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Grade 8 Mathematics Module 6, Topic A: Linear Functions

Classroom Resource Information

Title:

Grade 8 Mathematics Module 6, Topic A: Linear Functions

URL:

https://www.engageny.org/resource/grade-8-mathematics-module-6-topic-overview

Content Source:

EngageNY

Type:

Lesson/Unit Plan

Overview:

Module 6, Topic A begins to examine the relationship between two variables using linear functions (8.F.B.4). Linear functions are connected to a context, using the initial value and slope as a rate of change to interpret the context. Students represent linear functions by using tables and graphs and by specifying the rate of change and initial value. The slope is also interpreted as an indication of whether the function is increasing or decreasing and as an indication of the steepness of the graph of the linear function (8.F.B.5). Nonlinear functions are explored by examining nonlinear graphs and verbal descriptions of nonlinear behavior.

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 8

16. Construct a function to model a linear relationship between two variables.

a. Interpret the rate of change (slope) and initial value of the linear function from a description of a relationship or from two points in a table or graph.

Unpacked Content

Evidence Of Student Attainment:

Students:

Create the graphical representation of linear function, given a linear equation in slope-intercept form, using the initial value and rate of change.
give meaning rates of change and the initial values of linear functions in different contexts.

Teacher Vocabulary:

Function
Linear
Non-linear
Slope
y-intercept

Knowledge:

Students know:

that the rate of change of a function is the ratio of change in the output to the change in the input.
how to find the rate of change/slope as well as the initial value/y-intercept.

Skills:

Students are able to:

construct the graph of a linear function.
Identify the slope and y-intercept of functions in different contexts.

Understanding:

Students understand that:

terms such as slope and y-intercept describe a graphical representation of a linear function and correlate their meaning to the rate of change and initial value, where the input is 0.
Using the units from a context appropriately is needed to make their description of rate of change and initial value accurate.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.8.16.1: Define function, rate of change, and initial value.
M.8.16.2: Recall how to complete an input/output function table.
M.8.16.3: Recall how to find the rate of change (slope) in a linear equation.
M.8.16.4: Recall how to name points from a graph (ordered pairs).
M.8.16.5: Analyze real-world situations to identify the rate of change and initial value from a table, graph, or description.

Prior Knowledge Skills:

Solve an equation by substituting a value to find an output.
Find the coordinates of an ordered pair.
Recognize how the steepness of a graphed line changes vertically and horizontally.

Mathematics
MA2019 (2019)
Grade: 8

17. Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph.

Unpacked Content

Evidence Of Student Attainment:

Students: Given graphical representations of functions,

Use mathematical reasoning to analyze the graphs and describe the functional relationships between two quantities.

Teacher Vocabulary:

Increasing
Decreasing
Linear
Non-linear

Knowledge:

Students know:

Characteristics of representations for functions in graphic form.

Skills:

Students are able to:

Use mathematical vocabulary and understanding of functions to describe relationships between two quantities.

Understanding:

Students understand that:

functions can be represented in a variety of ways, each of which provides unique perspectives of the relationship between the variables.
Graphs of functions are useful to compare characteristics of different relationships.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.8.17.1: Define qualitative, increase, and decrease.
M.8.17.2: Distinguish the difference between linear and nonlinear functions.
M.8.17.3: Recall how to plot points on a Cartesian plane.
M.8.17.4: Identify parts of the Cartesian plane.
M.8.17.5: Recognize ordered pairs.
M.8.17.6: Compare and contrast the relationship between two quantities in a graph.

Prior Knowledge Skills:

Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
Demonstrate an understanding of an extended coordinate plane.
Draw a four-quadrant coordinate plane.
Draw and extend vertical and horizontal number lines.
Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
Recall how to graph points in all four quadrants of the coordinate plane.

Alabama Alternate Achievement Standards

AAS Standard:
M.AAS.8.17 Given a simple scatter plot of points in a straight line, describe the relationship between the two quantities.

Tags:

function, graph, linear relationship, model, rate of change, slope, table

License Type:

Custom Permission Type
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Accessibility

Text Resources: Content is organized under headings and subheadings

Comments

There are five lessons in this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site.

This resource provided by:

Author:

Hannah Bradley

ALEX Classroom Resource

Grade 8 Mathematics Module 6, Topic A: Linear Functions