In this lesson, students practice using exponents of 2 and 3 to express products and to write square and cubic units. Along the way, they look for and make use of structure in numerical expressions (MP7). They also look for and express regularity in repeated reasoning (MP8) to write the formula for the surface area of a cube. Students will continue this work later in the course, in the unit on expressions and equations.
Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.
Lesson overview
- 18.1 Warm-up: Exponent Review (5 minutes)
- 18.2 Activity: The Net of a Cube (20 minutes)
- 18.3 Activity: Every Cube in the Whole World (10 minutes)
- Lesson Synthesis
- 18.4 Cool-down: From Volume to Surface Area (5 minutes)
Learning goals:
- Generalize a process for finding the surface area of a cube, and justify (orally) why this can be abstracted as \(6 \cdot s^2\).
- Interpret (orally) expressions that include repeated addition, multiplication, repeated multiplication, or exponents.
- Write expressions, with or without exponents, to represent the surface area of a given cube.
Learning goals (student facing):
- Let’s write a formula to find the surface area of a cube.
Learning targets (student facing):
- I can write and explain the formula for the surface area of a cube.
- When I know the edge length of a cube, I can find its surface area and express it using appropriate units.
Required materials:
- geometry toolkits
Glossary:
- Access the complete Grade 6 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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