Algebra Tiles

Overview This set of tutorials provides 39 examples that use Algebra Tiles to solve a variety of algebra problems. These include the following types of problems:Adding integers (Examples 1–5)Subtracting integers (Examples 6-13)Solving one-step equations (Examples 14-21)Solving multi-step equations (Examples 22–29)Solving quadratic equations (Examples 30–33)Solving subtraction equations (Examples 34–39)These examples use the following Algebra Tiles conventions:

In this Example two positive integers are added. The sum is the total number of algebra tiles.

In this Example a positive integer and a negative integer are added. After eliminating zero pairs, the sum is a positive integer. Point out to students that the sign of the sum is based on the greater number of tiles of a particular color.

In this Example a positive integer and a negative integer are added. After eliminating zero pairs, the sum is a negative integer. Point out to students that the sign of the sum is based on the greater number of tiles of a particular color.

In this Example a positive integer and a negative integer are added. Because of the equal number of tiles, after eliminating zero pairs, the sum is zero.

In this Example two negative integers are added. The sum is the total number of algebra tiles.

In this Example, a smaller positive integer is subtracted from a larger positive integer. This is a straightforward example of the “take away” model of subtraction.

In this Example a larger positive integer is subtracted from a smaller positive integer. Since there aren’t enough positive tiles to take away, enough zero pairs are added. Once the positive tiles are taken away, what remains is a negative integer.

In this Example an equal number of positive integer tiles are subtracted, resulting in zero.

In this Example a negative number of tiles are subtracted from a positive number of tiles. Since there are no negative tiles, enough zero pairs are added. Once the negative tiles are removed the result is a larger positive number of tiles. This shows that subtracting negative numbers is the same as adding positive numbers.

In this Example a positive number of tiles is subtracted from a negative number of tiles. Since there aren’t any positive tiles, add enough zero pairs. Once the positive tiles are subtracted what results is a larger number of negative tiles (or a lesser integer value).

In this Example a negative number of tiles is removed from a negative number of tiles. Since there are more than enough negative tiles to take away, this is an example of the “take away” model of subtraction.

In this Example a negative number of tiles are subtracted when there aren’t enough negative tiles to take away. In this case add zero pairs. When the negative tiles are taken away, the result is a positive number of tiles.

In this Example an equal number of positive integer tiles are subtracted, resulting in zero.

In this Example, a one-step problem of the form x + a = b is solved. Zero pairs are used to isolate the variable. The solution is positive.

In this Example, a one-step problem of the form x + a = b is solved. Zero pairs are used to isolate the variable. The solution is negative.

In this Example, a one-step problem of the form x + a = b is solved. Zero pairs are used to isolate the variable. The solution is zero.

In this Example, a one-step problem of the form x – a = b is solved. Zero pairs are used to isolate the variable. The solution is positive.

In this Example, a one-step problem of the form x + a = –b is solved. Zero pairs are used to isolate the variable. The solution is negative.

In this Example, a one-step problem of the form x + (–a) = –b is solved. Zero pairs are used to isolate the variable. The solution is positive.

In this Example, a one-step problem of the form x + (–a) = –b is solved. Zero pairs are used to isolate the variable. The solution is negative.

In this Example, a one-step problem of the form x + (–a) = –b is solved. Zero pairs are used to isolate the variable. The solution is zero.

In this Example, there are positive tiles and x-tiles on both sides of the equation. By removing identical numbers of tiles from each side, the solution is found.

In this Example, there are positive tiles and x-tiles on both sides of the equation. By removing identical numbers of tiles from each side, then adding zero pairs, the solution is found.

In this Example, there are positive tiles and x-tiles on both sides of the equation. By removing identical numbers of tiles from each side, the solution is found. In this case an equal number of integer tiles are on each side, resulting in a solution of zero.

In this Example, there are positive tiles and x-tiles on both sides of the equation. By removing identical numbers of tiles from each side, adding zero pairs, then dividing, the solution is found. The result is a rational number.

In this Example, there are positive tiles and x-tiles on both sides of the equation. By removing identical numbers of tiles from each side, adding zero pairs, then dividing, the solution is found. The result is a negative number.

In this Example, there are positive tiles and x-tiles on both sides of the equation. By removing identical numbers of tiles from each side, adding zero pairs, then dividing, the solution is found. The result is a rational number.

In this Example, there are positive tiles and x-tiles on both sides of the equation. By removing identical numbers of tiles from each side, then dividing, the solution is found. The result is a negative rational number.

In this Example, there are positive tiles and x-tiles on both sides of the equation. By removing identical numbers of tiles from each side, then dividing, the solution is found. Because there are an equal number of integer tiles on each side, the solution is zero.

In this Example a quadratic equation with a single positive solution is found. The quadratic term factors into a perfect square.

In this Example a quadratic equation with a single negative solution is found. The quadratic term factors into a perfect square.

In this Example a quadratic equation with two solutions is found. The quadratic term factors into the product of two binomials.

In this Example a quadratic equation with two solutions is found. The quadratic term factors into the product of two binomials.

In this Example, a subtraction equation is modeled. The steps include modeling the variable term, adding enough zero pairs to model the subtraction, then modeling the rest of the equation to solve for x. In this variation a positive number of tiles is subtracted from the variable term. The solution is positive.

In this Example, a subtraction equation is modeled. The steps include modeling the variable term, adding enough zero pairs to model the subtraction, then modeling the rest of the equation to solve for x. In this variation a positive number of tiles is subtracted from the variable term. The solution is negative.

In this Example, a subtraction equation is modeled. The steps include modeling the variable term, adding enough zero pairs to model the subtraction, then modeling the rest of the equation to solve for x. In this variation a positive number of tiles is subtracted from the variable term. The solution is zero.

In this Example, a subtraction equation is modeled. The steps include modeling the variable term, adding enough zero pairs to model the subtraction, then modeling the rest of the equation to solve for x. In this variation a negative number of tiles is subtracted from the variable term. The solution is positive.

In this Example, a subtraction equation is modeled. The steps include modeling the variable term, adding enough zero pairs to model the subtraction, then modeling the rest of the equation to solve for x. In this variation a negative number of tiles is subtracted from the variable term. The solution is negative.

In this Example, a subtraction equation is modeled. The steps include modeling the variable term, adding enough zero pairs to model the subtraction, then modeling the rest of the equation to solve for x. In this variation a negative number of tiles is subtracted from the variable term. The solution is zero.