Essential Questions:
How can I tell if an equation is linear from looking at its equation?
Big Idea:
Analyze linear and nonlinear equations in two variables, model with multiple representations.
Unit 4 instruction is focused on the following power standards:
8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.F.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions).
8.F.A.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are linear.
8.F.A.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.
Unit 4 instruction will be supported by the following standards:
8.EE.B.6: Use similar triangles to explain why the slope m is the same between an 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.
8.EE.C.7: Solve linear equations in one variable.
8.F.A.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.A.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.
How can I tell if an equation is linear from looking at its equation?
Big Idea:
Analyze linear and nonlinear equations in two variables, model with multiple representations.
Unit 4 instruction is focused on the following power standards:
8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.F.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions).
8.F.A.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are linear.
8.F.A.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.
Unit 4 instruction will be supported by the following standards:
8.EE.B.6: Use similar triangles to explain why the slope m is the same between an 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.
8.EE.C.7: Solve linear equations in one variable.
8.F.A.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.A.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.
What to TeachPrerequisite Skills from 7th Grade
|
Lesson Ideas |
Student PracticeIXL.com
|
Topic 1: Proportional Relationships
|
Topic 2: Working with Functions from Tables
|
Topic 3: Working with Functions from Equations
|
Topic 4: Working with Functions from Graphs
|
Topic 5: Comparing Functions
|
vocabularyfunction
function notation increasing at a constant rate decreasing at a constant rate positive slope negative slope linear nonlinear input output y-intercept initial value rate of change x-intercept horizontial veritcal parallel perpendicular sets ordered pairs tables coordinates rise over run slope origin x-axis y-axis undefined slope intercept form standard form independent variable dependent variable graph equation interpret |
Unit ResourcesAssessmentPre Assessment
Real World Experience Post Assessment Formative Assessment Student Reflection and Goal Setting |
Learn the MathParent Letter |