Mathematical Practice(S): 1 Make Sense of Problems and Persevere, 4 Modeling, 6 Attend

Lesson Standard: 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Content Objective: Students will be able to apply the volume of a sphere to multi-step problems involving prisms, cylinders, cones, and spheres.

Mathematical practice(s): 1 Make sense of problems and persevere, 4 Modeling, 6 Attend to precision

Lesson Design / What will the teacher be doing? / What will the students be doing?
(Structured Student Interaction) / What will the teacher be listening for?
(What do we expect students to say?) / Probing Questions for Differentiation
Assessing Questions
(“stuck”) / Advancing Questions
(further learning)
Engage (Launch)
Pose the tennis ball question:
A job that makes 350k a year designing packaging.
You are the designer. You have four tennis balls to package. / Pose the scenario
What are some things to consider when designing packaging? / Partner talk
Share out whole group / Stacking issues
Empty space
Activity or Task 1
Provide the three packaging options:
Brandon came up with these 3 ideas:
Cylinder, Rectangular prism (4 high), rectangular prism (2x2)
Display the picture under doc cam and model the balls in the containers. / Brandon figured out that when tennis balls are packaged they need to be pressurized.
Will the tennis balls take up the entire volume of the packages?
Which package do you think is most efficient?
Strategy discussion:
What do we need to do mathematically to prove the package is most efficient? / Whole class discussion
Students raise hands
Talk in groups
Whole class discussion / No
Least amount of dead space is most efficient
Find volume of packages
Find volume of sphere (multiply by 4)
Subtract them / Is it better to have more of that dead space or less of the dead space?
Activity or Task 2
Have student come up to measure the height of the tennis ball (2.5 inches) / Where else does the 2.5 inches show up in the figures? / Students use transparencies to manipulate with the tennis balls / Radius, diameter, height
Activity or Task 3
Find which container would be most efficient for packaging the four tennis balls. / Pose question and roam room / Working in groups with paper / What are the dimensions of the three packages?
What is the amount of dead space for each package? How do you know?
Which package if the most efficient, least dead space? / What about a triangular prism?
Can you design an even more efficient package?
Why do the two rectangular prisms come out the same?
Closure
Select a group to share out.
Or
“Spies” / Ask students to add on, revise thinking…
Or
Spy Question:
How did you guys know which package was most efficient? / Whole class share out
One student moves groups and poses the question. That student then returns to their group and shares the findings.

Name: ______

Find the dimensions of the three packages and find the volume of each?

What is the amount of empty space for each package? How do you know?

Which package is the most efficient (has the least empty space)?