Algebra Match

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SWBAT write and solve two-step and multi-step linear equations in one variable and justify each procedural step with its property.

Big Idea

Students not only need to be skilled at writing and solving equations, but they must also know how to justify the steps they take.


15 minutes


Before we begin:

1. Make a copies of the resource Equation_matchAlgMatch

2. Provide one pair of scissors for each pair of students

3. Make a transparency for the resource EQUALITY_PROPERTIES

I begin the lesson by projecting the properties of equality on the board for all to see. 


For all real numbers xy, and z,

Addition Property

if x = y, then x + z = y + z.

Subtraction Property

if x = y, then x – z = y – z.

Multiplication Property

if x = y, then xz = yz.

Division Property

if x = y, and z ≠ 0, then x/z = y/z.

Distributive Property

 x(y  + z) = xy + xz

x(y – z) = xy – xz

Multiplicative Inverse Property 
  a cannot = 0

 a(1/a) = 1





Then I write the four equations across the board and randomly call on students to come up and solve each of them. For each step in the process, they must also write the property that justifies the step, in parenthesis next to the step. Each student should check their answer right below their work, by substituting their result back into the equation. They should note that Equation 3 has no solution. 


1.  3(x + 2) – 5  = 50


2.  x/2  + 4/5 =  56


3.   x – 11 = 3 +  x


4. (3/5)x   =  –10


Scaffold: For students that need work with solving multi-step equations, I direct them to the website. This can be done at home, or if time permits, after the APK section. Ask the students to read each slide and keep clicking “next”.  




30 minutes

2. New Info/Application (30min)

1. Write the following  two-step algebra equation on the whiteboard.

“3(x + 5) = 29”


2. Ask students what they would choose as the first step in solving this equation.

(students will probably use the distributive property…ask them to try another first

approach; A student may begin by subtracting , explain why this is incorrect. You

may have to solve and demonstrate that the value obtained is not the solution)

3. Prove that the different  routes lead to equivalent equations because they lead to the same solutions. Before actually performing each step, ask out load what property is being used.

After the operations are shown, ask them which operation they think simplify finding the solution the most.   (They should say using the distributive property, then adding  – 5 to both sides, more-so than dividing by 3, and then adding -5)


Group Activity

Pair up students and hand each pair one copy of resource. Equation_ Match

The six equations focus on the HSS.A.REI standards. Ask each pair of students to cut out the strips with the steps and properties and place them where they belong in the chart. Once a group is finished they should raise their hands so the teacher can go over and check.




15 minutes

3. Closure:


Each pair of students should play the role of the teacher and prepare a ONE PROBLEM QUIZ to give to their classmates. Pairs must provide the ANSWER KEY as well. The quiz should meet each of the following criteria:

  • An equation to solve or word problem involving an equation
  • Should address any 3 of the properties to justify the steps in solving the equation, seen in this lesson (include distributive property)
  • Think about one possible mistake that a student could make in the process. Include an “error analysis” explanation in your answer key.  

Students must hand the Quiz in as an “exit pass”.


Homework: Homework_AlgebraMatch (1).pdf