Modeling Prompt 8
A New Container
Geometry
Standards Addressed
HSG-GMD.A.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
HSG-MG.A.1
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
HSG-MG.A.3
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
In-Class Launch
Use after Unit 5, Lesson 14
Ask students to describe or sketch the shapes of drink containers that they have seen. Display a few examples or sketch them from student descriptions for all to see. Ask students to think about the geometric shapes they have been studying—what kind of container could they make from each shape? After some quiet think time, tell students that, in this activity, they will design a new kind of container.
Task Statement 1
Teacher Instructions
Building prototypes from physical materials can help students make connections between the formulas for the volumes of geometric shapes and the dimensions of physical objects. Provide materials such as cardboard, aluminum foil, poster board, and plastic containers. If students make their prototype out of water-resistant material, they can check their volume calculations by filling the prototype with water and measuring its volume. Dynamic digital geometry tools also can help students visualize their designs.
Once students have completed the task, invite them to look at each other’s designs, for example by conducting a Gallery Walk. Here are some possible questions for discussion:
- “The containers were made of which basic geometric shapes?” (Prisms, cones, pyramids, hemispheres)
- “What strategy did you use to make sure your container would have the right volume?” (I wasn’t sure how tall to make my container, so I wrote a formula for the volume where
represented the height, and then I graphed it to see which -value gave the right volume.) - “Did you see other strategies for designing a container that you like more than your strategy? What was good about the other strategies?” (Someone else used geometry software to represent their design and the shape changed when they changed the side lengths. I liked seeing what the shape would look like.)
Task Statement 2
Teacher Instructions
Building prototypes from physical materials can help students make connections between the formulas for the volumes of geometric shapes and the dimensions of physical objects. Provide materials such as cardboard, aluminum foil, poster board, and plastic containers. If students make their prototype out of water-resistant material, they can check their volume calculations by filling the prototype with water and measuring its volume. Dynamic digital geometry tools also can help students visualize their designs.
Once students have completed the task, invite them to look at each other’s designs, for example by conducting a Gallery Walk. Here are some possible questions for discussion:
- “The containers were made of which basic geometric shapes?” (Prisms, cones, pyramids, hemispheres)
- “What strategy did you use to make sure your container would have the right volume?” (I wasn’t sure how tall to make my container, so I wrote a formula for the volume where
represented the height, and then I graphed it to see which -value gave the right volume.) - “Did you see other strategies for designing a container that you like more than your strategy? What was good about the other strategies?” (Someone else used geometry software to represent their design and the shape changed when they changed the side lengths. I liked seeing what the shape would look like.)