Solve linear equations in one variable.
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
In the first topic of this 15 day module, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life. Once a formal definition of a function is provided, students then consider functions of discrete and continuous rates and understand the difference between the two. Students apply their knowledge of linear equations and their graphs from Module 4 to graphs of linear functions. Students inspect the rate of change of linear functions and conclude that the rate of change is the slope of the graph of a line. They learn to interpret the equation y=mx+b as defining a linear function whose graph is a line. Students compare linear functions and their graphs and gain experience with non-linear functions as well. In the second and final topic of this module, students extend what they learned in Grade 7 about how to solve real-world and mathematical problems related to volume from simple solids to include problems that require the formulas for cones, cylinders, and spheres.
Topic A: Functions (8.F.A.1, 8.F.A.2, 8.F.A.3)
Lesson 1: The Concept of a Function
Lesson 2: Formal Definition of a Function
Lesson 3: Linear Functions and Proportionality
Lesson 4: More Examples of Functions
Lesson 5: Graphs of Functions and Equations
Lesson 6: Graphs of Linear Functions and Rate of Change
Lesson 7: Comparing Linear Functions and Graphs
Lesson 8: Graphs of Simple Nonlinear Functions
Topic B: Volume (8.G.C.9)
Lesson 9: Examples of Functions from Geometry
Lesson 10: Volumes of Familiar Solids—Cones and Cylinders
Lesson 11: Volume of a Sphere