Investigation:Solving equations with Algebra tiles

We can use algebra tiles to solve equations with integers. Let's look at some examples, and then try a few of our own.

Using subtraction to solve an equation

The key idea here is to set-up our equation and then create zero pairs to end up with one +x tile on one side of the equation.

Practice questions

Use algebra tiles in the applet below to model and solve the following equations. Check your solutions with a partner, or by substituting the answer back in the equation.

1. x + 2 = 10
2. x + 3 = 5
3. 7 = x + 4
4. 14 = 7 + x

 Watch video

 

Reflection

5. Explain why it is important to subtract the same amount of +1-tiles to each side and not just one side of the equation.
6. The example video uses a property called the subtraction property of equality. Explain in your own words what this property allows you to do.

 

Using division to solve an equation

Remember that division relates to dividing into equal groups. 

 

Practice questions

Use algebra tiles in the applet below to model and solve the following equations. Check your solutions with a partner, or by substituting the answer back into the equation.

7. 2 x = 4
8. 5 x = 15
9. 3 x = 18
10. 12 = 4 x

Reflection

11. The example uses a property called the division property of equality. Explain in your own words what this property allows you to do.

Extension

12. There are two more properties of equality - the addition property of equality and the multiplication property of equality. See if you can demonstrate them using algebra tiles.
13. Algebra tiles are a nice tool for visualizing how to solve an equation, but we can't use Algebra tiles to solve every equation. Write an example of an equation that cannot be solved using Algebra tiles. Explain why it cannot be solved that way. Then, explain how you think it might be solved algebraically.
14. Explain how you could use algebra tiles to solve an equation like  3 x + 2 = 4.