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.7

Solve linear equations and inequalities in one variable.

• Buying Chips and Candy
In this task, students will write equations to solve problems about buying bags of chips and candy bars.
• Chapter 1 - Mathematical Foundation (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Analyzing and Solving Linear Equations.
• Chapter 1 - Student Workbook (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 8 student workbook. It covers analyzing and solving linear equations.
• Classifying Solutions to Systems of Equations
This lesson unit is intended to help educators assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations.
• Coupon versus discount
This task involves solving equations with rational coefficients, and requires students to use the distributive law ("combine like terms"). The equation also provides opportunities for students to observe structure in the equation to find a quicker solution, as in the second solution presented.
• Expressions and Equations
A set of short tasks for grades 7 and 8 dealing with expressions and equations.
• 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 2: Exponents and Equations (Georgia Standards)
In this unit student will distinguish between rational and irrational numbers and show the relationship between the subsets of the real number system; recognize that every rational number has a decimal representation that either terminates or repeats; recognize that irrational numbers must have decimal representations that neither terminate nor repeat; understand that the value of a square root can be approximated between integers and that nonperfect square roots are irrational; locate rational and irrational numbers on a number line diagram; use the properties of exponents to extend the meaning beyond counting-number exponents; recognize perfect squares and cubes, and understanding that non-perfect squares and non- perfect cubes are irrational.
• Hot Under The Collar
In this task students will compare two methods of converting temperature measurements from Celsius to Fahrenheit.
• IXL Game: Linear Functions
Designed for eighth graders, this game will help the student understand linear functions, specifically how to graph a line from an equation. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• 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.
• Mixture Problems
Learning to think of a mixture as a kind of rate is an important step in learning to solve these types of problems. Any situation in which two or more different variables are combined to determine a third is a type of rate. Speed and time combine to give us distance. Wages and hours worked produce earnings.
• Multiple Solutions
In this task, students will look at a number of equations and inequalities that have more than one solution.
• Sammy's Chipmunk and Squirrel Observations
This task provides a context for setting up a linear equation whose solution requires some algebraic manipulation. Because the numbers involved are not too large, students can also experiment with some small values and eventually find the solution this way; a first solution with a table is provided showing this method. On the other hand, the reasoning required without using an equation is complex enough that the simplicity and elegance of the algebraic approach can be highlighted.
• Solving Equations
This task requires students to solve 5x+1=2x+7 in two ways: symbolically, the way you usually do with equations, and also with pictures of a balance. Show how each step you take symbolically is shown in the pictures.
• Solving Equations video
Answers the questions "what are equations?" and "how do we solve them?"
• Solving Systems of Linear Equations by Elimination
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 Substitution
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.
• The Sign of Solutions
It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation.
• Two Lines
In this task, we are given the graph of two lines including the coordinates of the intersection point and the coordinates of the two vertical intercepts, and are asked for the corresponding equations of the lines. It is a very straightforward task that connects graphs and equations and solutions and intersection points.

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.