Lesson 17: Fitting Boxes into Boxes

An artist makes necklaces. She packs each necklace in a small jewelry box that is $1\frac34$ inches by $2\frac14$ inches by $\frac34$ inch.

A department store ordered 270 necklaces. The artist plans to ship the necklaces to the department store using flat-rate shipping boxes from the post office.

Which of the flat-rate boxes should she use to minimize her shipping cost?

1. Read the problem statement. What additional information will you need to solve this problem?
2. Discuss this information with your group. Make a plan for using this information to find the most inexpensive way to ship the jewelry boxes. Once you have agreed on a plan, write down the main steps.

Work with your group to find the best plan for shipping the boxes of necklaces. Each member of your group should select a different type of flat-rate shipping box and answer the following questions. Recall that each jewelry box is $1\frac34$ inches by $2\frac14$ inches by $\frac34$ inch, and that there are 270 jewelry boxes to be shipped.

For each type of flat-rate shipping box:

1. Find how many jewelry boxes can fit into the box. Explain or show how the jewelry boxes can be packed in the shipping box. Draw a sketch to show your thinking, if needed.
2. Calculate the total cost of shipping all 270 jewelry boxes in shipping boxes of that type. Show your reasoning and organize your work so it can be followed by others.

1. Share and discuss your work with the other members of your group. Your teacher will display questions to guide your discussion. Note the feedback from your group so you can use it to revise your work.
2. Using the feedback from your group, revise your work to improve its correctness, clarity, and accuracy. Correct any errors. You may also want to add notes or diagrams, or remove unnecessary information.
3. Which shipping boxes should the artist use? As a group, decide which boxes you recommend for shipping 270 jewelry boxes.
   Be prepared to share your reasoning.