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In this section, students find the surface area and volume of right prisms and the volume of cylinders. They begin with making sense of the structure of a prism using cross-sections parallel to the base of the prism. They build on this idea, and on their work in earlier grades with rectangular prisms, to conclude that the volume of any...
In this section, students extend their understanding of volume from right prisms and cylinders to right cones and spheres. After gaining familiarity with a formula for the volume of a cylinder by using it to solve problems, students perceive similar structure in a formula for the volume of a cone.
There are two optional lessons. In the first, students use...
Let’s explore cones and their volumes.
Let’s figure out the dimensions of cones.
Let’s see how changing one dimension changes the volume of a shape.
Let’s change more dimensions of shapes.
Let’s estimate volumes of hemispheres with figures we know.
Let’s explore spheres and their volumes.
Let’s find the volume of shapes.
This section introduces students to functions and develops the idea of a function as a rule that assigns to each allowable input exactly one output.
A focus of this section is on examples of “input–output rules,” such as “Divide by 3” or “If even, then . . . . If odd, then . . . .” In the starting examples,...
Let’s draw a graph from a story.