Math 7 Unit 9

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Section 9.1 begins with students investigating the relationship between circumference and diameter for circles, finding it to be proportional with π as a multiplier. Then students learn how to find the area of composite shapes built from triangles, circles, and other shapes. These skills are then applied to finding volume of right prisms in Section 9.2.

In the second section of this chapter, students study three‑dimensional shapes. This focus will begin with students building cereal boxes (out of cubes), each of which have equal volumes but different dimensions and surface areas. They will also visualize the cross sections of a rectangular prism.

Later in the section, students will learn two strategies for calculating the volume of a prism. They will dissect shapes into rectangle-based and triangle-based prisms, calculate those volumes separately, and combine them to calculate the volume of the original shape. They will also develop a method of slicing a prism parallel to the base in order to create one-unit tall layers that have equal volume.

Finally, Section 9.3 offers several class activities to help pull ideas from the entire course together. These activities are designed to enable students to reflect on 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.

The seven lessons in Chapter 9 present your final opportunity to work with your students on abstract and quantitative reasoning. By this time, they should expect to make sense of problems and persevere in solving them and attention to precision should be a habit.

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. If so, note that even though you have worked to develop them in your class this year, Standards 7 and 8 are difficult for students at this age to comprehend. Your explicit focus might be on only the first 6 Standards.

7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

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