WVU K12 Partnerships Learning Module Agreement & Construction Tool
Course: Math 8
Unit: 6 - Cylinders and Cones and
Spheres! Oh my!
Lesson: 4 (end of course presentation)
Time: At least one, 50-minute
Standards & Objectives:
M.8.G.9 know the formulas for the volumes of cones, cylinders and spheres and use them to solve realworld and mathematical problems.
Mathematical Practices:
1. Make sense of problems and persevere in solving them.
When completing the cups and cones activity, students may need to look for entry points to
determine the volume of the cup shaped like a truncated cone. They will need to plan a solution
pathway and work using simpler forms (cylinders). Students make conjectures about relationships
among shapes and their volumes ask themselves, "Does this make sense?"
2.
Reason abstractly and quantitatively.
While doing Capstone Challenge, students make sense of quantities and their relationships in a
problem situation. They must decontextualize or abstract a given situation when using a formula
and contextualize, to take into consideration the symbols involved. They consider the units
involved.
3.
Construct viable arguments and critique the reasoning of others.
In Lesson 4, students will used stated assumptions definitions and previously established results in
construction arguments. They construct arguments from drawings. Students can listen to the arguments of
others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
4.
Model with mathematics
In Lesson 4, students will apply the mathematics they know to solve problems arising in everyday
21st Century Technology Tools & Learning Skills: This lesson is aligned to the 21st Century Teaching
and Technology Tools.
Overview

Driving Question: How can you use your knowledge about volumes of cones and cylinders to solve
everyday problems?

Overview: In this lesson, you will have the opportunity to see how the use of mathematics connects
to real life. You will extend your knowledge about the formulas you have explored and used to find
WVU K12 Partnerships Learning Module Agreement & Construction Tool
volumes of cones and cylinders in order to solve problems which require the use of both exact
calculations and estimation skills.
Capstone Performance Task – The Capstone Task is introduced in Lesson 4 of Unit 8. All materials
and directions are located there. The presentations for the task are suggested to take place on the
last day of the Unit.

Introduction to Task (The reason why)
Your school is purchasing a water cooler for a visitors’ lounge. There is an option of ordering
one of two different types of cups. Your task is to make a recommendation about which type of
cup should be ordered. Be sure to use appropriate units in your work.

Performance Objectives (What needs to be accomplished)
Prepare a short presentation that explains your choice of cup. The presentation should include:
 a description of the problem
 mathematical work (including units)giving the volumes found for Cup A and Cup B,
 information that you found about the volume of water that a cooler typically holds,
 the volume of water a typical 8 ounce cup holds,
 the typical price of cups when sold in bulk,
 other information that may support your choice,
 and, your choice of Cup A or Cup B with your reasoning

Materials
Cup A is a thin paper cup in the shape of a cone. Cup B is a thicker paper cup. It is suitable for both hot and cold
beverages and is in the shape of a "truncated" cone.
3 inches
4 inches
WVU K12 Partnerships Learning Module Agreement & Construction Tool
3 inches
4 inches
2 inches
Procedure (What to do)
∙
∙
∙
Explore the sizes of water containers that fit onto the typical water cooler.
What volume of water (in cubic inches) will the typical container hold?
What is the volume (in cubic inches) of an 8 ounce cup of water?
How do the volumes of Cup A and Cup B compare?
Explore the price of water cooler cups (typically shaped like cones) or hot and cold beverages cups
(typically shaped like truncated cones) sold in bulk.
o Which seems to be a better buy?
Capstone Performance Task Evaluation:
Challenge Rubric
Possible Points
Criteria
5
Defines the problem (Explain the challenge)
50
Explains calculations for the volume of each
Cup A and Cup B (Includes mathematics and appropriate
units)
15
Communicates information (with sources and/or calculations)
typical volume of water cooler container (cubic
inches)
volume of an 8 ounce glass of water (cubic inches)
prices per unit of typical cups of specified shapes
10
Gives considered solutions with reasoning
10
Communicates final solution with reasoning
10
Presentation is clear, well organized, and easy to follow
Points
WVU K12 Partnerships Learning Module Agreement & Construction Tool
100
Total