 # Distributive Property with Algebra Tiles

If you have taught the distributive property without manipulatives, you know that students often forget to distribute the front number to both terms inside the parenthesis.  For example, if given the expression 3(n + 5), students incorrectly write 3n + 5.  When students do this, it shows that they do not have a true understanding of the distributive property.  Using algebra tiles is a great tool to help students really understand what is going on when they distributive.  If you are not familiar with Algebra tiles, make sure you read my previous post.

Give students the expression 2(n + 4).  Explain that this means two groups of n + 4.  Next, have students use the Algebra tiles to show two groups of n + 4. Students will easily see that 2n + 8 is the same as 2(n + 4). The same works for subtraction.  3(2h – 3) means three groups of (2h – 3). Students can use the Algebra tiles to show how this simplifies to be 6h – 9. It gets a little trickier when you have to distributive a negative number.  For instance, with the problem -2(g – 1).  A negative means the opposite.  So in the above example, it means the opposite of 2 groups of (g – 1).  Students should first make 2 groups of g – 1, and then turn all of the tiles over to show the opposite. When problems get more complicated like in the problem 3(g – 1) + 4g – 8.  Students will just have to take a few more steps.  First, they need to represent 3 groups of g – 1 and 4g – 8. Then, they can combine like terms to see that the final answer is 7g – 11. I love using the algebra tiles for a problem like this because it makes students realize that doing the distribute property first is necessary before you can combine like terms.

Once your students feel comfortable simplifying expressions with the Algebra Tiles, you can give them strategies for simplifying expressions without the tiles.  For example, underlining and circling like terms.  If students have a true understanding first with the Algebra Tiles, when you have them simplify with paper and pencil they will be much more successful.  Please post any questions or comments below!