Unit 1, Lesson 17
Putting All the Solids Together
Integrated Math 3
17.1
Warm-up
Materials
NoneActivity Narrative
This Math Talk focuses on calculating volumes of solids. It encourages students to think about dimensions and to consider the order in which to perform the required arithmetical operations to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students do more complex volume calculations.
To think flexibly about volume formulas, students need to look for and make use of structure (MP7).
Launch
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
- Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
- Invite students to share their strategies and record and display their responses for all to see.
- Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.
Keep all previous problems and work displayed throughout the talk.
Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization
Supports accessibility for: Memory, Organization
Activity
NoneEvaluate the volume of each solid mentally.
Student Response
Activity Synthesis
To involve more students in the conversation, consider asking:
- “Who can restate ’s reasoning in a different way?”
- “Did anyone use the same strategy but would explain it differently?”
- “Did anyone solve the problem in a different way?”
- “Does anyone want to add on to ’s strategy?”
- “Do you agree or disagree? Why?”
- “What connections to previous problems do you see?”
MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy:
Advances: Speaking, Representing
- "First, I _____ because _____."
- "I noticed _____ so I _____."
Advances: Speaking, Representing
Student Lesson Summary
Before computing volume, it’s important to select the right formula and find all the dimensions represented in the formula. For example, consider a company that makes two chew toys for dogs. One toy is in the shape of a cylinder with radius 9 cm and height 2.5 cm. The other looks like the cone in the image. The company wants to know which toy uses more material. The toys are solid, not hollow.
To calculate the cylinder toy’s volume, use the expression . The radius measures 9 cm, so the area of the base, , is cm2. The volume is , or approximately 636 cm3, because .
For the cone, the height is unknown. A right triangle is formed by the radius 6 cm and the height , with hypotenuse 16 cm. By the Pythagorean Theorem, . Solving, we get .
Since this is a cone, use the expression . The area of the base, , is cm2. The volume is approximately 559 cm3 because . The cylinder-shaped toy uses more material.