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6th-8th Grade Math: Practice & Review55 chapters | 466 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, we take a look at using algebra tiles to represent our numbers and variables. See how to use these to help model and solve equations.

In this lesson, we'll take a look at algebra tiles and how to use them to model and solve our equations. **Algebra tiles** are square and rectangle-shaped tiles that represent numbers and variables. Using algebra tiles provides a more visual way for us to solve our problems. It helps us to see just what quantities we're working with. It's like we are using building blocks to help us.

Each square tile stands for the number one. If we have two tiles, then we have the number two. If our numbers are negative, then our square tiles can be a different color to show the difference. For example, blue square bricks can be positive numbers and red square bricks can be negative numbers. The rectangle tiles stand for our variable. If we have one *x*, then we have one rectangle tile. If we have 2*x*, then we will have two rectangle tiles.

We can also use different colors here to represent positive and negative variables. For example, green rectangle tiles can represent positive variables and yellow rectangle tiles can represent negative variables. To use algebra tiles, we place square and rectangle tiles on either side of our equation until we have all the numbers and variables covered.

Let's take a look at how we can use algebra tiles to help us model and solve an equation. Let's take a look at the equation 2*x* - 4 = 10.

First, we are going to model this equation with our square and rectangle tiles. We see our equals sign, so we will place square and rectangle tiles on either side to represent what is on either side of the equation. On the left side, we have 2*x* and a -4. So on that side, we will have two green rectangle tiles to represent our 2*x* and four red square bricks to represent our -4. On the right side, we have ten blue square tiles to represent our 10.

Now that we have modeled our equation with our algebra tiles, we can play around with the tiles to help us solve the problem. Our goal is still the same. We still want to isolate our variable. In this case, we want to isolate the rectangle tiles. We want to move all the square tiles to one side and keep all the rectangle tiles on the other side.

For our equation, we have two green rectangle tiles on the left side with four red square tiles. We have ten blue square tiles on the right side. So, we want to get the two green rectangle tiles by themselves. We need to move the four red tiles. To move them, we need to pair them up with a different colored square.

Since our square tiles are red, we need to pair each of them with a blue square tile. Alternately, if our tiles were blue, we would need to pair them up with a red tile. So, we match the four red square tiles up with four blue square tiles. We remember that whatever we do to one side, we also must do to the other side. So, we also add four blue square tiles to the right side.

Whenever we have a red and blue pair of tiles, we can take them out of the problem. It's as if they cancel each other out. This leaves us with just the green tiles on the left and our blue tiles on the right.

Now, to finish solving our equation, we see that we have two rectangle tiles on the left. So, to find our answer, we need to split the blue tiles on the right side into two even groups. We can move the four blue tiles near the bottom so that two go on the top row and the other two go on the second row.

Now, we can solve our problem by looking at our tiles. We see that each green rectangle tile is equal to seven blue square tiles. So that means our *x* is equal to 7.

Let's take a look at another example. This time around, see if you can follow along yourself as we go through this problem. Use algebra tiles to model and solve the equation 3*x* = 12.

For this equation, we see that we have a 3*x* on the left side. This tells us that we will have three green rectangle tiles on the left side. The right side will have 12 blue square tiles. Since we have three green rectangle tiles on the left, let's see if we can split the 12 blue square tiles on the right side into three even groups. If we regrouped the 12 into three rows, we see that each row has 4 tiles. This tells us that each rectangle tile equals 4 square tiles. This tells us that our variable is equal to 4, and we are done!

Let's review what we've learned. **Algebra tiles** are square and rectangle shaped tiles or tiles that represent numbers and variables. For example, we can use square tiles to represent numbers. Each square tile is equal to one. So, four can be represented by four square tiles.

We can designate a different color to represent our negative numbers. We can use a rectangular tile to represent our variable. We can also have a different color to represent a negative variable. To use algebra tiles to model an equation, we place the relevant number of variable rectangle tiles and number square tiles for the left side of the equation and for the right side of the equation.

Then we play around with our tiles so that we end up with the rectangle tiles by themselves on one side. We do this by moving the square tiles. To move the square tiles, we match them up with another square tile of a different color. So if our numbers are positive, we match the square tiles with negative square tiles, and if our numbers our negative, we match them up with positive square tiles. We remember that whatever we do to one side, we also do to the other side.

After matching up our tiles, we then can take away any positive-negative pairs of tiles. This leaves us with our answer. If we have more than one rectangle tile on the rectangle side, then we will group our square tiles on the other side into the same number of groups. This then will tell us what each rectangle tile equals. This gives us our answer.

Upon completing this lesson, you will be able to:

- Explain what algebra tiles are and how they can be used
- Solve an algebra equation using algebra tiles

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6th-8th Grade Math: Practice & Review55 chapters | 466 lessons

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