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Grade 8 Math Unit 5

Functions of Geometry

Unit description: In this unit the students will  learn to define, evaluate, and compare functions. They will solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 

Download the complete Grade 8 Math Unit 5 framework to customize for your own planning.

Essential Outcomes of the Unit

Functions

Define, evaluate, and compare functions.

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Other Standards Addressed in the Unit

Functions

Define, evaluate, and compare functions.

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and nonlinear.

Geometry

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.9 Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real world problems.

Essential Questions and Big Ideas

  • How do you use functions to model relationships between quantities? 
    • A function is a rule that assigns to each input exactly one output. 
    • The rule for a function determines the relationship.  

  • How can algebra, graphs, tables, and verbal descriptions be used to represent and compare functions?  
    • Functions can be compared based on their rates of change. 
    • Functions can be compared based on their slopes.  
    • Functions can be compared based on their y-intercepts.  

  • Are all linear equations functions? Are all functions linear? How do you know?
    • Functions written in the form y = mx+b are linear functions.  
    • Linear functions have a constant rate of change.  

  • What is the relationship between volume of cones, cylinders, and spheres?
    • The volume of a cylinder can be found by 𝛑r2 h
    • The volume of a cone can be found by 𝛑r2 (h3).
    • The volume of a sphere is 43𝛑r3

  • The volume of a cone is ⅓ of the volume of a cylinder.  
    • When h = 2r, the volume of a cone and a sphere together create a cylinder.