Grade 08 Mathematics - EC: M08.B-F.1.1.3

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

Instructional activities designed to be integrated into planned lessons
Questions/activities that grow in complexity
Opportunities for differentiation for each student’s level of performance

Grade Levels

8th Grade

Course, Subject

Mathematics

Related Academic Standards / Eligible Content

M08.B-F.1.1.3 M08.B-F.1.1.3

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.

Activities

In questions 1 and 2, identify each graph as representing a linear or nonlinear function:

Does the given table represent a linear or nonlinear function? Explain.

Does the given table represent a linear or nonlinear function? Explain.

Describe each of the following equations as linear or nonlinear and explain why.

Construct a table to represent a linear function and a table to represent a nonlinear function. Be prepared to trade with a partner and explain your answers.

Answer Key/Rubric

Linear

Nonlinear

Linear
Explanations may include, but are not limited to:

As x increases by 3, y increases by 5. The rate of change is constant and therefore the function is linear.

Nonlinear
Explanations may include, but are not limited to:

As x increases by 2, y decreases by different amounts. The rate of change is not constant and therefore the function is not linear.

Answers as follows. Explanations may include, but are not limited to those given below.
1. Linear. The equation is written in the slope-intercept form.
2. Linear. The equation can be written in the slope-intercept form; fractions in a problem don’t automatically mean it is nonlinear.
3. Nonlinear. The x squared means this is nonlinear. The equation cannot be written in slope-intercept form.

Answers will vary. Students should provide an answer key along with their tables explaining why they think it is linear or nonlinear.