Math Focus 9
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# Logo Designs on Boxes

### INTRODUCTION

The company Bright Ideas ships its craft supplies in boxes that are decorated with company logos. They need a variety of shapes of boxes to ship different craft supplies.

 Your task is to choose sizes of boxes and plan designs for arranging the Bright Ideas logos on one side of each box chosen. • The Bright Ideas logo is a square with a thin silver line from corner to corner as shown at the right. • All logos on a box must be the same size. • There can be space around the edge of a logo design, but there cannot be space between the logos. • Since the silver string is made with different material, it needs to be ordered separately.

### THE PROCESS

1. Visit Packing and Storage Boxes and Shipping Boxes to find boxes with different dimensions. Choose a box with a square side.
2. Use to convert the units to metric.
3. Plan the four different designs below to display the Bright Ideas logo. Sketch each design with the measurements on plain paper, 1 cm square dot paper, or 2 cm square dot paper. Show your calculations.
• Design 1: one logo that is as large as possible
• Design 2: one row of logos to fill as much of the width as possible, or one column of logos to fill as much of the length as possible
• Design 3: a rectangle with rows and columns of logos
• Design 4: another design for a rectangle with rows and columns of logos that are a different size than the logos in Design 3
1. Determine the length of silver tape for each design in step 3.
2. Choose a box with a side that is not a square and repeat steps 2 to 4.
1. Suppose that to get opinions about the designs from people in the company, you need to meet with three people and ask each of them to meet with three more people. How many people, including you, would have been involved in the meetings after 3 rounds?
2. Suppose that to get opinions about the designs from people outside the company, you need to ask a number of people and have each of them ask the same number of people. Plan a number of people to be asked in each round to get between 200 and 250 opinions. How many rounds would you use?

### RESOURCES

Websites:

Shipping Boxes

Length Conversions

Files:

1 cm square dot paper

2 cm square dot paper

Materials:

a pencil
plain paper (optional)
a ruler
a calculator

### ASSESSMENT

 Work meets standard of excellence Work meets standard of proficiency Work meets acceptable standard Work does not yet meet acceptable standard Problem Solving: Make a Plan Develops a thorough plan for solving the problems about the designs and about opinion gathering. Chooses an efficient and effective strategy. Develops a workable plan for solving the problems about the designs and about opinion gathering. Chooses an appropriate and workable strategy. Develops a basic plan for solving the problems about the designs and about opinion gathering. Chooses a simplistic and routine strategy. Develops a minimal and/or flawed plan for solving the problems about the designs and about opinion gathering. Chooses an inappropriate or unworkable strategy. Problem Solving: Carry out the Plan Shows flexibility and insight when solving the problems, adapting if necessary. Shows thoughtfulness when solving the problems. Shows understanding when solving the problems. Attempts to solve the problems. Problem Solving: Look Back Verifies solutions by explaining and justifying work and correctly determines appropriateness of the response. Verifies solutions by explaining and justifying work and reasonably determines appropriateness of the response. Attempts to verify solutions by explaining and justifying work and determine appropriateness of the response. Has difficulty verifying solutions by explaining and justifying work.