Triangles, Rectangles, Squares, and Circles - Pueblo County School ...

LESSON

21

? Triangles, Rectangles,

Squares, and Circles

Power Up

multiples

Power Up K

The multiples of 7 are 7, 14, 21, and so on. On your hundred

number chart, circle the numbers that are multiples of seven.

Which of the circled numbers is an even number as well as a

multiple of five? 70

mental

math

a. Number Sense: 44 + 32

76

b. Number Sense: 57 + 19

76

c. Number Sense: 32 + 43 + 100

175

d. Number Sense: What number should be added to 6 to get

a total of 9? 3

e. Money: What is the total value of 2 quarters, 3 dimes, and

1 nickel? 85?

f. Money: What is the total cost of a $200 bicycle and a

$24 helmet? $224

g. Estimation: Round $13.89 to the nearest dollar. $14

h. Estimation: Round 73 yards to the nearest ten yards. 70 yd

problem

solving

Choose an appropriate problem-solving strategy to solve

this problem. The P.E. instructor divided the 21 students

into four teams. If the P.E. instructor divided the class as

evenly as possible, how many students were on each of the

four teams? one team of 6 students and three teams of 5 students

New Concept

In this lesson we will practice drawing triangles, rectangles,

squares, and circles.

Lesson 21

127

Example 1

Represent

Draw a triangle whose sides all have the same

length.

Math Language

A triangle whose

sides are all equal

in length is called

an equilateral

triangle.

You may need to practice on a separate sheet of paper to

understand how to draw this triangle. A triangle has three sides, but

those sides can be positioned many different ways. If you start with

a ¡°square corner,¡± the third side will be too long.

This side is longer than

the other two sides.

square corner

A triangle whose sides are the same length looks like this:

Example 2

Represent

Draw a rectangle whose sides all have the same

length.

A rectangle has four sides and square corners. It does not have

to be longer than it is wide. A rectangle whose sides are the same

length looks like this:

This figure looks like a square. We know that it is a square because

it has 4 sides with the same length. It is also a rectangle. A square

is a special kind of rectangle.

Example 3

Thinking Skill

Analyze

Represent

Draw a rectangle that is 3 cm long and 2 cm wide.

We use a centimeter ruler to help us make the drawing.

cm 1

What is the

perimeter of this

rectangle?

10 cm

2

cm 1

128

Saxon Math Intermediate 4

2

3

A circle is a closed, curved shape in which all points on the shape

are the same distance from the center. To draw circles, we can use

a tool called a compass. Below we show two types of compasses:

Math Language

When we talk

about one radius,

we say ¡°radius.¡±

When we talk

about more than

one radius, we say

¡°radii.¡± The plural

of radius is radii.

cm

1

2

3

4

5

1

in.

6

2

7

8

3

9

10

11

4

There are two points on a compass: a pivot point and a pencil

point. We swing the pencil point around the pivot point to draw a

circle. The distance between the two points is the radius of the

circle.

The radius of a circle is the distance from the center of the circle

to the edge of the circle. The diameter of a circle is the distance

across the circle through the center. As the diagram below

illustrates, the diameter of a circle equals two radii.

Math Language

The circumference

of a circle is the

distance around¡ª

or the perimeter

of¡ªa circle.

radius

radius

diameter

Activity

Drawing a Circle

Material needed:

? compass

Represent

Use a compass to draw a circle with a radius of

2 cm. Label the diameter and the radius.

Example 4

If the radius of a circle is 2 cm, then what is the diameter of the

circle?

Since the diameter of a circle equals two radii, the diameter of a

circle with a 2-cm radius is 4 cm.

Lesson 21

129

Lesson Practice

a. Draw a triangle with two sides that are the same length.

See student work.

b. Draw a rectangle that is about twice as long as it is wide.

c.

See student work.

1 in.

c. Use a compass to draw a circle with a radius of 1 inch.

See student work.

d. What is the diameter of a circle that has a 3-cm radius?

6 cm

e. What is another name for a rectangle whose length is equal

to its width? square

Written Practice

Distributed and Integrated

Write and solve equations for problems 1 and 2.

1. Hiroshi had four hundred seventeen marbles. Harry had two hundred

twenty-two marbles. How many marbles did Hiroshi and Harry have

in all? 417 + 222 = t; 639 marbles

(1, 13)

* 2. Tisha put forty pennies into a pile. After Jane added all of her pennies,

there were seventy-two pennies in the pile. How many pennies did

Jane add to the pile? 40 + j = 72; 32 pennies

(11, 14)

3. The ones digit is 5. The number is greater than 640 and less than 650.

(4)

What is the number? 645

* 4.

(16)

* 5.

(6)

Represent

700 + 50 + 3

Write seven hundred fifty-three in expanded form.

If x + y = 10, then what is the other addition fact for x, y,

and 10? What are the two subtraction facts for x, y, and 10?

Connect

y + x = 10; 10 ? x = y, 10 ? y = x

* 6. These thermometers show the average daily low and high

(18)

temperatures in San Juan, Puerto Rico, during the month

of January. What are those temperatures? 71¡ãF and 82¡ãF













&

130

Saxon Math Intermediate 4

&

* 7.

Model

(Inv. 2)

Use a centimeter ruler to measure the rectangle below.

a. What is the length?

4 cm

b. What is the width?

2 cm

c. What is the perimeter?

8.

(13)

493

+ 278

12 cm

9.

(13)

$486

+ $378

771

* 11.

(Inv. 2,

21)

10.

(13)

$524

+ $109

$633

$864

Draw a triangle. Make each side 2 cm long. What is the

perimeter of the triangle? 6 cm

2 cm

Represent

2 cm

2 cm

* 12.

(Inv. 2,

21)

Draw a square with sides 2 inches long. What is the

perimeter of the square? 8 in.

Represent

2 in.

2 in.

13.

17

? a

9

8

17.

24

+ d

45

21

21.

46

35

27

+ 39

(12)

(14)

(17)

(15)

(3,

Inv. 1)

45

? 29

15.

(12)

16

147

* 25.

14.

Conclude

18.

14

? b

2

22.

14

28

77

+ 23

(16)

(17)

12

* 19.

(16)

23.

(17)

142

15 9

? b

6

y

? 36

53

14

23

38

+ 64

89

16.

(15)

62

? 45

17

* 20.

(16)

24.

(17)

75

? p

45

30

15

24

36

+ 99

139

174

Write the next three numbers in each counting sequence:

a. . . . , 28, 35, 42, 49 , 56 , 63 , . . .

b. . . . , 40, 30, 20, 10 ,

0

, ?10 , . . .

Lesson 21

131

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download