EE.3.7.a

Solve linear equations in one variable.

a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

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Formative Assessments
Formative Assessments
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CPALMS: Students are asked to identify and explain whether given equations have one solution, no solutions, or infinitely many solutions.

Counting Solutions

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CPALMS: Students are asked to solve a linear equation in one variable with rational coefficients.
Linear Equations – 2
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CPALMS: Students are asked to write examples of equations with one solution, no solutions, and infinitely many solutions.

Equation Prototypes

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CPALMS: Students are asked to solve a linear equation in one variable with rational coefficients and variables on both sides of the equation.
Linear Equations – 3
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CPALMS: Students are asked to solve a linear equation in one variable with rational coefficients.

Linear Equations – 1

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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CPALMS: This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers.

Algebra Balance Scales – with Negatives

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CPALMS: In this online game, students find the matching pairs by solving equations to find the value of x in each equation. Correct answers reveal a hidden picture. Levels 1 & 2 most appropriate for Grades 6-7. Level 3 is best for Grade 8.

Equation Match

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Assessment Questions
Assessment Questions
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Equation Editor 2
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Equation Editor 6
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Open Response
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Equation Editor 3
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Equation Editor 4
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Videos of Expert Instruction
Videos of Expert Instruction
Decorative Light Bulb. Image includes gray lightbulb on purple background.
Mixture problems can involve mixtures of things other than liquids. This video shows how Algebra can be used to solve problems involving mixtures of different types of items.
Solving Mixture Problems with Linear Equations
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Guess whether or not the two ditch diggers will meet. If they don't meet, what is the closest you think they will come to each other?
Ditch Diggers
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Hook/Performance Tasks
Hook/Performance Tasks
Achievement Level Descriptors Logo. Includes a dark gray document symbol on a yellow background.
Illustrative Mathematics: This task involves solving equations with rational coefficients and requires students to use the distributive law (``combine like terms``). It also provides opportunities for students to observe structure in the equation to find a quicker solution.

Coupon versus Discount

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Illustrative Mathematics: This task turns the focus away from the familiar “finding the solution” problem to thinking about what it really means for a number to be a solution of an equation. Work in high school in A-SSE domain will naturally build on this type of thinking skill.

The Sign of Solutions

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Illustrative Mathematics: This task provides a context for setting up a linear equation whose solution requires some algebraic manipulation. Since numbers involved are not too large, students can experiment with small values and eventually find the solution this way.

Sammy’s Chipmunk and Squirrel Observations

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Illustrative Mathematics: This task takes students through a progression of earlier learning on concrete to abstract solving equations. There are different parts then where students are asked to solve equations using pictures and symbols to discuss issues that may arise.

Solving Equations

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