 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.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

• Bike Ride
In this task, students interpret a distance/time graph describing a bike ride.
• Bivariate Data and Analysis: Anthropological Studies
This lesson opens with a video from an anthropologist explaining how he uses bivariate data to examine the impact that slavery had on the slave's height and weight. Students then use his data in the classroom activity which has them study the relationship between tibia and femur measurements and a person's stature. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• 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.
• Chapter 2 - Student Workbook (UMSMP)
This is Chapter 2 of the Utah Middle School Math: Grade 8 student workbook. It covers Proportional and Linear Relationships.
• Coffee by the Pound
Given a statement about the price of coffee, students are asked to answer a number of questions about the cost per pound and draw a graph in the coordinate plane of the relationship between the number of pounds of coffee and the total cost.
• Comparing Speeds in Graphs and Equations
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.
• 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.
• Graphing Linear Equations - Full Body Style
This Teaching Channel video and lesson plan shows students graphing a line given slope-intercept on a giant coordinate plane. (4 minutes)
• Journey
In this task, students will read a description of a car journey and draw a distance-time graph to represent it.
• 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.
• Peaches and Plums
This task allows students to reason about the relative costs per pound of the 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.
• 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.
• Solving Systems of Equations by Graphing
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Systems of Linear Equations by Graphing
This is a video introduction and explanation of the topic.
• Sore Throats, Variation 2
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 6.EE.9. On the other hand, part (d) is 8th grade work.
• 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.
• Who Has the Best Job?
Given a table students are asked to make graphs representing the relationship between the time a student worked and the money they earned. 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.

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