When introducing equations, all students can benefit from using a model of a balance scale. Here, a matchbox represents the unknown variable, and a match represents the value one. Be aware that the unknown variable has to be a positive integer.
Let’s look at the example 2x + 3 = x + 5.
How to Prepare
- For each scale model, you need as many matchboxes as the number of unknowns in the original equation. In this case, we need three boxes.
- Solve the equation, and put this number of matches in each box. Our equation has the solution x = 2, so each box will contain two matches.
With Students
Ask the students to model and solve the equation using match boxes and matches. How many matches are hidden in each box?
The equations left hand side 2x + 3 is represented by two boxes and three matches.
The right hand side x + 5 is represented by one box and five matches.
By removing three matches and one box from each side, the students will conclude that each box contains two matches, so x = 2.
Let the students check their answer by opening the box and revealing the number of matches.
