Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Number:**MAFS.8.EE.2

**Title:**Understand the connections between proportional relationships, lines, and linear equations. (Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**8

**Domain-Subdomain:**Expressions & Equations

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Tasks

## Student Center Activity

## Teaching Ideas

## Tutorials

## Unit/Lesson Sequences

## Video/Audio/Animation

## Virtual Manipulative

## Student Resources

## Original Student Tutorial

Learn how similar right triangles can show how the slope is the same between any two distinct points on a non-vertical line as you help Hailey build stairs to her tree house in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Tasks

In this task, students are asked to determine the unit price of a product under two different circumstances. They are also asked to generalize the cost of producing *x* items in each case.

Type: Problem-Solving Task

This task asks the student to graph and compare two proportional relationships and interpret the unit rate as the slope of the graph.

Type: Problem-Solving Task

In this example, students will answer questions about unit price of coffee, make a graph of the information, and explain the meaning of slope in the given context.

Type: Problem-Solving Task

This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. Students who prefer to work with specific numbers can write in scales on the axes to help them get started.

Type: Problem-Solving Task

This task asks students to reason about the relative costs per pound of two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.

Type: Problem-Solving Task

This task asks the student to understand the relationship between slope and changes in *x*- and *y*-values of a linear function.

Type: Problem-Solving Task

This activity challenges students to recognize the relationship between slope and the difference in *x-* and *y-*values of a linear function. Help students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation.

Type: Problem-Solving Task

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

This tutorial shows how to find the slope from two ordered pairs. Students will see what happens to the slope of a horizontal line.

Type: Tutorial

In this tutorial, you will use your knowledge about similar triangles, as well as parallel lines and transversals, to prove that the slope of any given line is constant.

Type: Tutorial

This tutorial shows an example of finding the slope between two ordered pairs. Slope is presented as rise/run, the change in y divided by the change in x and also as m.

Type: Tutorial

This tutorial will help you to explore slopes of lines and see how slope is represented on the x-y axes.

Type: Tutorial

## Video/Audio/Animation

"Slope" is a fundamental concept in mathematics. Slope of a linear function is often defined as " the rise over the run"....but why?

Type: Video/Audio/Animation

## Parent Resources

## Problem-Solving Tasks

In this task, students are asked to determine the unit price of a product under two different circumstances. They are also asked to generalize the cost of producing *x* items in each case.

Type: Problem-Solving Task

The purpose of this task is to show how the ideas in the RP and EE domains in 6th and 7th grade mature in 8th grade. Parts (a)-(c) could easily be asked of 7th grade students. Part (a) asks students to do what is described in 7.RP.2.a, Part (b) asks students to do what is described in 7.RP.2.c, and Part (c) is the 7th grade extension of the work students do in .

On the other hand, part (d) is 8th grade work. It is true that in 7th grade, "Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope". However, in 8th grade students are ready to treat slopes more formally: 8.EE.5 says students should "graph proportional relationships, interpreting the unit rate as the slope of the graph" which is what they are asked to do in part (d).

Type: Problem-Solving Task

This task asks the student to graph and compare two proportional relationships and interpret the unit rate as the slope of the graph.

Type: Problem-Solving Task

In this example, students will answer questions about unit price of coffee, make a graph of the information, and explain the meaning of slope in the given context.

Type: Problem-Solving Task

This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. Students who prefer to work with specific numbers can write in scales on the axes to help them get started.

Type: Problem-Solving Task

This task asks students to reason about the relative costs per pound of two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.

Type: Problem-Solving Task

This task asks the student to understand the relationship between slope and changes in *x*- and *y*-values of a linear function.

Type: Problem-Solving Task

This activity challenges students to recognize the relationship between slope and the difference in *x-* and *y-*values of a linear function. Help students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation.

Type: Problem-Solving Task