Patterns: They re Grrrrrowing!
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1 Lesson 1.1 Assignment 1 Name Date Patterns: The re Grrrrrowing! Eploring and Analzing Patterns 1. A jewelr bo compan offers simple jewelr boes with decorative tiles. The top and bottom of each bo are adorned with heart tiles while the sides consist of diamond tiles. Pictures of the first 3 jewelr bo designs and their corresponding tile laouts are shown. Design 1 Design 2 Design 3 a. Sketch the tile laout for Design 4 on the grid provided. Chapter 1 Assignments 1
2 1 Lesson 1.1 Assignment page 2 b. Analze the jewelr bo designs. Describe as man patterns as ou can. c. Determine a method ou can use to calculate the number of diamond tiles, the number of heart tiles, and the total number of tiles used for an design. d. The compan has 4 times as man heart tiles as the have diamond tiles in their inventor. The owner decides to advertise a sale on the bo design which uses 4 times as man heart tiles as diamond tiles. Determine which design the owner will have the sale on. 2 Chapter 1 Assignments
3 Lesson 1.1 Assignment page 3 1 Name Date 2. Susan starts her own telemarketing compan b recruiting 3 emploees into what she calls Recruiting Group 1. She requires each emploee in Recruiting Group 1 to recruit 3 additional emploees for Recruiting Group 2. The emploees in each successive recruiting group must meet the same requirement of recruiting 3 additional emploees. a. Create a visual model to represent the number of emploees in the compan. Onl include the first 3 recruiting groups in our model. Do not include Susan as an emploee. b. Determine a method to calculate the number of emploees in an given recruiting group. Use that method to calculate the number of emploees hired in each of the first 6 recruiting groups. c. Susan can onl afford to hire a total of 800 emploees. She tells the emploees to halt all recruiting as soon as the 800th emploee is hired. Which recruiting group will be partiall completed at that time? Eplain our reasoning. Chapter 1 Assignments 3
4 1 4 Chapter 1 Assignments
5 Lesson 1.2 Assignment 1 Name Date Are The Saing the Same Thing? Using Patterns to Generate Algebraic Epressions 1. Hatt Home Improvement uses H-shaped tile designs on their buildings, advertisements, and vehicles. The designs the use follow a specific pattern. The first three designs are shown. Design 1 Design 2 Design 3 a. Describe the pattern in the designs. b. Write two different epressions to represent the number of tiles used in Design n. Use algebraic properties to prove the two epressions are equivalent. c. Eplain how ou could use a graphing calculator to prove the two epressions in part (b) are equivalent. Chapter 1 Assignments 5
6 1 Lesson 1.2 Assignment page 2 d. Create a table which displas the number of tiles used in each of the first 6 designs. e. Create a graph of the data points in our 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? Eplain our reasoning Design Number g. Describe the pattern as linear, eponential, quadratic, or none of these. Eplain our reasoning. h. The owner of Hatt Home Improvement wants to put 1 of their designs on an empt rectangular sign in front of their headquarters. The empt sign is 10 feet tall and 12 feet wide. If he uses square tiles measuring 1 foot b 1 foot, what is the number of the largest design that will fit on the sign? How man tiles will that design require? Number of Tiles Chapter 1 Assignments
7 Lesson 1.3 Assignment 1 Name Date 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() F2. f() 5 4 F3. f() G1. G2. G T1. T2. T 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? Eplain our reasoning. Chapter 1 Assignments 7
8 1 Lesson 1.3 Assignment page 2 b. A mechanic drops a wrench from a fling 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? Eplain our reasoning. c. Scientists watch as a single cell divides into 4 cells over the course of an hour. During the net 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? Eplain our 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 gra blocks represent border blocks of a single color. Design 1 Design 2 Design 3 a. Analze the quilt designs. Describe as man patterns as ou can. 8 Chapter 1 Assignments
9 Lesson 1.3 Assignment page 3 1 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 b the function t(n) 5 (n 1 2)(n 1 3). Use the functions ou wrote to show that t(n) 5 p(n) 1 b(n). Chapter 1 Assignments 9
10 1 Lesson 1.3 Assignment page 4 f. Will there alwas be an even number of total blocks in each design? Eplain our reasoning. g. An art museum hires Ingrid to make one of her quilt designs to displa pictures of each of their 90 paintings in 90 individual picture blocks. Which design does the art museum choose? How man total blocks are in the design? 10 Chapter 1 Assignments
11 Lesson 1.4 Assignment 1 Name Date Water Under the Bridge Modeling 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 maimize the area of the field in order to give his horse the most pasture possible. Help Mr. Jones design his field to achieve the maimum area. width length a. Complete the table to show the length of the field for each given width. Width (feet) Length (feet) b. Define the function <(w) to represent the length of the field as a function of the width. Eplain our reasoning. c. Define the function A(w) to represent the area of the field as a function of the width. Eplain our reasoning. d. Determine the maimum area of the field as well as the length and width that will result in the maimum area. Eplain our reasoning. Chapter 1 Assignments 11
12 1 Lesson 1.4 Assignment page 2 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 tring to decide which of the two designs shown will give her animals the maimum fenced area. Design 1 Design 2 length width width length Determine the design and the dimensions of the design that will give Mrs. Williams the maimum fenced area. Show our work and eplain our reasoning. 12 Chapter 1 Assignments
13 Lesson 1.5 Assignment 1 Name Date I ve Created a Monster, m() Analzing Graphs to Build New Functions 1. Analze the graphs of the functions f() and g() f() g() a. Predict the function famil of h() 5 f() 1 g(). Eplain our reasoning. b. Plot 3 points that will lie on the graph of h(). c. Determine the equations of the functions f() and g(). Chapter 1 Assignments 13
14 1 Lesson 1.5 Assignment page 2 d. Determine the equation of the function h() 5 f() 1 g(). Then, graph h(). e. Does h() belong to the function famil ou predicted? Does the graph of h() pass through the 3 points ou plotted? 2. Analze the graphs of the functions m() and n() m() n() a. Predict the function famil of t() 5 m()? n(). Eplain our reasoning. b. Plot 3 points that will lie on the graph of t(). 14 Chapter 1 Assignments
15 Lesson 1.5 Assignment page 3 1 Name Date c. Complete the table of values. m() n() t() 5 m()? n() d. Do the values in the table verif our prediction about the function famil of t()? Eplain our reasoning. e. Determine the equations of the functions m() and n(). f. Determine the equation of the function t() 5 m()? n(). Then, graph t(). g. Does t() belong to the function famil ou predicted? Does the graph of t() pass through the 3 points ou plotted? Chapter 1 Assignments 15
16 1 16 Chapter 1 Assignments
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