*For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.*

### Clarifications

**Examples of Opportunities for In-Depth Focus**

When students work toward meeting this standard, they build on grades 6–7 work with proportions and position themselves for grade 8 work with functions and the equation of a line.

**Subject Area:**Mathematics

**Grade:**8

**Domain-Subdomain:**Expressions & Equations

**Cluster:**Level 2: Basic Application of Skills & Concepts

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

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.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

**Assessment Limits :**Numbers in items must be rational numbers

**Calculator :**Yes

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**The graph of a proportional relationship is shown.

What is the amount of savings per week?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 2**Question:**The graph of a proportional relationship and an equation are shown.

What is the greater unit rate?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 3**Question:**A tub that holds 18 liters of water fills with 2 liters of water every 2.5 minutes.

A. Use the Add Arrow tool to create a graph that models the situation for the first 5 minutes.

B. At what rate is the tub filling with water? Drag symbols to the circle and numbers to the boxes to show the rate.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Problem-Solving Tasks

## Student Center Activity

## Teaching Ideas

## Tutorial

## Unit/Lesson Sequences

## Video/Audio/Animation

## Virtual Manipulative

## MFAS Formative Assessments

Students are asked to identify, describe and compare the slopes of two proportional relationships given the graph of one and the equation of the other.

Students are asked to graph a proportional relationship, given a table of values, and find and interpret the slope.

Students are given a graph of a proportional relationship and asked to determine the unit rate of the relationship and compare it to the slope of the graph.

## Student 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

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

## 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