Unit 1, Lesson 17
Squares and Cubes
Grade 6
Preparation
Lesson Narrative
In this lesson, students learn about perfect squares and perfect cubes. They see that these names come from the areas of squares and the volumes of cubes with whole-number side lengths. Students are introduced to exponents in this context.
Students learn to use the exponent 2 to express multiplication of two side lengths of a square and the exponent 3 to express multiplication of three edge lengths of a cube. They learn that the words squared and cubed can be used to describe expressions with exponents 2 and 3 and see the geometric motivation for this terminology. (The term “exponent” is deliberately not defined more generally at this time. Students will work with exponents in more depth in a later unit.)
Throughout the lesson, students attend to precision (MP6) as they think about the units for length, area, and volume. To write the formula for the volume of a cube, students also look for and express regularity in repeated reasoning (MP8).
Today’s activity is for students to individually reflect on the norms generated so far. During the Cool-down, students provide feedback on the norms, sharing those they agree with and those they feel need revision or removal. These suggestions will inform the next version of the classroom norms.
- Generalize a process for finding the volume of a cube, and justify (orally) why this can be abstracted as $s^3$.
- Include appropriate units (orally and in writing) when reporting lengths, areas, and volumes, e.g., cm, cm2, cm3.
- Interpret and write expressions with exponents 2 and 3 to represent the area of a square or the volume of a cube.
Let’s investigate perfect squares and perfect cubes.
Required Preparation
Prepare sets of 32 snap cubes for each group of 2 students.
For the digital version of the activity, acquire devices that can run the applet.