## 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.