Embedded Files
Lesson Video
Lesson Video
Focus Standards
Focus Standards
Learning Focus
Learning Focus
Additional Resources
Additional Resources
A Solidify Understanding Task
Deepens understanding of volume formulas for rectangular prisms and cylinders by examining the proportionality relationships of lengths, areas, and volumes when geometric figures are scaled up.
Use similarity to scale area and volume.
We have learned about dilation transformations in two dimensions. What happens when a solid undergoes a 3-D dilation?
How does such a dilation affect the area and volume of the solid?
A Solidify Understanding Task
Deepens understanding of the volume formulas for prisms, pyramids, and cylinders by examining informal dissection arguments for each.
Derive and use formulas for right prisms and pyramids.
How are the formulas for pyramids and cones related to the formulas for prisms and cylinders?
Can we visualize why this is so?
A Develop Understanding Task
Provides ways to visualize 2-D cross-sections of 3-D objects in order to create a formal definition of cross-sections.
A Develop Understanding Task
Develops understanding of solids of revolution by visualizing the result of a 2-D object rotated about an axis. Introduces the idea that cross-sections perpendicular to the axis of revolution will always be circular.
Identify shapes formed by slicing a solid with a plane.
How can I visualize the slices formed when a solid object, such as a cube, sphere, or pyramid, is run through a meat slicer? What would the slices look like if the object is oriented in different ways before being sliced?
Develop a strategy for drawing solids of revolution.
The blur of a spinning penny takes on the visual shape of a sphere. What might a spinning triangle, rectangle, or trapezoid look like?
How would the shape created by the spinning object change if the object is rotated about a different axis?
A Solidify Understanding Task
Builds on understanding of solids of revolutions by developing a strategy for finding volumes of frustums. Teaches how to decompose a figure with curved edges into cylinders, frustums, and cones to approximate its volume.
Calculate the volume of solids of revolution that can be approximated by cylinders and portions of cones.
How do I find the volume of a solid of revolution that isn’t a cylinder or part of a cone?
How can I approximate the volume of a solid of revolution that has a curved silhouette like a vase or a bottle?
A Practice Understanding Task
Solidify understanding of solids of revolution in a geometric modeling context requiring decomposition of the figure into familiar objects whose volume can be calculated.
Apply geometric modeling to solve a real-world problem.
How can I use quantities and units to guide my computational thinking in a modeling context?
How can I model geometric contexts using properties of shapes and measurement?
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