## 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!

## Simplifying Expressions with Algebra Tiles

Algebra tiles are a great way to teach your students how to simplify expressions.  If you are not familiar with Algebra Tiles, firsts read my previous post here.

To begin, Students need to understand what a zero pair is.  A zero pair, is made by opposites that cancel out to be zero.  For example, -2 and 2 are a zero pair.  2n and -2n are a zero pair.

Next, students need to understand that pieces that are the exact same size are called like terms.  Like terms can be combined.  Have students represent the expression 2n + 5 + n + 2.

Explain to students that we need to combine our like terms, the pieces that are the same size.  Therefore, we can combine the 2n and the n to make 3n and we can combine the 5 and the 2 to make 7.

Have students try several problems like this, with only addition. When students have mastered that, have students represent 5n + 4 + n – 1.

Have students combine the like terms.

Then, have students cancel out any zero pairs.  In this problem, the minus 1 and positive 1 make a zero pair.  The remaining pieces are your answer.  5n + 2.

Have students try several problems similar to this until they are comfortable.  You can also add in exponents.  For instance, g² + 2g + 2 – g + g².

Students should first combine the like terms.

Then, cancel out any zero pairs. The final answers would be 2g² + g + 2.

Once you have spent a significant amount of time practicing simplifying expressions with the Algebra tiles, you can move to practicing simplifying expressions with paper and pencil.  Make sure you always spend time with the hands-on lesson before moving to paper and pencil.  The visual helps students  understand what they are doing.  Please comment below if you try this lesson in your classroom and let me know how it goes!

## Using Algebra Tiles

Algebra tiles are a great way to make an abstract concept like Algebra, visual.  You will be amazed at the difference this tool will make for students.  Today I will first explain what the tiles represent.    Then, over the next few days I will be posting some lessons you can do using the Algebra Tiles.  The Algebra tiles I use can be purchased “>here, or you can download a free version here.

The small squares represent units.  The yellow side means to add and the red side means to subtract (or add a negative).  Therefore, to represent adding 5, I would use 5 yellow tiles.

To represent subtracting 3, I would use three red tiles.

The long tiles represent an unknown quantity, your variable.  The green side is for positive variables and the red side is for negative variables.  Therefore, to represent 3n, I would use three of the long green tiles.

To represent subtracting 2y or -2y, I would use two long red tiles.

Last, are the large square tiles.  These represent your variable squared, n².  Just like when using an area model to understand multiplication, you can see that n x n = n², our large square.

So, to represent 2w² you would use two large blue squares.

To represent subtracting g², or-g² you would use one large red square.

This is what the expression n² + 4n – 5 would look like.

Have your students practice representing simple expressions with the tiles so they fully understand how they work before moving forward with another lesson.

Comment below if you have used algebra tiles in your classroom or if you have any questions!

## Hello!

It is my mission to deliver visual, hands-on lessons that deepen mathematical understanding.  I have been a middle school math teacher for 14 years and have made it my mission to get my students to not just “do” math, but to understand math.  I do this by providing visuals and hands-on lessons to aid in students understanding.  I am writing this blog for all the math teacher out there who are searching for ways to make their math lessons hands-on with a focus on true understanding.  I hope you enjoy!