Solving equations using algebra tiles worksheets answer key

• Stephanie Stanglin

  Stephanie Stanglin is a license secondary mathematics teacher with 4.5 years experience as math teacher, .66 years as a K-12 mathematics coach, and .33 years as a 3-10 mathematics tutor. She holds a B.A. in Mathematics Education, a M.S.Ed. in Educational Leadership, and is finishing an M.Ed. in Curriculum and Instruction, STEM concentration.

  View bio
• Instructor Yuanxin (Amy) Yang Alcocer

  Amy has a master's degree in secondary education and has been teaching math for over 9 years. Amy has worked with students at all levels from those with special needs to those that are gifted.

  View bio

Discover what are algebra tiles. Learn how to use the algebra tile model. Practice solving math problems using algebra tiles examples. Find out which polynomial is represented by the algebra tiles. Updated: 01/18/2022

Algebra tiles are colored blocks that are used to represent algebraic expressions or equations.

There are three types of algebra tiles:

• Small Square: These represent 1, a constant in the expression. The yellow side is positive and the red side is negative. The length and the width are 1, showing that the area is 1.
• Rectangle: These represent x, a linear term in the expression. The green side is positive and the red side is negative. The length is x and the width is 1, showing that the area is 1*x or x.
• Large Square: These represent {eq}x^2 {/eq}, a quadratic term in the expression. The blue side is positive and the red side is negative. The length and the width are x, showing that the area is {eq}x^2 {/eq}.

Algebra Tiles

Algebra Tiles

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 2x, 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.

• Video
• Quiz
• Course

How to Use Algebra Tile Model for Math Problems

Example: Represent {eq}2x^2-3x+1 {/eq} using algebra tiles.

This expression means there are two of the positive {eq}x^2 {/eq} tiles, 3 of the negative x tiles, and 1 of the positive constant tiles.

Algebra Tiles for the Given Expression

Which Polynomial is Represented by Algebra Tiles?

These problems can also be done the opposite way where, given a set of algebra tiles, the expression can be determined.

Example:

Which polynomial is represented by these algebra tiles?

A. {eq}x^2+4x+2 {/eq}

B. {eq}x^2+4x-2 {/eq}

C. {eq}5x^2-2 {/eq}

D. {eq}-x^2-4x+2 {/eq}

Example of Algebra Tiles

There is one large blue square, four green rectangles, and two small red squares. That means the correct expression that represents these algebra tiles is {eq}x^2+4x-2 {/eq}

Algebra Tiles for Basic Math Operations

Algebra tiles can be used to combine like terms using the four operations of addition, subtraction, multiplication, and division.

Addition

Add the two polynomial expressions together

Algebra Tiles with Addition Example

The first polynomial has two large blue squares, one green rectangle, and three small yellow squares; this represents the expression {eq}2x^2+1x+3 {/eq}. The second polynomial has one red large square, two green rectangles, and one small red square, this represents the expression {eq}-x^2+2x-1 {/eq}. Together this makes {eq}2x^2+1x+3-x^2+2x-1 = x^2+3x+2 {/eq}.

Subtraction

Subtract the two polynomials.

Subtraction with Algebra Tiles Example

The first polynomial has one large blue squares, two green rectangles, and two small yellow squares; this represents the expression {eq}x^2+2x+2 {/eq}. The second polynomial has one blue large square, one red rectangle, and one small yellow square, this represents the expression {eq}x^2-1x+1 {/eq}. Together this makes {eq}x^2+2x+2-(x^2-1x+1) = x^2+2x+2-x^2+1x-1=3x+1 {/eq}.

Multiplication

Multiply the two polynomials.

Multiplication with Algebra Tiles Example

The first polynomial has two red rectangles and three small yellow squares; this represents the expression {eq}-2x+3 {/eq}. The second polynomial has one green rectangle and two small red squares, this represents the expression {eq}x-2 {/eq}. Together this makes {eq}(-2x+3)(x-2) = -2x^2+4x+3x-6 = -2x^2+7x-6 {/eq}.

Division

Divide the two polynomials.

Division with Algebra Tiles Example

Modeling an Equation

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 2x - 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 2x and a -4. So on that side, we will have two green rectangle tiles to represent our 2x and four red square bricks to represent our -4. On the right side, we have ten blue square tiles to represent our 10.

Solving the Equation

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.

Algebra Tiles

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 2x, 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.

Modeling an Equation

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 2x - 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 2x and a -4. So on that side, we will have two green rectangle tiles to represent our 2x and four red square bricks to represent our -4. On the right side, we have ten blue square tiles to represent our 10.

Solving the Equation

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.

What is an algebra tile model?

An algebra tile model is a visual diagram that consists of some combination of algebra tiles. The purpose of a model is represent a polynomial expression or equation.

How do algebra tiles work?

Algebra tiles are blocks that can be used to represent constant, linear, and quadratic terms. Constant blocks are small yellow squares, linear blocks are green rectangles, and quadratic blocks are large blue squares; the other side of all blocks are red, which means negative.

How do you create algebra tiles?

To create algebra tiles, look at the polynomial expression or equation and identify how many of each block there is. Then, match that with the type of block and be careful to note whether the blocks are negative or positive.

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.

Become a Member

Already a member? Log In

 Back

Resources created by teachers for teachers

Over 30,000 video lessons & teaching resources‐all in one place.

Video lessons

Quizzes & Worksheets

Classroom Integration

Lesson Plans

I would definitely recommend Study.com to my colleagues. It’s like a teacher waved a magic wand and did the work for me. I feel like it’s a lifeline.

Back

Create an account to start this course today

Used by over 30 million students worldwide

Create an account