Unit 6: Functions and Volume

Students are introduced to functions as relationships between inputs and outputs, then apply functions to find volumes and surface areas of prisms, cylinders, cones, and spheres.

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Unit

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Concept

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Practice

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Set 1

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Set 2

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Advanced

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What this unit covers

A Representing and Interpreting Functions · 7 lessons

Goals

• Comprehend the structure of a function as having one and only one output for each allowable input.
• Draw the graph of a function that represents a context, and explain which quantity is a function of which.
• Interpret multiple representations of functions, including graphs, tables, and equations, and explain how to find information in each type of representation.

Lessons

1. Inputs and Outputs
2. Introduction to Functions
3. Equations for Functions
4. Graphs of Functions
5. Even More Graphs of Functions
6. Connecting Representations of Functions
7. Linear Functions and Models

B Prisms and Cylinders · 7 lessons

Goals

• Calculate the surface area and volume of a prism.
• Calculate the volume of a cylinder.

Lessons

1. Slicing Solids
2. Volume of Right Prisms
3. Decomposing Bases for Area
4. The Volume of a Cylinder
5. Finding Cylinder Dimensions
6. Surface Area of Right Prisms
7. Applying Volume and Surface Area

C Cones and Spheres · 7 lessons

Goals

• Calculate the value of one dimension of a cone, and explain the reasoning.
• Calculate the volume of a cone or sphere.
• Solve problems involving cones, cylinders, and spheres.

Lessons

1. The Volume of a Cone
2. Finding Cone Dimensions
3. Scaling One Dimension
4. Scaling Two Dimensions (Optional)
5. Estimating a Hemisphere
6. The Volume of a Sphere
7. Cylinders, Cones, and Spheres

D Let's Put It to Work · 2 lessons

Lessons

1. Building Prisms (Optional)
2. Volume as a Function of . . . (Optional)