 Mathematics Grade 8

Strand: EXPRESSIONS AND EQUATIONS (8.EE)

Work with radical and integer exponents (Standards 8.EE.1-4). Understand the connections between proportional relationships, lines, and linear relationships (Standards 8.EE.5-6). Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations (Standards 8.EE.7-8).

Standard 8.EE.6

Use similar triangles to explain why the slope m is the same between any 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.

• Bike Ride
In this task, students interpret a distance/time graph describing a bike ride.
• Chapter 2 - Mathematical Foundation (UMSMP)
This is Chapter 2 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Proportional and Linear Relationships.
• Different Areas?
The goal of this task is to motivate a discussion of similarity and slope via a counterintuitive geometric construction where it appears as if area is not conserved by cutting and reassembling a simple shape.
• DVD Profits, Variation 1
The first two problems in this task ask students to find the unit cost per DVD for making a million DVDs. Even though each additional DVD comes at a fixed price, the overall cost per DVD changes with the number of DVDs produced because of the startup cost of building the factory.
• Equations of Lines
This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.
• Find the Change
This task is designed to help students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. It may also produce a reasonable starting place for discussing point-slope form of a linear equation.
• Folding a Square into Thirds
The purpose of this task is to find and solve a pair of linear equations which can be used to understand a common method of folding a square piece of origami paper into thirds.
• GeoGebra: Derivation of the line
Use this file to see the derivation of the line y=mx.
• Grade 8 Math Module 4: Linear Equations (EngageNY)
In 8th grade Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module. Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.
• Grade 8 Unit 5: Linear Functions (Georgia Standards)
In this unit students will graph proportional relationships; interpret unit rate as the slope; compare two different proportional relationships represented in different ways; use similar triangles to explain why the slope is the same between any two points on a non-vertical line; derive the equation y = mx for a line through the origin; derive the equation y = mx + b for a line intercepting the vertical axis at b; and interpret equations in y = mx + b form as linear functions.
• Journey
In this task, students will read a description of a car journey and draw a distance-time graph to represent it.
• Lines and Linear Equations
This lesson unit is intended to help educators assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.
• Manipulating Graphs
This video demonstrates how to use the slope-intercept of a line to the graph of that line. The classroom activity has them demonstrate their understanding by finding equations for a set of lines through the origin. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Proportional relationships, lines, and linear equations
The purpose of this task is to assess whether students understand certain aspects of the relationship between proportional relationships, lines, and linear equations. In particular, it requires students to find the slope of the line defined by the equation 4y=x and to write the equation of a line knowing its slope and y-intercept.
• Shelves
In this task, students must figure out how many planks and bricks are needed to build a bookcase.
• Slope and House Construction
A video with This Old House's carpenter demonstrates how the use of slope is critical in the building of a house. The students then practice working with slope to not only build a playground slide, but identify other real-world uses of slope. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Slopes Between Points on a Line
The purpose of this task is to help students understand why the calculated slope will be the same for any two points on a given line. This is the first step in understanding and explaining why it will work for any line (not just the line shown).
• Stairway Slope
Students learn how to use stairs to understand and calculate the slope of a line. The classroom activity then has students use the real-world situation of a wheelchair and a the slope of a ramp to calculate the length needed for the ramp. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Stuffing Envelopes
This task provides students with an opportunity to take the step from unit rates in a proportional relationship to the rate of change of a linear relationship. Students should already be familiar with proportional relationships from their work in prior grades. http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.