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. (Note: Function notation is not required in Grade 8.)

8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a tableof values and a linear function represented by an algebraic expression,determine which function has the greater rate of change. https://learnzillion.com/lessonsets/271

8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a functionof its side length is not linear because its graph contains the points (1,1),(2,4) and (3,9), which are not on a straight line. https://learnzillion.com/lessonsets/561

https://learnzillion.com/lessonsets/277 Use functions to model relationships between quantities. 8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. https://learnzillion.com/lessonsets/358

Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.5:Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-timegraph to a distance-time equation to determine which of two movingobjects has greater speed. https://learnzillion.com/lessonsets/275

8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Understand the connections between proportional relationships, lines, and linear equations.

8.EE.7: Solve linear equations in one variable.

a. 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).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. https://learnzillion.com/lessonsets/49

FunctionsDefine, 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. (Note: Function notation is not required in Grade 8.)https://learnzillion.com/lessonsets/420

8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).For example, given a linear function represented by a tableof values and a linear function represented by an algebraic expression,determine which function has the greater rate of change.https://learnzillion.com/lessonsets/271

https://learnzillion.com/lessonsets/52

8.F.3: Interpret the equationy=mx+bas defining a linear function, whose graph is a straight line; give examples of functions that are not linear.For example, the function A = s2 giving the area of a square as a functionof its side length is not linear because its graph contains the points (1,1),(2,4) and (3,9), which are not on a straight line.https://learnzillion.com/lessonsets/561

https://learnzillion.com/lessonsets/277

Use functions to model relationships between quantities.8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.https://learnzillion.com/lessonsets/357

https://learnzillion.com/lessonsets/686

https://learnzillion.com/lessonsets/52

8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.https://learnzillion.com/lessonsets/358

https://learnzillion.com/lessonsets/705

Analyze and solve linear equations and pairs of simultaneous linear equations.8.EE.5:Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.For example, compare a distance-timegraph to a distance-time equation to determine which of two movingobjects has greater speed.https://learnzillion.com/lessonsets/275

8.EE.6: Use similar triangles to explain why the slopemis the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equationy=mxfor a line through the origin and the equationy=mx+bfor a line intercepting the vertical axis atb.https://learnzillion.com/lessonsets/274

Understand the connections between proportional relationships, lines, and linear equations.8.EE.7: Solve linear equations in one variable.a

. 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 formx=a,a=a, ora=bresults (whereaandbare different numbers).https://learnzillion.com/lessonsets/124

https://learnzillion.com/lessonsets/419

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.https://learnzillion.com/lessonsets/49

https://learnzillion.com/lessonsets/128

https://learnzillion.com/lessonsets/560