Introducing Simple Algebra Equations

I have introduced the process of solving simple equations for a variable with second and third graders, but OFTEN with students in pre-algebra who are intent on solving problems mentally, but lack accuracy and logic skills to show their work.  I have found that the consistency of the process helps students get a good foundation and confidence to progress in algebra.

I use a primary balance scale, green and red bingo spotter counting chips, and a scrap of paper with a X or a letter for the variable.  I color-code the counting chips with green for positive integers and red for negative.  I have written an = sign in marker on the fulcrum of the balance.  For more complex equations, an algrebra balance with 2 pans on each side can demonstrate positive and negative numbers.

To show the steps of X + 4 = 9, have the student copy the equation on paper and write down each step as it is done:

1.  Place the X paper on one side of the scale along with 4 green counters.

2.  Place 9 green counters on the other side of the scale.

3.  Introduce the concept of "isolate the variable," by having the student remove the 4 chips, leaving the paper X.  Underneath the + 4 in the original equation, write down – 4 to show that the chips were taken out.

4.  In order to keep the balance balanced, what we do to one side must be done to the other side.  Have the student take out 4 chips from the 9 on the other side of the balance and write – 4 underneath the original equation to show that 4 chips were removed from that side.

5.  Each side now has a subtraction problem.  I have students cross off the 4-4 problem because there are no chips left.  Have the student bring the X down to the next row to show what is still on the balance. 

6.  On the other side, have the student solve 9-4 and write the answer (5) below to show X=5. Circle the answer.

7.  Have the student count the chips on the balance to check.

As your student progress, using algebra tiles or an algebra balance can continue to help those visual students or struggling students with concepts by maintaining manipulatives that accurately demonstrate the principles of equations.  You can find any of these materials at either of our websites: or


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