# Lesson 23

Making and Measuring Boxes

### Lesson Narrative

In this optional culminating lesson of the unit, students construct open-top origami boxes by folding different-size square paper. Before folding, they make conjectures about how the paper size affects the length and area measurements of the boxes. Later, they test their conjectures by finding and analyzing those measurements (MP8). While arithmetic operations on decimals are central to this work, students also build on their geometric work from earlier units. As they investigate the relationship between the side lengths of the origami paper and the edge lengths of the boxes, they also connect to their work on ratios.

This lesson is organized into two parts:

• Part 1: Measure, predict, and fold. Students carefully measure the sheets of square paper, predict the measurements of the boxes created from different-size sheets, and fold their paper into a box.
• Part 2: Measure, calculate, and compare. Students carefully measure the dimensions of the boxes, calculate their surface areas, and then compare the sizes of the boxes. They also reflect on the accuracy of their predictions from Part 1.

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:

• The size of the class.
• How familiar students are folding paper into shapes.
• How student work is ultimately shared with the class (not at all, informally, or with formal presentations).

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

### Learning Goals

Teacher Facing

• Apply operations with decimals to calculate the surface area of paper boxes.
• Describe (orally) sources of measurement error, and justify an appropriate level of precision for reporting the answer.
• Measure and compare (orally and in writing) the dimensions of paper boxes.

### Student Facing

Let’s use what we know about decimals to make and measure boxes.

### Required Preparation

Choose at least three different sizes of origami paper for students to use. Common length and width sizes of square origami paper include 6 inch, 7 inch, 8 inch, 9 inch, and 9.75 inch. If origami paper is not available, cut squares of paper from available paper (thinner is better). Pre-make sample boxes of different sizes.

In order to help students fold their own origami boxes, both an embedded video and printed instructions are provided. The printed instructions are in the Folding Paper Boxes blackline master. If using the printed instructions, prepare 1 copy for every 2 students. These can be re-used with multiple classes.

### Student Facing

• I can use the four operations on decimals to find surface areas and reason about real-world problems.