Math 8 Unit 10

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In the first section of this chapter, students will study three-dimensional shapes. This focus will begin with students looking at the volume of a cube and determining how to find the length of one side of the cube. This investigation introduces the cube root operation. Then students work on developing strategies to find the surface area and volume of several non-rectangular based prisms, beginning with cylinders. They also learn to find the volumes of cones and pyramids by comparing cylinders and cones with equal heights and congruent bases, as well as prisms and pyramids with equal heights and congruent bases. Students will explore the relationships between the volumes of these different solids, and will use that relationship to determine volumes of pyramids and cones. Similarly, at the end of the section, students compare the volumes of spheres and cylinders with similar dimensions to develop the formula to calculate the volume of a sphere.

Finally, Section 10.2 offers several class activities to help pull ideas from the entire course together. These activities are designed to enable students to reflect about what they have learned as well as draw connections between different topics. It also offers students an opportunity to review the mathematical ways of thinking (math practices) developed and used often in this course. See the Course Closure notes below.

In Section 10.1, students make sense of and persevere in solving volume problems. They create mathematical models, which they use as tools, to help them solve these problems.

Section 10.2 is an opportunity for students to attend to precision as they construct viable arguments and critique the reasoning of others while working on culminating problems. If you have spent time this year explicitly teaching the 8 Standards for Mathematical Practice, you might split the class into teams that create presentations or posters with exemplars pulled from their experiences throughout this year.

8EE.2 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

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