Standards in Unit:

8.F.1 - Understand that a function is a rule that assigns to each input exactly one output. Recognize functions when graphed as the set of ordered pairs consisting of an input and exactly one corresponding output. Recognize functions given a table of values or a set of ordered pairs.

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

8.F.3 - Identify linear functions from tables, equations, and graphs.

8.F.4 - Analyze functions that model linear relationships:

• Understand that a linear relationship can be generalized by y = mx + b.
• Write an equation in slope-intercept form to model a linear relationship by determining the rate of change and the initial value, given at least two (x, y) values or a graph.
• Construct a graph of a linear relationship given an equation in slope-intercept form.
• Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of the slope and y-intercept of its graph or a table of values

8.F.5 - Qualitatively analyze the functional relationship between two quantities.

• Analyze a graph determining where the function is increasing or decreasing; linear or non-linear.
• Sketch a graph that exhibits the qualitative features of a real-world function.

8.EE.8 - Analyze and solve a system of two linear equations in two variables in slope-intercept form.

• Understand that solutions to a system of two linear equations correspond to the points of intersection of their graphs because the point of intersection satisfies both equations simultaneously.
• Solve real-world and mathematical problems leading to a system of linear equations by graphing the equations.

Summary of Unpacking for Each Standard:

8.F.1- Students will define functions for the first time in this standard and be able to recognize functions and non-functions in multiple representations (graphs, tables, sets of ordered pairs). Students can learn “tricks” such as the vertical line test, but they must be able to explain why the vertical line test determines a function. Function notation, such as f(x), is NOT required at this level.

8.F.2 -Students will interpret linear functions to determine their key characteristics (slope, intercepts, etc.) and compare them in different representations. A conceptual understanding of the meanings of these key characteristics is essential, as students will not have to remember different algorithmic methods of determining these key features if they understand the concepts and can convert one representation to another. At this level, all equations will be given in slope-intercept form, and all written descriptions will be easily translated into slope-intercept form.

8.F.3 -Students will understand linear functions as having a constant rate of change for all points in the function, and they will be able to recognize functions that are linear from tables (constant increase or decrease in y as x increases), equations (y = mx + b), and graphs (graph is a straight line). Students will not have to differentiate between types of non-linear functions (i.e. they won’t have to identify a quadratic vs. exponential function at this level), but they will have to differentiate between linear vs. non-linear.

8.F.4 -Students will build on their understanding of graphs and equations of proportional relationships from 7th grade to build the slope-intercept form of the equation of a line. They will be able to determine the rate of change, or slope, of a line from a graph, two points, or written context, and they will be able to write the equation of a line from any of these representations. This standard must be taught before 8.F.2, as 8.F.2 asks students to determine and compare these key features from all representations.

8.F.5 -Students will show their understanding of the concept of functions, graphs, and independent/dependent variables by sketching graphs from written context and analyzing given graphs in context of various functional relationships. These relationships can include linear and non-linear relationships in mathematical and real-world contexts.

8.EE.8 -Students will explore the concept of systems of equations, learning why they need two equations to solve for two variables, in mathematical and real-world context. They will understand and prove that the solution to a system of equations is the point of intersection on a graph. Students will understand characteristics of systems that have 1 solution, 0 solutions, and infinite solutions. Note: In the 2018-19 standards, students will only solve systems of equations by graphing at this level.

Prerequisite Skills:

• Understanding and calculation of unit rate
• Equations of proportional relationships
• Understanding of the coordinate plane

Future Skills:

• Domain and range
• Analyzing and determining key features of all types of functions
• Calculating and interpreting average rate of change for an interval of any function
• Function notation

Key Vocabulary:

• Relation
• Function
• Input / Domain / Independent Variable
• Output / Range / Dependent Variable
• Linear
• Direct Variation
• Rate of Change / Slope
• Y-intercept
• Slope-Intercept Form
• Point-Slope Form

Cornerstone Task

College Bound (Links to an external site.)Links to an external site.

MTSS/Remediation Resources

Math Topic/DPI Bucket: Linear Equations/Algebraic Expressions and Equations

Engage NY F2F Intervention: Grade 8, Module 4 (Links to an external site.)Links to an external site., Topic A,B,C,D

Edgenuity Online Intervention: Grade 8, Linear Functions Unit

Math Topic/DPI Bucket: Concept of Function/Algebraic Expressions and Equations

Engage NY F2F Intervention: Grade 8, Module 5 (Links to an external site.)Links to an external site., Topic B

Edgenuity Online Intervention: Grade 8, Input-Output Relationships Unit

Math Topic/DPI Bucket: Linear Functions/Algebraic Expressions and Equations

Engage NY F2F Intervention: Grade 8, Module 6 (Links to an external site.)Links to an external site., Topic A