Unit 3, Lesson 23
Making and Measuring Boxes (Optional)
Accelerated 6
Preparation
Lesson Narrative
This culminating lesson is optional. Students apply their understanding of decimals to record, calculate, and analyze measurements of two- and three-dimensional objects: open-top paper boxes constructed by folding square paper of different sizes.
Before folding, students measure the side lengths of square pieces of paper and notice their relative sizes. Then, they make conjectures about how the length and area measurements would compare after the paper is folded into boxes.
Next, students measure the edge lengths of the paper boxes and calculate the surface area of each box, applying their knowledge of operations on decimals.
Finally, in an optional activity, students test their conjectures by making multiplicative comparisons—dividing the measurements of one box by those of another—and reflect on the accuracy of their predictions.
While arithmetic operations are central to the work in this lesson, students also build on concepts of geometry and ratios from earlier units. In each step along the way, as they deal with decimal measurements and calculations, students also need to consider the appropriate level of precision in the numbers and units they use and report (MP6).
Depending on the instructional choices made and students’ experience with paper folding, this lesson could take one or more class meetings.
- Compare the measurements of different paper boxes multiplicatively, and determine, by estimation or calculation, how many times as great one set of measurements are as another.
- Describe (orally) sources of measurement error, and justify an appropriate level of precision for reporting measurements or results of calculation.
- Measure the decimal edge lengths of paper boxes and calculate their surface area.
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. Though less common, larger sizes such as 10 inches and 12 inches are also available. To see the mathematical structure more clearly, using 6-inch paper for the smallest size and 12-inch paper for the largest is recommended. If origami paper is not accessible, cut squares of paper from available paper (thinner is better). Prepare at least 1 sheet for each student.
Pre-make sample boxes of different sizes to show students. To prepare to demonstrate the folding, consider practicing the steps and the verbal instructions.
To help students fold their own origami boxes, both an embedded video and printed instructions are provided. If using the printed instructions from the blackline master, prepare 1 copy for every 2 students. The instructions can be re-used with multiple classes.