# Lesson 22

Fitting Boxes into Boxes

### Lesson Narrative

In this three-part culminating activity, students use what they have learned to determine the most economical way to ship jewelry boxes using the United States Postal Service (USPS) flat-rate options.

In Part 1, students make sense of the task, outline what they will need to know and do to answer the question, and map out their plan. In Part 2, they model the problem, calculate the number of jewelry boxes that will fit into each shipping box, and determine the associated costs. Students experiment with different orientations for the jewelry boxes to optimize space and minimize cost. In Part 3, they present, reflect, and discuss. Students explain their strategies and reasoning (MP3) and evaluate the decisions about how to fit all 270 jewelry boxes so they ship at the lowest cost (MP4). As a class, students reflect on how the orientation of the jewelry boxes and the size of the shipping boxes affected the unit cost for shipping each box of jewelry.

Depending on the instructional choices made, this lesson could take one or more class meetings. The time estimates are intentionally left blank because the amount of time needed might vary depending on factors such as:

• If students will research the flat-rate options themselves, or be provided with this information.
• If each group will explore all size options or only one option.
• How much organizational support is given to students.
• How student work is ultimately shared with the class (e.g., not at all, informally, or with formal presentations).

Consider defining the scope of work further and setting a time limit for each part of the activity to focus students’ work and optimize class time.

Teacher Notes for IM 6–8 Accelerated
This culminating lesson is optional.

### Learning Goals

Teacher Facing

• Compare and contrast (orally and using other representations) different ways jewelry boxes could be packed inside larger shipping boxes.
• Determine which size shipping box is least expensive, and present (orally and in writing) a justification.
• Make simplifying assumptions and determine what information is needed to solve a problem about shipping costs.

### Student Facing

Let’s use what we learned about fractions to find shipping costs.

### Required Preparation

Bring in samples of United States Postal Service flat-rate boxes, or have images of these boxes available.

### Student Facing

• I can use multiplication and division of fractions to reason about real-world volume problems.