Exploring and Analyzing Patterns - HHS Algebra...

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Chapter 1 Assignments 1

1Lesson 1.1 Assignment

Name Date

Patterns: They’re Grrrrrowing!Exploring and Analyzing Patterns

1. A jewelry box company offers simple jewelry boxes with decorative tiles. The top and bottom of each box are adorned with heart tiles while the sides consist of diamond tiles. Pictures of the first 3 jewelry box designs and their corresponding tile layouts are shown.

Design 1 Design 2

Design 3

a. Sketch the tile layout for Design 4 on the grid provided.

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2 Chapter 1 Assignments

1b. Analyze the jewelry box designs. Describe as many patterns as you can.

c. Determine a method you can use to calculate the number of diamond tiles, the number of heart tiles, and the total number of tiles used for any design.

d. The company has 4 times as many heart tiles as they have diamond tiles in their inventory. The owner decides to advertise a sale on the box design which uses 4 times as many heart tiles as diamond tiles. Determine which design the owner will have the sale on.

Lesson 1.1 Assignment page 2

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1Lesson 1.1 Assignment page 3

Name Date

2. Susan starts her own telemarketing company by recruiting 3 employees into what she calls Recruiting Group 1. She requires each employee in Recruiting Group 1 to recruit 3 additional employees for Recruiting Group 2. The employees in each successive recruiting group must meet the same requirement of recruiting 3 additional employees.

a. Create a visual model to represent the number of employees in the company. Only include the first 3 recruiting groups in your model. Do not include Susan as an employee.

b. Determine a method to calculate the number of employees in any given recruiting group. Use that method to calculate the number of employees hired in each of the first 6 recruiting groups.

c. Susan can only afford to hire a total of 800 employees. She tells the employees to halt all recruiting as soon as the 800th employee is hired. Which recruiting group will be partially completed at that time? Explain your reasoning.

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1

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Are They Saying the Same Thing?Using Patterns to Generate Algebraic Expressions

1. Hyatt Home Improvement uses H-shaped tile designs on their buildings, advertisements, and vehicles. The designs they use follow a specific pattern. The first three designs are shown.

Design 3Design 2Design 1

a. Describe the pattern in the designs.

b. Write two different expressions to represent the number of tiles used in Design n. Use algebraic properties to prove the two expressions are equivalent.

c. Explain how you could use a graphing calculator to prove the two expressions in part (b) are equivalent.

Lesson 1.2 Assignment

Name Date

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1 Lesson 1.2 Assignment page 2

d. Create a table which displays the number of tiles used in each of the first 6 designs.

e. Create a graph of the data points in your table on the coordinate plane shown. Draw a smooth curve to connect the points.

f. Do all of the points on the smooth curve make sense in terms of the problem situation? Explain your reasoning.

g. Describe the pattern as linear, exponential, quadratic, or none of these. Explain your reasoning.

h. The owner of Hyatt Home Improvement wants to put 1 of their designs on an empty rectangular sign in front of their headquarters. The empty sign is 10 feet tall and 12 feet wide. If he uses square tiles measuring 1 foot by 1 foot, what is the number of the largest design that will fit on the sign? How many tiles will that design require?

x

0 2

60

4 6Design Number

Num

ber

of T

iles

8 10

y

80

100

40

20

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1

Are All Functions Created Equal?Comparing Multiple Representations of Functions

1. The functions, graphs, and tables that represent 3 different scenarios are shown.

F1.

f(x) 5 216 x 2 1 1900

F2.

f(x) 5 4 x

F3.

f(x) 5 250x 1 450

G1.

x

0 1

600

2 3 4 5

y

800

1000

400

200

G2.

x

0 2

300

4 6 8 10

y

400

500

200

100

G3.

x

0 2

1200

4 6 8 10

y

1600

2000

800

400

T1.

x y

0 1

1 4

2 16

3 64

4 256

T2.

x y

0 1900

2 1836

4 1644

6 1324

8 876

T3.

x y

0 450

2 350

4 250

6 150

8 50

a. Juanita is driving home from her vacation spot at a constant rate. Which function, graph, and table represent her distance from home as a function of the number of hours she has traveled? Explain your reasoning.


Name Date

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b. A mechanic drops a wrench from a flying helicopter. Which function, graph, and table represent the height of the wrench above the ground as a function of the time since it was dropped? Explain your reasoning.

c. Scientists watch as a single cell divides into 4 cells over the course of an hour. During the next hour, each of the 4 new cells divides into 4 cells and the process continues. Which function, graph, and table represent the total number of cells as a function of time? Explain your reasoning.

2. Ingrid makes quilts in designs that follow a specific pattern. The first three designs are shown. In the designs, the white blocks represent blocks containing pictures while the gray blocks represent border blocks of a single color.

Design 1 Design 2 Design 3

a. Analyze the quilt designs. Describe as many patterns as you can.

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Name Date

b. Complete the table.

Design Number

Number of Picture Blocks

Number of Border Blocks

Total Number of Blocks

c. Write the function p(n) to represent the number of picture blocks in Design n.

d. Write the function b(n) to represent the number of border blocks in Design n.

e. The total number of blocks in Design n can be represented by the function t(n) 5 (n 1 2)(n 1 3). Use the functions you wrote to show that t(n) 5 p(n) 1 b(n).

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f. Will there always be an even number of total blocks in each design? Explain your reasoning.

g. An art museum hires Ingrid to make one of her quilt designs to display pictures of each of their 90 paintings in 90 individual picture blocks. Which design does the art museum choose? How many total blocks are in the design?

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1

Water Under the BridgeModeling with Functions

1. Mr. Jones wants to fence in a rectangular field for his horse using the 600 feet of fence he has stored in his barn. He wants to maximize the area of the field in order to give his horse the most pasture possible. Help Mr. Jones design his field to achieve the maximum area.

width

length

a. Complete the table to show the length of the field for each given width.

Width (feet) 0 50 100 150 200 250 300

Length (feet)

b. Define the function <(w) to represent the length of the field as a function of the width. Explain your reasoning.

c. Define the function A(w) to represent the area of the field as a function of the width. Explain your reasoning.

d. Determine the maximum area of the field as well as the length and width that will result in the maximum area. Explain your reasoning.


Name Date

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2. Mrs. Williams wants to fence in a rectangular area of her field using the 1200 feet of fence she has. She wants the area to have four congruent sections. She is trying to decide which of the two designs shown will give her animals the maximum fenced area.

width

length

Design 1

width

length

Design 2

Determine the design and the dimensions of the design that will give Mrs. Williams the maximum fenced area. Show your work and explain your reasoning.

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1

I’ve Created a Monster, m(x)Analyzing Graphs to Build New Functions

1. Analyze the graphs of the functions f(x) and g(x).

x

4

24

84028 24 6226 22

y

28

22

26

8

2

6

f(x)

g(x)

a. Predict the function family of h(x) 5 f(x) 1 g(x). Explain your reasoning.

b. Plot 3 points that will lie on the graph of h(x).

c. Determine the equations of the functions f(x) and g(x).


Name Date

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d. Determine the equation of the function h(x) 5 f(x) 1 g(x). Then, graph h(x).

e. Does h(x) belong to the function family you predicted? Does the graph of h(x) pass through the 3 points you plotted?

2. Analyze the graphs of the functions m(x) and n(x).

x

4

24

84028 24 6226 22

y

28

22

26

8

2

6

m(x)

n(x)

a. Predict the function family of t(x) 5 m(x) ? n(x). Explain your reasoning.

b. Plot 3 points that will lie on the graph of t(x).

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Name Date

c. Complete the table of values.

x m(x) n(x) t(x) 5 m(x) ? n(x)

26

24

22

0

2

d. Do the values in the table verify your prediction about the function family of t(x)? Explain your reasoning.

e. Determine the equations of the functions m(x) and n(x).

f. Determine the equation of the function t(x) 5 m(x) ? n(x). Then, graph t(x).

g. Does t(x) belong to the function family you predicted? Does the graph of t(x) pass through the 3 points you plotted?

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Exploring and Analyzing Patterns - HHS Algebra...

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