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.8

Analyze and solve pairs of simultaneous linear equations.

In this task, students will write equations to solve problems about buying bags of chips and candy bars.
• Cell Phone Plans
This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations. The students are required to find the solution algebraically to complete the task.
• 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.
• Expressions and Equations
A set of short tasks for grades 7 and 8 dealing with expressions and equations.
• Fixing the Furnace
This task can be used to both assess student understanding of systems of linear equations or to promote discussion and student thinking that would allow for a stronger solidification of these concepts. The solution can be determined in multiple ways, including either a graphical or algebraic approach.
• 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.
• Grade 8 Unit 7: Solving Systems of Equations (Georgia Standards)
In this unit students will understand the solution to a system of equations is the point of intersection when the equations are graphed; understand the solution to a system of equations contains the values that satisfy both equations; find the solution to a system of equations algebraically; estimate the solution for a system of equations by graphing; understand that parallel lines have will have the same slope but never intersect; therefore, have no solution; understand the two lines that are co-linear share all of the same points; therefore, they have infinitely many solutions; and apply knowledge of systems of equations to real-world situations.
• Hot Under The Collar
In this task students will compare two methods of converting temperature measurements from Celsius to Fahrenheit.
• How Many Solutions?
Given an equation students are asked to find a second linear equation to create a system of equations that has one, two, none, or an infinity of solutions.
• 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.
• 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.
• More Complicated Functions: Introduction to Linear Functions
This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
• Multiple Solutions
In this task, students will look at a number of equations and inequalities that have more than one solution.
• Quinoa Pasta 1
This task asks students to find the amount of two ingredients in a pasta blend. The task provides all the information necessary to solve the problem by setting up two linear equations in two unknowns.
• Rate Problems
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.
• Repeating Decimals
This lesson unit is intended to help educators assess how well students are able to translate between decimal and fraction notation, particularly when the decimals are repeating, create and solve simple linear equations to find the fractional equivalent of a repeating decimal, and understand the effect of multiplying a decimal by a power of 10.
• Simultaneous Linear Equations
This website offers students instruction on various methods of solving simultaneous equations and practice examples for each method.
• Solving Equations video
Answers the questions "what are equations?" and "how do we solve them?"
• Solving Linear Equations in One Variable
This lesson unit is intended to help educators assess how well students are able to solve linear equations in one variable with rational number coefficients, collect like terms, expand expressions using the distributive property, and categorize linear equations in one variable as having one, none, or infinitely many solutions.
• Solving Real-Life Problems: Baseball Jerseys
This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods to use, explore the effects of systematically varying the constraints, interpret and evaluate the data generated and identify the break-even point, checking it for confirmation, and communicate their reasoning clearly.
• Summer Swimming
The purpose of this task is for students to represent relationships between quantities in a context with equations and interpret the resulting system of equations in the context. This task has a wide array of uses: it could be an introductory task to systems of equations or used in assessment.
• The Intersection of Two Lines
The purpose of this task is to introduce students to systems of equations. It takes skills and concepts that students know up to this point, such as writing the equation of a given line, and uses it to introduce the idea that the solution to a system of equations is the point where the graphs of the equations intersect (assuming they do). This task does not delve deeply into how to find the solution to a system of equations because it focuses more on the student's comparison between the graph and the system of equations.
• 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.