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Common Core State Standards

444 Unit 6 Geometry

Advance PreparationMake one copy of Math Masters, page 428 per four children. Have a few extras available.

Teacher’s Reference Manual, Grades 1–3 p. 161

Measuring AnglesObjective To guide children as they measure angles.

Key Concepts and Skills• Determine fractional parts of a circle. 

[Number and Numeration Goal 2]

• Identify quarter-turns and 90 degrees

as measures of right angles. 

[Geometry Goal 1]

• Investigate the degrees of a circle. 

[Geometry Goal 2]

• Introduce the degree as a unit of measure

for turns. 

[Measurement and Reference Frames Goal 1]

Key ActivitiesChildren model turns by rotating connected

straws. They make an angle measurer by

folding a circle and then measure angles

with it.

Ongoing Assessment: Informing Instruction See page 447.

Ongoing Assessment: Recognizing Student Achievement Use journal page 144.  [Geometry Goal 1]

Key Vocabularydegree

MaterialsMath Journal 1, pp. 143 and 144

Home Link 6�7

Math Masters, p. 428

transparency of Math Masters, p. 428

(optional) � tool-kit clocks � 2 straws and

1 twist-tie per child � scissors � calculator

(optional) � wax paper (optional)

Finding Area and PerimeterMath Masters, p. 205A

Children determine the areas of given

shapes and select the shape with the

shortest perimeter measure.

Math Boxes 6�8Math Journal 1, p. 145

Children practice and maintain skills

through Math Box problems.

Home Link 6�8Math Masters, p. 182

Children practice and maintain skills

through Home Link activities.

ENRICHMENTSolving Degree Problems Using a Clock FaceMath Masters, pp. 183 and 184

straws and twist-ties

Children solve degree problems on a clock.

EXTRA PRACTICE

Minute Math +Minute Math ®+, p. 59

Children use degree measures to

describe shapes.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

�������

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143

Marking Angle MeasuresLESSON

6 �8

Date Time

Connect 2 straws with a twist-tie. Bend the twist-tie at the connection

to form a vertex.

� Place the straws with the vertex on the center of the circle.

� Place both straws pointing to 0°.

Keep one straw pointing to 0°. Move the other straw to form angles.

0°

EM3MJ1_G3_U06_128-156.indd 143 1/18/11 3:31 PM

Math Journal 1, p. 143

Student Page

Lesson 6 �8 445

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

Have children turn the minute hand on their tool-kit clocks as you

go over the answers. 1 _ 4 turn = 15 minutes; 1 _ 2 turn = 30 minutes;

3 _ 4 turn = 45 minutes; all the way around = 60 minutes

Ask: How long does it take the minute hand to turn 1 _ 3 of the way

around the clock face? 20 minutes 2 _ 3 of the way? 40 minutes 1 _ 6 of

the way? 10 minutes How long does it take to make 1 1 _ 2 turnsaround the clock face? 90 minutes

� Introducing the Degree as WHOLE-CLASS ACTIVITY

a Unit of Measure for Turns(Math Journal 1, p. 143)

A standard unit of measure called the degree is used to measure turns and angles. To support English language learners, discuss the different contexts and meanings of the word degree. Show a 1° angle on the overhead projector and point out that it is very small. Have children generate a list of objects that are about the size of a 1° angle. A sliver of wood, the tip of a pencil, a pin, and so on

To measure the size of a turn, we think of a circle being divided into 360 equal parts. Each part is called a degree. Ask children to imagine a round pizza cut into 360 equal pieces. Think about how small the pieces would be! Write the symbol for degrees (°) on the board. For example, 30 degrees can be written using the word or the symbol (30°).

ELL

Getting Started

Math Message How many minutes does it take the minute

hand on a clock to turn 1

_ 4 of the way around the clock face?

1

_ 2 of the way around?

3

_ 4 of the way around?

All the way around?

Home Link 6�7 Follow-Up Draw a circle like the one on Home Link 6-7 on the board. Ask volunteers to mark the answers on the circle. Note that there is more than one correct answer for Problems 4, 5, and 6.

Mental Math and Reflexes Pose multiplication number stories like the following. Children share solution strategies. Encourage children to use division to check their results.

5 people. 4 slices of pizza per person. How many slices of pizza in all? 20 slices of pizza

3 dogs. 4 legs per dog. How many legs in all? 12 legs

6 jackets. 4 pockets per jacket. How many pockets in all? 24 pockets

6 boxes. 6 crayons per box. How many crayons in all? 36 crayons

3 boxes. 1 dozen doughnuts per box. How many doughnuts in all? 36 doughnuts

6 hours. 60 minutes per hour. How many minutes? 360 minutes

NOTE To review acute

and obtuse angles, go to

www.everydaymathonline.com.

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446 Unit 6 Geometry

Circles for Angle Measures

Name Date Time

Cut the sheet into four parts along the dashed lines.

Share the circles with the members of your group. Each person will cutout his or her own circle.

Math Masters, p. 428

Teaching Aid Master

Links to the Future

Adjusting the Activity

315˚

360˚0˚

45˚

90˚

135˚

180˚

225˚

270˚

Have children form an angle with two straws and a twist-tie. Ask children to open their journals to page 143. Show them how to place the straws with the vertex on the center of the circle, with both straws pointing approximately to the 0-degree mark.

Have children keep one straw pointing to the 0-degree mark and move the other straw clockwise all the way around the circle. The full turn measures 360°.

Next have children move the straw clockwise 1 _ 4 turn. Ask: What isthe degree measure of a quarter turn? 90°; a full turn measures

360°, and 1 _ 4 of 360° = 90° Tell children to make a mark on therim of the circle at the quarter-turn point and to label it 90°. Ask: What is another name for a 90° angle? A right angle

Repeat this routine with a half-turn and a three-quarter turn. Before each turn, children return both straws to the starting position. They move one straw the specified fraction of a turn clockwise and make a mark on the rim. They share strategies for finding the number of degrees of the turn, and record the number

of degrees next to the mark. 1 _ 4 turn: 90°, so 1 _ 2 turn: 2 × 90°, or

180°; 3 _ 4 turn: 3 × 90° or 270°

Finally, repeat the above routine with 1 _ 8 , 3 _ 8 , 5 _ 8 , and 7 _ 8 turns.

1 _ 8 turn is 1 _ 2 of 1 _ 4 turn and 1 _ 4 turn is 90°, so 1 _ 8 turn is 1 _ 2 of 90°, or 45°

3 _ 8 turn: 3 × 45°, or 135°

5 _ 8 turn: 5 × 45°, or 225°

7 _ 8 turn: 7 × 45°, or 315°

Have children use calculators to determine the degree measures. Note

that some calculators have Deg keys on them. This key sets the unit of measure

for advanced functions and has nothing to do with the use of degrees in this

activity.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

Expect that some children will be able to determine the number of degrees in

turns with the use of a calculator, but do not expect that all children will be able

to multiply fractions or work with multiplication fact extensions at this time. In

Unit 7, children revisit using basic multiplication facts to compute fact extensions.

Solving problems involving the multiplication of fractions is a Grade 5 Goal.

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Lesson 6 �8 447

0°

360°

180°

270°

315°

225°

90°

45°

135°

An angle measurer

Measuring AnglesLESSON

6 �8

Date Time

A

B CD

EF

Use your angle measurer to measure the angles on this page.

Record your measurements in the table. Then circle the right angle below.� Angle Measurement

A about 45 °

B about 90 °

C between 90 ° and 135 °

D about 180 °

E about 135 °

F about 225 °

EM3MJ1_G3_U06_128-155.indd 144 2/10/10 1:51 PM

Math Journal 1, p. 144

Student Page

� Making an Angle Measurer SMALL-GROUP ACTIVITY

(Math Masters, p. 428)

Divide the class into groups of four. Give each group a copy of Math Masters, page 428 and proceed as follows:

1. Children cut the master into four parts along the dashed lines.

2. Each child carefully cuts out one circle.

NOTE It is helpful to model Steps 3, 4, and 5 for the children with an extra circle.

3. To divide the circle into eight equal parts, children fold their circles in half, in half again, and then in half once more.

4. Children unfold their circles, make marks on the rim at the folds, and label each mark with the appropriate degree measure, as shown in the margin. Have children add an arrow at the 0° mark.

5. Children punch a small hole in the center of the circle with the point of a pencil or pen.

NOTE An angle measurer can also be made from a piece of wax paper the size

of the circles on Math Masters, page 428. The advantage to the wax paper

measurer is that it is transparent enough to be placed directly over the angles on

journal page 144.

� Measuring Angles with WHOLE-CLASS ACTIVITY

the Angle Measurer(Math Journal 1, p. 144; Math Masters, p. 428)

Show children how to use the angle measurer using the transparency of Math Masters, page 428.

1. Place the hole in the center of the measurer over the vertex of the angle.

2. Align the 0° mark on the measurer with the side of the angle where the curved arrow begins.

3. Look in the direction of the curved arrow. Read the degree measure where the other side of the angle crosses the rim of the measurer.

Children measure each angle and record the result in the table. For angle C, suggest that they express the result as between x degrees and y degrees. Circulate and help as needed. Bring the class together to compare measurements.

Ongoing Assessment: Informing Instruction

Watch for children who have difficulty lining up the 0° mark on the measurer

with the side of the angle where the arrow begins. Have them trace their fingers

along the arrow that denotes the turning prior to using the angle measurer.

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448 Unit 6 Geometry

Name Date Time

LESSON

6�8 Area and Perimeter

In the spring, the Garden Club will plant a garden. Each child will have

one square meter of dirt to plant. There are 16 children in the club, so

the area of the garden has to equal 16 square meters. The children

drew the shapes below for the garden.

1. Circle the shapes that have areas of 16 square meters. Cross out

the shapes that do not have areas of 16 square meters. Show how

you found the areas.

16 m 1m

a. b.

Area = 7 square meters Area = 16 square meters

c. d.

Area = 16 square meters Area = 16 square meters

2. The club wants to build a fence around their garden, but they don’t

want to spend a lot of money. They need to find a shape that has an

area of 16 square meters and the shortest perimeter.

Which of the above shapes has an area of 16 square meters and

the shortest perimeter? Shape b

How did you find the perimeter for this shape? Sample answer: Since

each side is 4 meters, I multiplied 4 × 4 to find the

perimeter. The perimeter is 16 meters.

1 m

7 m 4 m

4 m

2 m

5 m

5 m

3 m

2m

3m

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Math Masters, p. 205A

Teaching Master

5. Write the letter that names the right

angle.

B

3. Write these numbers in order from

smallest to largest:

0.2; 0.02; 0.19

0.02

0.19

0.2

smallest largest

Date Time

2. If each grid is ONE, what part of each

grid is shaded? Write the decimal.

0.73

0.8

Circle the smaller number.

4. 49 people in all. 7 people per van.

How many vans?

6. Complete the Fact Triangle.

Write the fact family.

7 × 8 = 56

8 × 7 = 56

56 ÷ 7 = 8

56 ÷ 8 = 7

Math BoxesLESSON

6 �8

197

36

34 36

259

98 55

1. Continue the pattern.

7 8

56

×,÷

people

per van

7

vans peoplein all

49?

Number model: 49 ÷ 7 = ?

A B

DC

or ? × 7 = 49Answer: 7 vans

EM3MJ1_G3_U06_128-156.indd 145 1/21/11 3:29 PM

Math Journal 1, p. 145

Student Page

Links to the FutureThe activities in this lesson are an early

exposure to measuring angles. Determining

angle measures is a Grade 5 Goal.

Ongoing Assessment: Journal

page 144 �Recognizing Student Achievement

Use journal page 144 to assess children’s ability to recognize a right angle.

Children are making adequate progress if they circle the right angle on the

journal page. Some children may recognize which angles are larger or smaller

than 90° without measuring.

[Geometry Goal 1]

2 Ongoing Learning & Practice

� Finding Area and Perimeter PARTNER ACTIVITY

(Math Masters, p. 205A)

Children determine which of the shapes on Math Masters, page 205A have areas of 16 square meters. They also select the shape with an area of 16 square meters that has the shortest perimeter measure and explain how they calculated the perimeter. Have partners work together to complete page 205A.

� Math Boxes 6�8 INDEPENDENTACTIVITY

(Math Journal 1, p. 145)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-6. The skill in Problem 6 previews Unit 7 content.

Writing/Reasoning Have children write an answer to the following: Explain how the shaded grids in Problem 2 help you decide which decimal is smaller. Sample answer:

Because both grids are ONE, the grid with fewer squares shaded shows a smaller decimal.

� Home Link 6�8 INDEPENDENTACTIVITY

(Math Masters, p. 182)

Home Connection Children estimate the sizes of angles and match given angles with estimated measures.

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LESSON

6�8

Name Date Time

Clock Angles

12 12

3

4567

8

9

1011

1. How many minutes does the minute hand

take to move ...

from 10:00 to 11:00?

from 4:00 to 4:30?

from 6:00 to 6:15?

from 9:00 to 9:05?

2. Through how many degrees does the minute hand move ...

from 10:00 to 11:00?

from 4:00 to 4:30?

from 6:00 to 6:15?

from 9:00 to 9:05?

3. Through how many degrees does the hour hand move ...

in 3 hours?

in 2 hours?

in 1 hour?

Make up your own clock-angle problems.

4. Through how many degrees does the hand

move ...

in ?

in ?

30 degrees

60 degrees

90 degrees

30 degrees

90 degrees

180 degrees

360 degrees

5 minutes

15 minutes

30 minutes

60 minutes

Answers vary.

EM3MM_G3_U06_167-205.indd 183 1/18/11 12:56 PM

Math Masters, p. 183

Teaching Master

Lesson 6 �8 449

LESSON

6�8

Name Date Time

Modeling Angles on a Clock Face

Connect 2 straws with a twist-tie.

� Model the movement of the minute hand as suggested in each

problem on Math Masters, page 183.

� Refer to your angle measurer to help you figure out the

measurements in Problems 2 and 3.

12 12

3

4567

8

9

1011

EM3MM_G3_U06_167-205.indd 184 1/18/11 12:56 PM

Math Masters, p. 184

Teaching Master

py

gg

p

Name Date Time

Degree MeasuresHOME LINK

6�8

Our class has been learning about turns, angles, and angle measures. A full turn can be represented by an angle of 360°, a 1 _

2 turn by an angle of 180°, a 1 _

4 turn by an angle of 90°,

and so on. Help your child match the measures below with the angles pictured. (It is not necessary to measure the angles with a protractor.)

Please return this Home Link to school tomorrow.

Family Note

Tell which angle has the given measure.

1. about 180° angle

2. about 90° angle

3. about 270° angle

4. between 0° and 90° angle

5. between 90° and 180° angle A or B

C or D

E

D

A

A

B

C DE

Rotation Degrees

1

_ 4 turn 90°

1

_ 2 turn 180°

3

_ 4 turn 270°

full turn 360°

EM3MM_G3_U06_167-205.indd 182 1/18/11 12:56 PM

Math Masters, p. 182

Home Link Master

3 Differentiation Options

ENRICHMENT PARTNER ACTIVITY

� Solving Degree Problems 15–30 Min

Using a Clock Face(Math Masters, pp. 183 and 184)

To explore the relationship between angle measures and a clock face, have children use straws and twist-ties to model the movement of the minute hand on Math Masters, page 184. Children calculate how many degrees the hands of a clock move in given amounts of time on Math Masters, page 183.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

� Minute Math+ 5–15 Min

To offer children more experience with degree measures, see the following page in Minute Math+:

Geometry: p. 59, Level 3.

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Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

205A

Name Date Time

LESSON

6�8 Area and Perimeter

In the spring, the Garden Club will plant a garden. Each child will have

one square meter of dirt to plant. There are 16 children in the club, so

the area of the garden has to equal 16 square meters. The children

drew the shapes below for the garden.

1. Circle the shapes that have areas of 16 square meters. Cross out

the shapes that do not have areas of 16 square meters. Show how

you found the areas.

16 m 1m

a. b.

Area = square meters Area = square meters

c. d.

Area = square meters Area = square meters

2. The club wants to build a fence around their garden, but they don’t

want to spend a lot of money. They need to find a shape that has an

area of 16 square meters and the shortest perimeter.

Which of the above shapes has an area of 16 square meters and

the shortest perimeter?

How did you find the perimeter for this shape?

1 m

7 m 4 m

4 m

2 m

5 m

5 m

3 m

2m

3m

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