Tuesday, October 15, 2013

Free Lesson Plans: 2-Step Equation with Variables

This lesson plan is meant to help students understand two-step equations with variables a little better. It really helped my students catch up to their peers in math class. They really enjoyed learning about equations this way and grasped the concept very quickly.

Age Group:

 6-9 (It should be 6th, however, I know a good deal of older students that need help with this.)

Common Core Standards:

• CCSS.Math.Content.HSA-REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

• CCSS.Math.Content.HSA-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

CCSS.Math.Content.6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.

(Once you get this down it’s easy to find real-world problems to include so that you can also hit the following common core standards)

CCSS.Math.Content.6.EE.A.2a Write expressions that record operations with numbers and with letters

• CCSS.Math.Content.6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

• CCSS.Math.Content.6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

• CCSS.Math.Content.6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

• CCSS.Math.Content.6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

I Can: 

I can solve 2-step equations with variables.

Materials Needed:

Student volunteers


Print out sheets with the stick-figures already drawn.
When they are beginning the equations, give them stick-figures to help out with the order.
Student aid
Teacher aid


It would be great if you can have the students stand up and demonstrate this, but if your class is a little too unruly, you can just draw it on the board.

Imagine there’s three people walking together. The middle one is holding on to the other two so they don’t get separated. The one on the left has their arm linked with the middle person, but the one on the right is holding hands with the middle person.

Now which person can be taken away from the middle person the easiest? The person on the right is easier to get away from the middle person than the one on the right.

Multiplying and dividing numbers with the variable is like linking arms. Adding and subtracting numbers from variables is like holding hands.

So we want to get the variable all by itself, to find out who they are, but the people on either side is hiding the variable’s identity. We need to take them out. First we have to get rid of the person who’s connection is the weakest before going to the stronger connection.

Let’s take the problem 5x-3 = 22. Here’s how the people look:

So the 3 is the easiest target. We’ll eliminate them first. Remember the two important things we learned in 1-step equations with variables:

1. Use the opposite symbol to the one in the equation
     a. + and – are opposites
     b. X and / are opposites

2. Whatever you do on one side of the = you must do to the other, the exact same way.

5x – 3 = 22
      +3    +3
5x – 0 = 25

5x = 25

There! Now the one holding hands is gone!

Like we said, we want to get x by itself, but we’re still at 5x. Let’s eliminate that 5.

5x = 25
 5      5

1x = 5

x = 5.

There! Now x is by themselves and we know who they are!

But that x is a tricky one! Are we sure their true identity is 5? This is where we double-check by plugging it back in.

We know: 5x – 3 = 22 and x = 5
So (hopefully!)

5(5) – 3 = 22

Remember Order of Operations!

25 – 3 = 22

22 = 22

Is this true?


So x = 5.

Got ‘em!

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