## Math Central

Grade 6, Chapter 12 Investigation Organizer:

## Pack It Up

**Summary:** Have you seen how people unpack boxes from cartons? Your group's assignment is to pack 100 cereal boxes and 100 cans of food and send them to a flood relief center. To make the most of the space and use the fewest possible cartons, you need a plan. You will draw a diagram to show how you would pack these boxes and cans.

**1. Plan It**

** Measure the carton's dimensions.** Bring a cereal box or a cylindrical can from home. Measure the width, length, and height of your cereal box and the diameter and height of your can.

Record the weight of the packaging and contents for both your box and can.

**Can and box measurements taken and recorded**

**2. Put It Together**

** Think "inside of the box." ** Work together to pack 100 boxes of cereal and 100 cans in 19-in. by 12-in. by 16-in. cartons. Decide the best way to pack one carton. How many boxes fit into one carton? Experiment by drawing diagrams. For example, each box can be positioned in six different ways. Three pairs of different-sized faces can lie facedown on the bottom in either a left-to-right or a front-to-back orientation. Cans should stand on their circular ends.

Based on your group's discussion and experiments, find how many cartons you need to pack in order to complete the entire shipment. Draw a diagram to explain your solution.

**Our carton-packing method planned and diagrams drawn**

**3. Wrap It Up**

** Send them packing!** The cardboard for each empty carton weighs 2 oz. Find how much the contents of each carton weighs, including the carton itself. Round the weight to the next whole pound. How much will the entire shipment weigh?

How would you seal the boxes? How many feet of package tape do you need?

**Cartons weighed, sealed, and prepared for shipment**

**4. Discuss Your Results**

- How did your group use diagrams to solve this problem?
- How well can you explain your solution?
- How clear and complete is your final diagram?
- How well did your group work together to pack the cartons?
- Is there much unused space left in your carton? Suggest two carton sizes that would work better for your group's particular cereal box and can. Justify your reasoning.

**Review completed**

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