the sum. Use place-value blocks or drawings and partial sums to add.

Question 3.

Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
365 to the nearest hundred is 400
422 to the nearest hundred is 400
400 + 400 = 800
So, the estimated answer is 800.

Independent Practice

Leveled Practice In 4-11, estimate each sum. Use place-value blocks or drawings and partial sums to add.

Question 4.

Answer:
When rounding to the nearest hundred, look at the tens place of the number.
If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.
356 to the nearest hundred is 400
123 to the nearest hundred is 100
400 + 100 = 500
So, the estimated answer is 500.

Question 5.

Answer:
550 + 423 = 973
973 is close to 1000.
So, the estimated sum is 1000.

Question 6.
185 + 613
Answer:
185 + 613 = 798
798 is close to 800.
So, the estimated sum is 800.

Question 7.
730 + 168
Answer:
730 + 168 = 898
898 is close to 900.
So, the estimated sum is 900.

Question 8.
546 + 143
Answer:
546 + 143 = 689
689 is close to 700.
So, the estimated sum is 700.

Question 9.
362 + 524
Answer:
362 + 524 = 886
886 is close to 900.
So, the estimated sum is 900.

Question 10.
644 + 101
Answer:
644 + 101 = 745
745 is close to 700.
So, the estimated sum is 700.

Question 11.
463 + 315
Answer:
463 + 315 = 778
778 is close to 800.
So, the estimated sum is 800.

Problem Solving

Question 12.
Model with Math John read a book with 377 pages. Jess read a book with 210 pages. How many pages did John and Jess read? Use place-value blocks and partial sums to solve. Draw a model to represent the problem.
Answer:
Given,
John read a book with 377 pages. Jess read a book with 210 pages.
377 + 210 = 587
587 is close to 600.
So, the estimated sum is 600.

Question 13.
Explain how the solids shown in Group A and Group B could have been sorted.

Answer:

Question 14.
Henry believes the sum of 275 + 313 is 598. Is Henry correct? Use place-value blocks or drawings and partial sums in your explanation.

Answer:
Given,
Henry believes the sum of 275 + 313 is 598.
The sum of 275 and 313 os 588.
Henry is not correct.

Question 15.
Higher Order Thinking A school cafeteria sold 255 lunches on Monday, 140 lunches on Tuesday, and 226 lunches on Wednesday. Did the cafeteria sell more lunches on Monday and Tuesday or on Tuesday and Wednesday? Use place value blocks or drawings to solve.
Answer:
Given,
A school cafeteria sold 255 lunches on Monday, 140 lunches on Tuesday, and 226 lunches on Wednesday.
225 + 140 = 365
140 + 226 = 366
Thus cafeteria sells more lunches on Tuesday and Wednesday.

Assessment Practice

Question 16.
Which shows breaking 622 + 247 apart by place value to find the sum?
A. 600 + 200; 22 + 40; 2 + 7
B. 600 + 300; 20 + 40; 2 + 7
C. 600 + 200; 20 + 40; 2 + 7
D. 600 + 200; 20 + 47; 2 + 7
Answer: A. 600 + 200; 22 + 40; 2 + 7

Question 17.
Break 331 + 516 apart by place value. Find the sum.
A. 848
B. 847
C. 748
D. 488
Answer:
331 + 516 = 847
Thus the correct answer is option B.

Lesson 9.2 Use Regrouping to Add

Activity

Solve & Share

Suppose a bus travels 276 miles on Monday and 248 miles on Tuesday. How many miles does the bus travel?

You can use appropriate tools, such as place-value blocks, to add larger numbers. What other strategies can you use to solve
this problem?

Look Back! On Wednesday, the bus gets stuck in traffic. It travels 8 miles each hour for 8 hours. The bus needs to travel 600 miles total from Monday to Wednesday to make it to its destination. Does the bus make it to its destination? Why would it be a good idea to estimate first before you solve this problem?

Visual Learning Bridge

Essential Question
How Can You Use Regrouping to Solve Addition Problems?

You know one way to record partial sums.

A.
Jason’s family drove from Ocala, Florida to Miami. They drove 139 miles in the morning and 187 miles in the afternoon. How far did Jason’s family drive? Find 139 + 187. ?

Estimate: 139 + 187 is about 100 + 200, or 300 miles.
Jason’s family drove 326 miles. 300 is close to 326, so the sum is reasonable.

B.
Here is another way. Write the partial sums.

Regroup the ones. 16 ones = 1 ten + 6 ones

Regroup the tens. 12 tens = 1 hundred + 2 tens

When you regroup, you name a whole number in a different way.

139 + 187 = 326
Jason’s family drove 326 miles.

Convince Me!
Model with Math Show how to use place-value blocks to find 128 +235 using regrouping.

Another Example!

Find 154 + 163.

You can find partial sums. Then you can regroup place values to find the final sum.

Regroup the tens.
1 hundred + 1 ten = 11 tens
154 + 163 = 317

Guided Practice

Do You Understand?

Question 1.
When you add 3-digit numbers, how do you know if you need to regroup?
Answer: When you add 3-digit numbers if the sum of the place value is greater than 9 then we can know we have to regroup the addend.

Question 2.
To add 546 + 327, would you need to regroup? Explain.
Answer:
546 + 327
7 + 6 = 13, yes we need to regroup
546 + 327 = 873

Do You Know How?

In 3 and 4, estimate by rounding. Then find each sum. Use place-value blocks or drawings to help.

Question 3.

Answer:

Question 4.

Answer:

Independent Practice

In 5-12, estimate and then find each sum.

Question 5.

Answer:
The estimated number of 136 is 100.
The estimated number of 252 is 300.
The sum of 100 and 300 is 400.

Question 6.

Answer:
The estimated number of 678 is 700.
The estimated number of 129 is 100.
The sum of 700 and 100 is 800.

Question 7.

Answer:
The estimated number of 564 is 600.
The estimated number of 283 is 300.
The sum of 600 and 300 is 900.

Question 8.

Answer:
The estimated number of 118 is 100.
The estimated number of 335 is 300.
The sum of 100 and 300 is 400.

Question 9.
172 + 534
Answer:
The estimated number of 172 is 200.
The estimated number of 534 is 500.
The sum of 200 and 500 is 700.

Question 10.
324 + 508
Answer:
The estimated number of 324 is 300.
The estimated number of 508 is 500.
The sum of 300 and 500 is 800.

Question 11.
582 + 230
Answer:
The estimated number of 582 is 600.
The estimated number of 230 is 200.
The sum of 600 and 200 is 800.

Question 12.
207 + 238
Answer:
The estimated number of 207 is 200.
The estimated number of 238 is 200.
The sum of 200 and 200 is 400.

Problem Solving

In 13 and 14, use the table at the right.

Question 13.
How many soup can labels did Grades 1 and 2 collect? Estimate by rounding to the nearest hundred. Then solve. Write an equation that represents the problem.

Answer:
Estimate: 400 + 300 = 700
385 + 294 = 679, grade 1 and 2 collected 679 labels.

Question 14.
Make Sense and Persevere Is your answer to Exercise 13 reasonable? Explain.
Answer: Yes, 679 is close to my estimate of 700, so 679 is a reasonable answer.

Question 15.
Number Sense The roller coaster Kingda Ka is 192 feet taller than the first Ferris wheel. Use the symbols < and > to compare the heights of the two rides in two different ways.

Answer: 264 feet < 456 feet; 456 feet > 264 feet

Question 16.
Higher Order Thinking Pete can run 178 yards in one minute. Sharon can run 119 more yards than Pete in one minute. How many yards can they both run in one minute?
Answer:
Given,
Pete can run 178 yards in one minute.
Sharon can run 119 more yards than Pete in one minute.
178 + 119 = 297 yards
178 + 297 = 475 yards

Question 17.
Abi practiced her flute for 215 minutes last week and 178 minutes this week. How many minutes has Abi practiced?
Answer:
Given,
Abi practiced her flute for 215 minutes last week and 178 minutes this week.
215 + 178 = 393
Thus Abi practiced 393 minutes.

Assessment Practice

Question 18.
What is 126 + 229?
A. 355
B. 345
C. 255
D. 245
Answer: 355
The sum of 126 and 229 is 355.
Thus the correct answer is option A.

Question 19.
What is the value of the unknown in 248 + = 521?
A. 248
B. 263
C. 273
D. 283
Answer: 273
Let the missing number be x.
248 + x = 521
x = 521 – 248
x = 273
Thus the correct answer is option C.

Lesson 9.3 Add 3 or More Numbers

Activity

Solve & Share

A pet store has 162 goldfish, 124 angelfish, and 6 bowls with 9 pufferfish in each. How many fish are there in all?

You can generalize. Use what you know about adding two numbers to add three numbers.

Look Back! How can you decide if your answer is reasonable?

Visual Learning Bridge

Essential Question
How Can You Add More Than Two Numbers?

A.
Different kinds of birds are for sale at a pet store. How many birds are for sale?
Find 137 + 155 + 18.
Round to the nearest ten to estimate: 140 + 160 + 20 = 320.

B.
One Way
Use partial sums.

In all, 310 birds are for sale.

C.
Another Way
Use column addition.

The answer is reasonable because 310 is close to the estimate of 320.

In all, 310 birds are for sale.

Convince Me!
Model with Math For the partial sums above, Billy said, “20 plus 90 is 110. 110 plus 200 equals 310.” Is Billy correct? Use models, properties, or equations to represent and explain your thinking.

Guided Practice

Do You Understand?

In 1 and 2, look at the example on the previous page.

Question 1.
If you add the numbers in this order, do you get the same sum? Explain why or why not.

Answer:

Question 2.
Why is the 20 crossed out in the column addition problem?
Answer: 5 + 7 + 8 = 20

Do You Know How?

In 3 and 4, estimate and then find each sum.

Question 3.

Answer:
The number 123 round to the nearest ten is 120.
The number 168 round to the nearest ten is 170.
The number 36 round to the nearest ten is 40.

Thus the estimated sum is 330.

Question 4.

Answer:
The number 247 round to the nearest ten is 250.
The number 362 round to the nearest ten is 360.
The number 149 round to the nearest ten is 150.

Thus the estimated sum is 760.

You can use partial sums or column addition to add.

Independent Practice

Leveled Practice In 5-15, estimate and then find each sum.

Question 5.

Answer:
The number 64 round to the nearest ten is 60.
The number 42 round to the nearest ten is 40.
The number 88 round to the nearest ten is 90.
60 + 40 + 90 = 190

Thus the estimated sum is 190.

Question 6.

Answer:
The number 354 round to the nearest ten is 350.
The number 85 round to the nearest ten is 90.
The number 72 round to the nearest ten is 70.
350 + 90 + 70 = 510

Thus the estimated sum is 510.

Question 7.

Answer:
The number 307 round to the nearest ten is 310.
The number 37 round to the nearest ten is 40.
The number 234 round to the nearest ten is 230.
310 + 40 + 230 = 580

Thus the estimated sum is 580.

Question 8.

Answer:
The number 714 round to the nearest ten is 710.
The number 163 round to the nearest ten is 160.
The number 99 round to the nearest ten is 100.
710 + 160 + 100 = 970

Thus the estimated sum of the above numbers is 970

Question 9.

Answer:
The number 602 round to the nearest ten is 600.
The number 125 round to the nearest ten is 130.
The number 231 round to the nearest ten is 230.
600 + 130 + 230 = 960
Thus the estimated sum of the above numbers is 960.

Question 10.

Answer:
The number 64 round to the nearest ten is 60.
The number 42 round to the nearest ten is 40.
The number 88 round to the nearest ten is 90.

Question 11.

Answer:
The number 64 round to the nearest ten is 60.
The number 42 round to the nearest ten is 40.
The number 88 round to the nearest ten is 90.

Question 12.

Answer:
The number 125 round to the nearest ten is 130.
The number 35 round to the nearest ten is 40.
The number 124 round to the nearest ten is 120.
The number 239 round to the nearest ten is 240.
130 + 40 + 120 + 240 = 530

So, the sum of 125, 35, 124, 239 is 523.

Question 13.
32 + 9 + 56 +8
Answer:
When we add 32 + 9 + 56 +8 we get 105.
The number 105 round to the nearest hundred is 100.
Thus the estimated sum is 100.

Question 14.
481 + 78 + 42
Answer:
When we add 481 + 78 + 42 we get 601.
The number 601 round to the nearest hundred is 600.
Thus the estimated sum is 600.

Question 15.
398 + 219 + 23 + 251
Answer:
When we add 398 + 219 + 23 + 251 we get 891.
The number 891 round to the nearest hundred is 900.
Thus the estimated sum is 900.

Problem Solving

Question 16.
Use the picture at the right to find the height of President Washington’s head carved in Mt. Rushmore. Write an equation to solve the problem.

Answer:
Add all the numbers to find the height of President Washington’s head carved in Mt. Rushmore.
228 + 252 + 240 = 720 inches

Question 17.
Algebra Jada spends $74 on a hat, shoes, and shorts. If the hat costs $22 and the shoes cost $33, how much were the shorts? Write and solve an equation. Use an unknown to represent the cost of the shorts.
Answer:
Given,
Jada spends $74 on a hat, shoes, and shorts.
The hat costs $22 and the shoes cost $33
22 + 33 + x = 74
55 + x = 74
x = 74 – 55
x = 19
Thus the cost of shorts is $19.

Question 18.
Higher Order Thinking Meg says 95 + 76 + 86 is greater than 300, but less than 400. Is Meg correct? Why or why not?
Answer:
No Meg is not correct.
95 + 76 + 86 = 257
So, 257 is smaller than 300.
By this we can say that Meg is wrong.

Question 19.
Reasoning Karin had cereal, a glass of milk, and a banana for breakfast. How many calories were in her meal? Round to the nearest ten to estimate and then solve. Write an equation that includes your solution.

Answer:
Given,
Karin had cereal, a glass of milk, and a banana for breakfast.
105 round to the nearest ten is 100.
110 round to the nearest ten is 110.
150 round to the nearest ten is 150.
Now add the numbers 100 + 110 + 150 = 360
Thus the equation is 100 + 110 + 150 = 360

Assessment Practice

Question 20.
Use place value, partial sums, or properties of operations to find each sum.

Answer:

Question 21.
Use place value, column addition, or of operations to find each sum.

Answer:

Lesson 9.4 Use Partial Differences to Subtract

Activity

Solve & Share

Find the difference of 534 – 108. Think about how place value can help you subtract.

You can use structure. How could you use place value to help solve the problem?

Look Back! Jim had 388 marbles. He gave 8 marbles to each of 7 friends. How many marbles does Jim have left? How can place value help you to subtract 3-digit numbers?

Visual Learning Bridge

Essential Question
How Can You Use Partial Differences to Subtract?

A.
At the end of the fourth round of a game of Digit Derby, Marco’s score was 462 points. During the fifth round of the game, Marco loses points. What is Marco’s score at the end of the fifth round? Find 462 – 181.

Estimate first.
462 – 181 = ?
500 – 200 = 300
Place value can help you break a subtraction problem into smaller problems.

B.
What You Think
Use place value to subtract.
Count back by hundreds, tens, and ones.
181 = 100 + 80 + 1
Start at 462. Count back 100 to 362.
Count back 80 to 282
Break apart 80 into 60 and 20.
Count back 1 to 281.

C.
What You Write

At the end of the fifth round, Marco’s score is 281 points.
The score is close to the estimate.
The difference is reasonable.

Convince Me!
Be Precise Why was 80 broken into 60 and 20 in the computation above?

Guided Practice

Do You Understand?

Question 1.
Why do you need to record the numbers you subtract at each step?
Answer:
To keep track of where you are in an equation, and to allow you to retrace your steps if you happen to do something wrong.

Question 2.
Ana is trying to find 634 – 210. She decides to start by subtracting 10 from 634. Do you agree with Ana? Explain.
Answer:

Do You Know How?

In 3 and 4, estimate and then use partial differences to subtract. Use open number lines to help.

Question 3.
Find 374 – 236.

Answer:

Question 4.
Find 369 – 175.

Answer:

Independent Practice

In 5-10, estimate and then use partial differences to subtract. Use open number lines to help.

Question 5.
738 – 523

Answer: 215

Question 6.
755 – 315

Answer: 440

Question 7.
336 – 217

Answer: 119

Question 8.
455 –   182

Answer: 273

Question 9.
865 – 506

Answer: 359

Question 10.
794 – 355

Answer: 439

Problem Solving

Question 11.
Don’s book has 316 pages. He read 50 pages last week. He read another 71 pages this week. How many more pages does Don have left to read?
Answer:
total number of pages in Don’s book = 316
Don’s read pages in last week = 50
Don’s read pages in this week = 71
Don have to left to read pages = 316 – 50 + 71 = 195

Question 12.
Vocabulary Explain why it is necessary to regroup when adding 172 + 264.
Answer:
264
172
436
Regrouping is used when the addition of two numbers is greater than 9.
Here 7 + 6 = 13
13 > 10
So, regrouping is necessary here.
Therefore regrouping is necessary when adding 172 + 264

Question 13.
Use Structure Beth had a necklace with 128 beads. The string broke, and she lost 49 beads. How many beads does Beth have left? Explain how you can break the problem into smaller problems to solve.
Answer:
Beth had a necklace with beads = 128
The string broke and she lost beads =49
Beads left with Beth = 128 – 49 = 79

Question 14.
Write the time shown on the clock in two different ways.

Answer:
9: 15
21 : 15

Question 15.
Higher Order Thinking Which weighs more, two Basset Hounds or one Great Dane? Show the difference in pounds between two Basset Hounds and a Great Dane. Draw bar diagrams to represent and help solve the problem.

Answer:
The weight of two basset hounds = 66 + 66 = 132pounds
The weight of one great dane = 145  pounds
The weight of one grate dane is greater than two basset hounds.

Assessment Practice

Question 16.
Which have a difference of 181? Use place value and partial differences to solve. Select all that apply.
428 – 247 = ?
562 – 381 = ?
498 – 307 = ?
875 – 696 = ?
946 – 765 = ?
Answer:
428 – 247 = 181
562 – 381 = 181
498 – 307 = 191
875 – 696 = 179
946 – 765 = 181

Question 17.
Which have a difference of 237? Select all that apply.
877 – 640 = ?
412 – 176 = ?
652 – 415 = ?
700 – 459 = ?
802 – 565 = ?
Answer:
877 – 640 = 237
412 – 176 = 236
652 – 415 = 237
700 – 459 = 241
802 – 565 = 237

Lesson 9.5 Use Regrouping to Subtract

Activity

Solve & Share

Last year, there were 347 houses for sale in Mill County and 289 houses for sale in Hunter County. Of the houses for sale in both counties, 162 were sold. How many houses were not sold? Solve this problem two different ways.

You can generalize when you subtract 3-digit numbers. Think about all the strategies you can use.

Look Back! How are your solution strategies alike and how are they different?

Visual Learning Bridge

Essential Question

How Can You Use Regrouping to Solve Subtraction Problems?

Glossary

A.
Mike and Linda play a game. Linda has 528 points. Mike has 349 points. How many more points does Linda have than Mike? Find 528 – 349.
Estimate:
528 – 349 = ?
530 – 350 = 180

B.
Draw place-value blocks to show 528.

C. Subtract 9 ones.

Regroup 1 ten as 10 ones.

You can use place value to regroup when subtracting.

Subtract 4 tens. 528

Regroup 1 hundred as 10 tens.

Subtract 3 hundreds.

179 is close to the estimate.

Convince Me!
Use Appropriate Tools How could you use a tool to find 326 – 143?

Guided Practice

Do You Understand?

Question 1.
In the example on the previous page, explain how to decide if regrouping is necessary
Answer:

Question 2.
What strategies could you use to find 507 – 348?
Answer:
using the mental math
500 + 7 – 300 + 40 + 8
500 + 7 – 300 + 48
200 +7 -48  = 159
Do You Know How?

In 3 and 4, estimate each difference and then use partial differences to subtract.

Question 3.

Answer:
estimated difference
370
–  180
190  

Question 4.

Answer:
estimated difference
860
– 220 
   640 

Independent Practice

In 5-12, estimate each difference and then use partial differences to subtract.

Question 5.

Answer:
estimated difference
430
-140
   290 

Question 6.

Answer:
estimated difference
280
–  100 
   180 

Question 7.

Answer:
estimated difference
520
–  400 
   120  

Question 8.

Answer:
estimated difference
530
–  240 
   290   

Question 9.
574 – 86
Answer:
estimated difference
570 – 90 = 480

Question 10.
629 – 453
Answer:
estimated difference
630 – 450 = 180

Question 11.
979 – 569
Answer:
estimated difference
980 – 570 = 410

Question 12.
764 – 237
Answer:
estimated difference
760 – 240 = 520

Problem Solving

Question 13.
At the end of their game, Lora had 426 points and Theo had 158 points. How many more points did Lora have than Theo?

Answer: 268
Given
Lora had 426 points and Theo had 158 points
to find How many more points did Lora have than Theo
hence 426 subtract with 158 we get 268

Question 14.
Model with Math Zac and Malcolm each wrote short stories. Zac’s story is 272 lines long. Malcolm’s story is 145 lines longer than Zac’s. How long is Malcolm’s story? Explain how you can model with math to solve this problem.
Answer:
Given,
Zac and Malcolm each wrote short stories. Zac’s story is 272 lines long.
Malcolm’s story is 145 lines longer than Zac’s.
272 + 145 = 417
Therefore, Malcolm wrote 417 lines long.

Question 15.
The world’s largest basket is 186 feet tall from the base to the top of the handles. What is the height of the handles?

Answer: 83 feet
given
The world’s largest basket is 186 feet tall from the base to the top of the handles.
base to basket 103 feets
to find the height of the handles
hence 186 feet subtract with 103 feet we get 83 feet

Question 16.
Higher Order Thinking How many more swimmers signed up for the 1st session at Oak Pool than the 1st and 2nd sessions at Park Pool combined? Write an equation that represents the problem and includes the solution.

Answer:
given data
we have to find How many more swimmers signed up for the 1st session at Oak Pool than the 1st and 2nd sessions at Park Pool combined
hence oak pool 1st session 763 subtract with 2nd session 586 we get 177
oak pool 1st session 314 subtract with 2nd session 179 we get  135
oak pool 1st session 256 subtract with 2nd session 163 we get  93

Assessment Practice

Question 17.
Which shows the estimate of 627 – 441 by rounding to the nearest ten, and then the correct difference?
A. 200; 186
B. 200; 176
C. 190; 186
D. 190; 176
Answer: C
estimate of 627 – 441 we get 186
estimated 630 – 440 we get 190

Question 18.
Which shows the estimate of 901 – 512 by rounding to the nearest ten, and then the correct difference?
A. 390; 389
B. 390; 379
C. 400; 389
D. 400; 379
Answer: A
estimate of 901 – 512 we get 389
estimated 900 – 510 we get 390

Lesson 9.6 Use Strategies to Add and Subtract

Activity

Solve & Share

Rick is allowed to receive 1,000 text messages each month. How many more text messages can Rick receive this month? Solve any way you choose. Explain how you found the answer.

Use reasoning. First think about the operations you should use.

Look Back! Is your answer reasonable? How can you check?

Visual Learning Bridge

Essential Question How Can You Use Strategies to Add and Subtract?

A.
There are 136 fewer cell phone towers in Jurloe County than in Fraser County. How many cell phone towers are there in Jurloe County? Choose a strategy, and then solve.

402 is about 400.
136 is about 100.
The difference is about 300.

You can use addition or subtraction to solve.
402 = ? + 136
402 – 136 = ?
Addition and subtraction are inverse operations.

B.
One Way Use the adding on strategy.
Find 402 = ? + 136.

There are 266 cell phone towers in Jurloe County.

C.
Another Way
The answer is reasonable because it is close to the estimate of 300.
Use partial differences to subtract.
The answer is reasonable because it differences to is close to the estimate of 300.
Find 402 – 136 = ?


There are 266 cell phone towers in Jurloe County.

Convince Me! Use Appropriate Tools Show how to use a tool (such as a number line or place-value blocks) to solve the problem above.

Another Example!
The Yellowstone River is 692 miles long. It is 51 miles shorter than the Kansas River. How long is the Kansas River? Choose a strategy, and then solve. Find 692 + 51 = ?


The Kansas River is 743 miles long.

Guided Practice

Do You Understand?

Question 1.
To subtract 507 – 348, how can you regroup the tens if there are 0 tens?
Answer:
Subtract the ones.
7 ones > 8 ones
Since there are no tens in 507, regroup the hundreds.
5 hundreds and 0 tens = 4 hundreds 10 tens
Regroup the tens
10 tens and 7 ones = 9 tens and 17 ones
Subtract the ones, tens and then the hundreds.
So, 507 – 348 = 159

Question 2.
How is using partial sums to add like using place-value blocks and regrouping?
Answer: Thinking of the place value of digits in the numbers, Finding partial sums by adding parts of numbers according to their place value, and • Adding partial sums together to get a total.

Do You Know How?

In 3-6, estimate and then find each sum or difference.

Question 3.

Answer:
816 subtract with 335 we get 481
estimated 820 subtract with 340 we get 480

Question 4.

Answer:
163 add with 50 we get 213
estimated 160 add with 50 we get 210

Question 5.

Answer:
900 subtract with 375 we get 535
estimated 900 subtract with 370 we get 530

Question 6.

Answer:
508 subtract with 247we get 261
estimated 510 subtract with 250 we get 260

Independent Practice

In 7-14, find each sum or difference. Then use estimation to check your answer.

Question 7.

Answer:
549 subtract with 167 we get 382
estimated 550 subtract with 170 we get 380

Question 8.

Answer:
411 subtract with 238 we get 173
estimated 410 subtract with 240 we get 170

Question 9.

Answer:
560 add with 144 we get 704
estimated 560 add with 140 we get 700

Question 10.

Answer:
783 add with 68 we get 851
estimated 780 add with 70 we get 850

Question 11.
400 – 219
Answer:
400 subtract with 219 we get 619
estimated 400 subtract with 220 we get 620

Question 12.
904 – 703
Answer:
904 subtract with 703 we get 201
estimated 900 subtract with 700 we get 200

Question 13.
700 + 64
Answer:
700 add with 64 we get 764
estimated 700 add with 60 we get 760

Question 14.
807 + 38
Answer:
807 add with 38 we get 845
estimated 800 add with 40 we get 840

Problem Solving

Question 15.
How much more money does the Elm School Art Club need to raise? Complete the bar diagram and solve the problem.
Elm School


Answer:
By seeing the above figure we can find the amount of money to reach the goal.

$305 – $178 = $127
Therefore, the amount of money to reach goal is $127.

Question 16.
There were some ears of corn for sale at the farmers’ market. Three hundred eighty-eight ears of corn were sold. At the end, there were 212 ears left. How many ears of corn were for sale at the start?
Answer:
Given,
There were some ears of corn for sale at the farmers’ market.
Three hundred eighty-eight ears of corn were sold.
At the end, there were 212 ears left.
388 + 212 = 600
Thus there were 600 ears of corn for sale at the start.

Question 17.
Dina was adding books to the library shelves. She put 117 nonfiction books on the shelves. Then there were 204 nonfiction books. How many nonfiction books were on the shelves before?
Answer:
Given,
Dina was adding books to the library shelves.
She put 117 nonfiction books on the shelves.
Then there were 204 nonfiction books.
204 – 117 = 87
Thus there were 87 on the shelves before.

Question 18.
Construct Arguments The students at Cleveland School are collecting soda can tabs. The goal of each class is to collect 500 tabs. So far, the second graders have collected 315 tabs. The third graders have collected 190 more tabs than the second graders. Have the third graders reached their goal? Construct an argument to explain.
Answer:
Given,
The students at Cleveland School are collecting soda can tabs.
The goal of each class is to collect 500 tabs.
So far, the second graders have collected 315 tabs.
The third graders have collected 190 more tabs than the second graders.
315 + 190 = 505
505 > 500
Yes, the third graders reached their goal.

Question 19.
Higher Order Thinking Dylan had $405 in his savings account and spent $253. Brian had $380 in his savings account and spent $48 less than Dylan. Now who has more money in his savings account? How much more?
Answer:
Given,
Dylan had $405 in his savings account and spent $253.
$405 – $253 = $152
Brian had $380 in his savings account and spent $48 less than Dylan.
$253 – $48 = $205
$380 – $205 = $175
Brian has more money in his savings account.

Assessment Practice

Question 20.
Use a place-value strategy to find the value of the unknown in 426 + ? = 712.
A. 186
B. 216
C. 284
D. 286
Answer: D
by subtracting 712 with 426 we get 286
hence 426+286 = 712

Question 21.
Use the relationship between addition and subtraction to find the value of the unknown in ? +334 = 800.
A. 434
B. 466
C. 534
D. 566
Answer: B
by subtracting 800 with 334 we get 466
hence 466 +334 = 800

Lesson 9.7 Construct Arguments

Activity

Problem Solving

Solve & Share

Use each of the digits 0, 1, 2, 3, 4, and 5 only once. Write the digits in the space below to make two 3-digit addends with the greatest sum. Write the sum of the two addends. How do you know you have made the greatest sum?

Thinking Habits
Be a good thinker! These questions can help you.
• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?

Look Back! Construct Arguments Make different 3-digit addends to find the least possible sum. What is the difference between the greatest possible sum and the least possible sum? Construct an argument to explain how you know that your answer is correct.

Visual Learning Bridge

Essential Question
How Can You Construct Arguments?

A.
Nancy has $457 in her savings account and wants to have $500 by the end of the year. Christopher has $557 in his savings account and wants to have $600 by the end of the year. Who needs to save more money by the end of the year? My conjecture: They both need to save the same amount.

A conjecture is a statement that you think is true. It needs to be proved or disproved.

How can I explain why my conjecture is correct?
I need to construct an argument to justify my conjecture.

Here’s my thinking.

B.
How can I construct an argument?
I can
• use numbers, objects, drawings, or actions correctly to explain my thinking.
• make sure my explanation is simple, complete, and easy to understand.

C.
I will use drawings and numbers to explain my thinking.
The distance from 457 to 500 on the number line is the same as the distance from 557 to 600.

The number lines show that it takes the same amount of money to get from $457 to $500 as it takes to get from $557 to $600.
So, 500 – 457 = 600 – 557. My conjecture is correct.

Convince Me! Construct Arguments Construct another math argument to justify the conjecture above.

Guided Practice

Construct Arguments
Mr. Lee had $375 in the bank. Then he spent $242. Ms. Davis had $675 in the bank, and then spent $542. Who has more money left? Conjecture: They both have the same amount of money left.

Question 1.
Draw a diagram to represent the math.
Diagrams can help you support an argument.

Answer:

Question 2.
Use your diagram to justify the conjecture.
Answer:

Independent Practice

Construct Arguments

A Grade 2 class has made 165 paper cranes and wants to reach a total of 250. A Grade 3 class has made 255 paper cranes and wants to reach a total of 350. Which class has fewer paper cranes left to make to reach its goal?
Conjecture: The Grade 2 class has to make fewer paper cranes to reach its goal.

Question 3.
Draw a diagram at the right to represent the math.
Answer:

Question 4.
Use your diagram to justify the conjecture.
Answer:

Question 5.
Explain another way you could justify the conjecture.
Answer:

Problem Solving

Performance Task

Band Practice
Some musicians set goals for the number of minutes they want to practice before a concert, which is 5 days away. They want to know who has to practice the least number of minutes to reach his or her goal.

Question 6.
Make Sense and Persevere How can you find the number of minutes Aria has to practice to reach her goal?
Answer:

Question 7.
Reasoning So far Dexter and Sawyer have both practiced the same number of minutes. Do they need the same amount of practice time to reach their goals? Explain.
Answer:

When you construct arguments, you explain why your work is right.

Question 8.
Reasoning Who has the least number of minutes left to practice to reach his or her goal?
Answer;

Question 9.
Construct Arguments Construct a math argument to explain why your answer to Exercise 8 is correct.
Answer:

Topic 9 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 1 and Partner 2 each point to a black number at the same time. Both partners add those numbers.
If the answer is on your color, you get a tally mark. Work until one partner has seven tally marks. While playing the game, partners can use subtraction to check their addition.

Topic 9 Vocabulary Review

Word List

• conjecture
• estimate
• inverse operations
• place value
• regroup
• round

Understand Vocabulary

Draw a line to match each term to an example.

Question 1.
place value 515 + 141 is about 660.
Answer:
515
+414
656
The actual number is 656.
Here ones place is greater than 5.
So, we have to add 1 to the next ten.
Thus the estimated number of 656 is 660.

Question 2.
estimate 305 + 299 = 604 and 604 – 299 = 305
Answer:
The estimated number of 305 is 300.

Question 3.
regroup 232 = 2 hundreds 3 tens 2 ones
Answer:
Given,
regroup 232 = 2 hundreds 3 tens 2 ones
We can regroup 232 as
1 hundred 13 tens 2 ones

Question 4.
inverse operations 47 = 3 tens 17 ones
Answer:
47 = 3 tens 17 ones
We can regroup 47 as 4 tens 7 ones

Write always, sometimes, or never.

Question 5.
When rounding to the nearest ten, a number with a 5 in the ones digit ___ rounds to the next ten.
Answer: When rounding to the nearest ten, a number with a 5 in the ones digit always rounds to the next ten.

Question 6.
A conjecture is ___ true.
Answer: A conjecture is never true.

Question 7.
A digit with a greater place value is ____ written to the right of a digit with a lesser place value.
Answer: A digit with a greater place value is sometimes written to the right of a digit with a lesser place value.

Question 8.
A ten can ____ be regrouped as 10 hundreds.
Answer: A ten can never be regrouped as 10 hundreds.

Use Vocabulary in Writing

Question 9.
Explain how to find 600 – 281, and then explain how to check that the difference is correct. Use at least 2 terms from the Word List in your explanation.
Answer:
We can find the difference of 600 and 281 by using estimation.
The estimation of 281 is 300.
600 – 300 = 300
Actual difference:
600 – 281 = 319
The nearest hundred to 319 is 300.

Topic 9 Reteaching

Set A
pages 337–340
Find the sum of 257 + 186.
You can break apart 257 + 186 by place value to solve.

Break apart each number by place value and find the sum of the numbers in each place. Then add the sums.

So, 257 + 186 = 443.

Remember that you can use place value to add numbers by breaking large addition problems into smaller addition problems.

In 1-5, use place-value blocks or drawings and partial sums to add.

Question 1.
135 + 152
Answer: 287

Question 2.
650 + 138
Answer: 788

Question 3.
535 + 423
Answer: 958

Question 4.
475 + 264
Answer: 739

Question 5.
Yvette took 137 photographs on Friday. She took 248 photographs on Saturday. How many did she take in all?
Answer:
Given,
Yvette took 137 photographs on Friday.
She took 248 photographs on Saturday.
137 + 248 = 385
Thus Yvette takes 385 photographs in all.

Set B
pages 341-344
Find 235 + 187.
Estimate by rounding: 240 + 190 = 430. Use place-value blocks to represent each number and find partial sums. Regroup to find the final sum.

Remember that an estimate can help you check whether your answer is reasonable.
In 1-6, estimate and find each sum.

Question 1.

Answer:
236 add with 217 we get 453
estimated 240 add with 220 we get 460

Question 2.

Answer:
407 add with 436 we get 843
estimated 410 add with 440 we get 850

Question 3.
235 +59
Answer:
235 add with 59 we get 294
estimated 230 add with 60 we get  290

Question 4.
584 + 326
Answer:
584 add with 326  we get 910
estimated 590 add with 230  we get  820

Question 5.
196 + 243
Answer:
196 add with 243 we get 439
estimated 200 add with 240 we get  440

Question 6.
465 + 357
Answer:
465 add with 357 we get 822
estimated 460 add with 360 we get  820

Set C
pages 345–348
Find 124 + 32 + 238.
Estimate by rounding:
120 + 30 + 240 = 390.
You can solve using partial sums.

You can solve using column addition.

So, 124 + 32 + 238 = 394.

Remember that adding three numbers is like adding two numbers. In 1-7, estimate and then use partial sums to add.

Question 1.

Answer:
estimated
210
50
+ 310
570 

Question 2.

Answer:
estimated
410
270
+ 140
820

Question 3.
146 +86 + 53
Answer:
estimated
150+90+50 by adding we get 290

Question 4.
125 + 224 + 306
Answer:
by adding 120,220,and 310 we get 650

Question 5.
A flower shop has 124 tulips, 235 roses, and 85 carnations. How many flowers does the flower shop have?
Answer: 444
given
A flower shop has 124 tulips, 235 roses, and 85 carnations
to find How many flowers does the flower shop have
hence by adding 124 tulips, 235 roses, and 85 carnations we get 444

Question 6.
Mike’s Café sells 237 sandwiches on Friday. It sells 448 sandwiches on Saturday and 102 sandwiches on Sunday. How many sandwiches are sold on all 3 days?
Answer:
Given,
Mike’s Café sells 237 sandwiches on Friday.
It sells 448 sandwiches on Saturday and 102 sandwiches on Sunday.
237 + 448 + 102 = 787
Therefore Mike’s cafe sold 787 sandwiches on all 3 days.

Question 7.
Three planes leave an airport. Each plane has 239 seats. The first plane has 224 passengers. The second plane has 189 passengers. The third plane has 122 passengers. How many passengers are on all 3 planes?
Answer:
Given,
Three planes leave an airport.
Each plane has 239 seats. The first plane has 224 passengers. The second plane has 189 passengers. The third plane has 122 passengers.
Add all the number of passengers in 3 planes.
224 + 189 + 122 = 535
Therefore, there are 535 passengers in all 3 planes.

Set D
pages 349-352

So, 548 – 263 = 285.

Remember that place value can help you break a subtraction problem into smaller problems.

In 1-6, find each difference. Estimate and then use place value and partial differences to subtract.

Question 1.
489 – 253
Answer:
489 subtract with 253 we get 236
estimated 490 subtract with 250 we get 240

Question 2.
544 – 162
Answer:
544 subtract with 162 we get 382
estimated 540 subtract with 160  we get 380

Question 3.
856 – 328
Answer:
856 subtract with 328 we get 528
estimated 860 subtract with 330 we get 530

Question 4.
349 – 98
Answer:
349 subtract with 98 we get 251
estimated 350 subtract with 100 we get 250

Question 5.
873 – 184
Answer:
873 subtract with 184 we get 689
estimated 870 subtract with 180 we get 690

Question 6.
526 – 207
Answer:
526 subtract with 207 we get 733
estimated 530 subtract with 210 we get 740

Set E
pages 353-356
Find 416 – 243.
Estimate: 420 – 240 = 180.

Remember to regroup if necessary.

In 1-8, estimate each difference. Then find each difference.

Question 1.

Answer:
458 subtract with 176 we get 634
estimated 460 subtract with 180 we get 640

Question 2.

Answer:
236 subtract with 79 we get 315
estimated 240  subtract with 80 we get 320

Question 3.

Answer:
863 subtract with 526 we get 337
estimated 860 subtract with 530 we get 330

Question 4.

Answer:
748 subtract with 279 we get 469
estimated 750 subtract with 280 we get 470

Question 5.
400 – 227
Answer:
400 subtract with 227 we get 173
estimated 400 subtract with 230 we get 170

Question 6.
306 – 198
Answer:
306 subtract with 198 we get 108
estimated 310 subtract with 200 we get 110

Question 7.
220 – 187
Answer:
220 subtract with 187 we get 33
estimated 220 subtract with 190 we get 30

Question 8.
657 – 122
Answer:
657 subtract with 122 we get 535
estimated 660 subtract with 120 we get 540

Set F
pages 357-360

Two hundred seventy-three people have finished a marathon. A total of 458 people entered the marathon. How many people are still running?

You can use a bar diagram and addition or subtraction to solve.

Remember to regroup when needed.
In 1 and 2, estimate. Then solve.

Question 1.
Damian’s conservation club wants to plant 640 seedlings. They have 172 seedlings that they still need to plant to meet their goal. How many seedlings have they planted so far?
Answer:
Given,
Damian’s conservation club wants to plant 640 seedlings.
They have 172 seedlings that they still need to plant to meet their goal.
640 – 172 = 468
Therefore they have planted 468 seedlings so far.

Question 2.
The Smith family is driving to Dallas. The trip is 450 miles. So far, they have driven 315 miles. How many miles are left in the trip?
Answer:
Given,
The Smith family is driving to Dallas.
The trip is 450 miles. So far, they have driven 315 miles.
450 – 315 = 135
Thus 135 miles are left in the trip.

Set G
pages 361-364

Think about these questions to help you construct arguments.

Thinking Habits
• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?

Remember that a conjecture needs to be proved to be true.
Emma has $191. She spends $105. She donates $52 to charity. Can Emma save $30?
Conjecture: Emma can save $30.

Question 1.
Draw a diagram to represent the math.
Answer:

Question 2.
Use your diagram to justify the conjecture.
Answer:

Topic 9 Assessment Practice

Question 1.
Find the sum of 337 and 285. Use place value and find the sums of the hundreds, tens, and ones.

Answer:

Question 2.
An estimate of 431 – 249 using compatible numbers is 425 – 250 = 175. Would it be reasonable for the exact difference to be 182? Explain.
Answer:

Question 3.
Which addends are broken apart correctly? broken apart correctly. Select all that apply.
320 + 148
(300 + 100) + (20 + 40) + (20 + 8)
270 + 341
(2 + 70) + (3+ 4+1)
318 + 393
300 + (10 + 90) + (8 + 3)
532 + 360
(500 + 300) + (30 + 60) + 2
526 + 230
(500 + 200) + (20 + 30) + 6
Answer:

Question 4.
Find the sum of 176, 204, and 59.
A. 329
B. 339
C. 429
D. 439
Answer: D
the sum of 176, 204, and 59
176+204+59 we get 439

Question 5.
What is 276 + 289?
A. 509
B. 537
C. 565
D. 593
Answer: C
by adding 276 and 289 we get 565

Question 6.
Find 237 + 20. Then subtract the sum from 302.
Answer:
The sum of 237 + 20 = 257
302 – 257 = 45

Question 7.
Subtract 168 from 300.
A. 32
B. 122
C. 132
D. 142
Answer:
300 – 168 = 132
Thus the correct answer is option C.

Question 8.
A. Is 268 + 37 less than 346? Make a conjecture.
B. Construct an argument to prove your conjecture.
Answer:
305 < 346

Question 9.
What is 825 – 647?
A. 78
B. 82
C. 128
D. 178
Answer:
The subtraction of 825 and 647 is 178.
Thus the correct answer is option D.

Question 10.
Find 335 + 108 + 12. Then subtract the sum from 600.
Answer:
The sum of 335 + 108 + 12 = 455
600 – 455 = 145

Question 11.
Find 283 + 45. Then subtract 139 from the sum. What is the difference?
A. 189
B. 328
C. 377
D. 467
Answer:
283 + 45 = 328
328 – 139 = 189
Thus the correct answer is option A.

Question 12.
Describe how to use place-value blocks to regroup to solve the subtraction problem below. What is the difference?

Answer:
3 hundreds 1 tens 6 ones
-2 hundreds 2 tens 6 ones
This can be regrouped as
2 hundreds 11 tens 6 ones
– 2 hundeds 2 tens 6 ones
0 hundreds 9 tens 0 ones
The solution is 90

Question 13.
Find the difference between 254 and 125.
A. If you need to regroup to find the difference, explain how to do it. If you do not need to regroup, explain why not.
B. Find the difference.
Answer: 129

Question 14.
Put the steps in order to find 756 – 345.

Answer:

Question 15.
What is the difference between 408 + 240 and 259?
Answer:
408 + 240 = 648
648 – 259 = 389

Question 16.
Use place value to subtract 639 from 737. How many times do you have to regroup?
A. 3
B. 2
C. 1
D. 0
Answer: 2

Question 17.
Subtract.
457 – 338
A. 109
B. 119
C. 121
D. 129
Answer:
457 – 338 = 119
Thus the correct answer is option B.

Question 18.
Subtract 246 from 332.
Answer:
332 – 246 = 82

Topic 9 Performance Task

Video Arcade
Nita, Arif, and Sarah have been playing games at the video arcade.
The Tickets Estimates list below shows the number of tickets the friends estimated they would win before they started playing.
The Tickets Won table shows the numbers of tickets each friend won.

Tickets Estimates
• Nita estimated she would win 165 tickets.
• Arif estimated he would win 150 tickets.
• Sarah estimated she would win 175 tickets.

Question 1.
How many tickets did each of the friends win in all?
Answer:
Tickets won playing sports games by Nita = 96 + 112 = 208
Tickets won playing sports games by Arif = 94 + 91 = 185
Tickets won playing sports games by Sarah= 104 + 117 = 221
208 + 185 + 221 = 614 tickets

Question 2.
Show how many more tickets each friend won than his or her estimate.
Answer:

Question 3.
Arif says if he won 24 more tickets, he would have won more tickets than Nita. Is he correct? Explain.
Answer:
Tickets won playing sports games by Nita = 96 + 112 = 208
Tickets won playing sports games by Arif = 94 + 91 = 185
208 – 185 = 23

Question 4.
The three friends put all of their tickets together. How many tickets did they win in all?
Answer:
Tickets won playing sports games by Nita = 96 + 112 = 208
Tickets won playing sports games by Arif = 94 + 91 = 185
Tickets won playing sports games by Sarah= 104 + 117 = 221
208 + 185 + 221 = 614 tickets

Tickets can be used to buy prizes. The Arcade Prizes table shows how many tickets each prize costs.

Use the Arcade Prizes table to answer Question 5.

Question 5.
Use the total number of tickets you found in Question 4. The 3 friends will use this number of tickets to get 1 prize each and 1 more prize as a gift. Stuffed Animal
There are 2 rules the friends must follow.
• They cannot use more than their total number of tickets.
• After their purchases, they do not want more than 50 tickets remaining.
Part A
Arif starts a prize log to record the prizes they will get. In the table below, record some prizes the friends could choose, the cost of the prize, and show how many tickets they will have left.

Part B
If the friends made your choices from Part A, how many of their tickets would they use to get prizes? Explain how you found the answer.
Answer: