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).
Student Handouts
Coming soon!
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 \(x\) represented the height, and then I graphed it to see which \(x\)-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.)
A juice company has commissioned you to create a new container design. The container should look different from others in order to stand out to customers—it could be a prism, a cone, a pyramid, a combination of more than one type of shape, or any three-dimensional geometric figure you can describe. Its volume must be 16 fluid ounces.
Once you create your design, you’ll present it to the company. For your presentation you will need:
- a prototype of the container, or an image of what it will look like, showing the dimensions.
- calculations that prove the container will hold 16 fluid ounces.
Your mathematical work should be clear. Remember that you’re explaining your design to people who may not be comfortable with math, so you’ll need to help them understand how you got your results.
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 \(x\) represented the height, and then I graphed it to see which \(x\)-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.)
A juice company has commissioned you to create a new container design. The container should look different from others in order to stand out to customers. It should be some combination of 2 different geometric shapes. Its volume must be 16 fluid ounces. One fluid ounce is approximately 29.57 cubic centimeters or about 1.80 cubic inches.
The company currently uses cans that are 6.19 inches tall (15.72 centimeters) and have a diameter of 2.43 inches (6.17 centimeters).
Once you create your design, you’ll present it to the company. For your presentation you will need:
- a prototype of the container, or an image of what it will look like, showing the dimensions.
- calculations that prove the container will hold 16 fluid ounces.
Your mathematical work should be clear. Remember that you’re explaining your design to people who may not be comfortable with math, so you’ll need to help them understand how you got your results.