topic 1 factors and area - kyrene school district · v. calculating area of composite figures a....

Factors and area: Skills Practice • 1

1. (29 1 17) 1 13

3. ( 1 __ 2 1 4 __ 9 ) 1 5 __ 9

5. 6.2 1 (0.8 1 2.54)

2. (18 1 75) 1 25

4. (2.2 1 1.01) 1 0.99

6. 2 __ 5 1 ( 8 __ 5 1 1 __ 3 )

B. Use the associative Property to rewrite each expression in order to add more efficiently. then determine the sum.

I. Commutative and Associative PropertiesA. Use the commutative Property to rewrite each expression in order to add more efficiently. then determine the sum.

2. 1 __ 2 1 3 __ 8 1 3 __ 2

4. 35 1 17 1 105

6. 5.04 1 8.35 1 1.16

1. 95 1 19 1 5

3. 0.1 1 3.93 1 2.9

5. 3 __ 4 1 6 1 __ 8 1 3 __ 8

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2 • Module 1: composing and decomposing

1. 5 3 (19 3 2)

3. 5 3 (18.5 3 20)

5. (1.25 3 7) 3 4

2. 20 3 (6 3 2)

4. 1 __ 2 3 ( 13 ___ 16 3 2)

6. ( 5 __ 8 3 1 ___ 12 ) 3 16

1. 7 1 6 1 3

3. 2 3 8 3 3 3 5

5. 8 3 2 3 8

2. 5 3 6 3 4

4. 9 1 4 1 11 1 16

6. 4 1 7 1 1 1 6 1 3

C. Use the commutative and associative Properties to rewrite each expression in order to multiply more efficiently. then determine the product.

D. Write an equivalent numeric expression for each using the commutative and associative Properties. then determine the sum or product.

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II. Exploring the Distributive Property with Numeric ExpressionsA. complete each to represent the shading in the model.

2. 1.

4. 3.

6. 5.

7 3 (4 1 3) 5 7 3 1 7 3

5 1 21

5

3 3 ( 1 2) 5 3 3 6 1 3 2

5 1 6

5

5 3 (6 1 3) 5 5 3 1 5 3

5 30 1

5

8 3 (5 1 4) 5 8 3 1 8 3

5 40 1

5

3 (3 1 8) 5 6 3 3 1 3 8

5 1 48

5

3 (7 1 5) 5 4 3 1 4 3 5

5 28 1

5

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1. 10 3 8

2. 9 3 12

3. 13 3 7

4. 9 3 8

5. 12 3 6

6. 13 3 11

a. 9(8 1 4)

b. 13(7 1 4)

c. 9(6 1 2)

d. 10(7 1 1)

e. 12(3 3 3)

f. 10(4 3 4)

g. 13(3 1 4)

h. 12(4 1 2)

1. 35 1 28

2. 18 1 36

3. 121 1 22

4. 14 1 77

5. 27 1 12

6. 56 1 42

a. 7 3 (8 1 6)

b. 7 3 (2 1 11)

c. 11 3 (11 1 2)

d. 6 3 (3 1 6)

e. 3 3 (9 1 4)

f. 7 3 (5 1 4)

B. Identify the expression that shows a correct way to decompose each.

C. Match each expression to the equivalent addition expression.

1. 8 3 12 5 8 3 ( 1 10) 2. 5 3 14 5 5 3 (10 1 )

D. complete each equation.

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3. 7 3 13 5 7 3 ( 1 10)

5. 11 3 15 5 11 3 ( 1 10)

4. 9 3 11 5 9 3 ( 1 1)

6. 12 3 12 5 12 3 (10 1 )

4. 3.

2. 1.

III. Calculating Area of Various FiguresA. calculate the area of each given figure.

4 mi

8 mi

11 mi

6 mi

8 in.

6 in.

11 mm

20 mm

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6. 5. 4 feet

3 feet

2 feet

5 yards 2 yards 8 yards

IV. Solving Area ProblemsA. Use the given information to answer each question.

1. a flag is folded into a triangle to be displayed in a triangular display with the dimensions shown in the diagram. How many square inches of glass are need to cover the display?

15 in.

8 in.

2. Yvonne cut a picture into the shape of a parallelogram to place into her scrapbook. the picture is shown. What is the area of the picture?

12 cm

7.5 cm

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3. the side of a staircase has the shape of a trapezoid with the dimensions shown in the diagram. You want to paint this side of the staircase. How many square feet will you need to cover with paint?

26 feet

13 feet

11 feet

5. the planning committee submitted a plan to the town architect to revitalize the town square. their plan includes a new flagpole with a concrete base in the shape of a trapezoid. the base of the trapezoid and its dimensions are shown. What is the area of the base proposed by the planning committee?

5 feet4 feet

7 feet

4. aisha wants to make a pennant using felt for her school’s football team. the pennant will be a triangle with the dimensions shown in the diagram. How many square yards of felt will the pennant be made of?

1 ydyd12

6. a pendant on a necklace is created from two congruent parallelograms that share a side. the pendant is shown below. Half of the pendant will be covered with gold leaf. How many square millimeters of gold leaf will be used?

25 mm

10 mm

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V. Calculating Area of Composite FiguresA. calculate the area of each shaded region.

2. the figure is composed of a kite and a square. Given: AG 5 7 meters, BG 5 FG 5

8 meters, DG 5 13.5 meters, and CE 5 9 meters

1. the figure is composed of 2 congruent rhombi.

4. the figure is composed of 2 congruent triangles and a rhombus.

3. the figure is composed of a trapezoid and a rhombus.

16 ft

20 ft

C

A

F

E

B

GD

8.5 in.

11 in.

10 in.

24 in. 4 in.

4 in.5 in.

4 in.

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6. the figure is composed of two trapezoids.5. the figure is composed of a square and a kite. Given: AE 5 9 inches, BE 5 DE 5

7 inches, and CE 5 15 inches.

C

A

EB D

8 cm

14 cm

25 cm

12 cm

10 cm

VI. Investigating Factors and Greatest Common FactorsA. list the factors of each number. Then, determine the greatest common factor.

2. 48, 20

4. 15, 16

6. 25, 36

1. 25, 45

3. 32, 56

5. 32, 80

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B. Write the prime factorization for each number. Then, determine the greatest common factor.

C. rewrite each numeric expression using the distributive Property and the GcF.

1. 18, 42

3. 54, 45

5. 72, 90

1. 56 1 35

3. 54 1 72

5. 32 1 28

1. 6, 9

2. 56, 72

4. 48, 108

6. 36, 60

2. 90 1 27

4. 36 1 60

6. 88 1 66

2. 12, 30

VII. Investigating Multiples and Least Common MultiplesA. list the multiples of each number. Then, determine the least common multiple.

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3. 4, 7

5. 8, 11

4. 42, 70

6. 24, 40

B. Write the prime factorization for each number. Then, determine the least common multiple.

1. 28, 32

3. 18, 45

5. 50, 105

2. 40, 100

4. 30, 70

6. 126, 84

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VIII. Solving LCM and GCF ProblemsA. Use the scenario to answer each question.

1. emilio’s family volunteers at the local soup kitchen every 30 days. emilio has swimming lessons every 9 days. He has both activities this saturday. When will he have both activities again on the same day?

2. Yuko is volunteering at the food bank. He is creating thanksgiving food baskets to give to local families. He has 192 cornbread muffins, 96 cans of vegetables, and 64 boxes of stuffing mix. What is the greatest number of baskets Yuko can create if he wants to use all of the items and have the same number of each item in each basket? How many of each item will be in a basket?

3. At the middle school, the bell rings every 40 minutes to tell the students to change classes. across the street the clock above city hall chimes every 30 minutes. Both the school bell and the clock ring at noon. When will both bells ring again at the same time?

4. Belinda babysits her neighbor’s children in the evening every 14 days. Belinda goes to visit her grandmother in the afternoon every 21 days. Belinda has both activities planned for today. Will Belinda have both activities again on the same day within 30 days? explain your reasoning.

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5. Hector is dividing students into groups for a nature hike. He wants to divide the boys and girls so that each group has the same number of both boys and girls. there are 21 boys and 56 girls signed up for the hike. Into how many groups can the students be divided? How many boys and how many girls will be in each group?

6. ramona is filling window box planters that will be sold to benefit a local charity. She has 56 pansies, 42 tulips, and 28 marigolds. What is the greatest number of planters she can fill if she wants to use all of the flowers and have the same number of each type of flower in each planter? How many of each flower type will be in a planter?

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topic 1 factors and area - kyrene school district · v. calculating area of composite figures a....

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