Algebra Tiles
What are they?
Algebra tiles are known as mathematical manipulatives that allow students to better understand ways of algebraic thinking and the concepts of algebra. These tiles have proven to provide concrete models for elementary school, middle school, and high school students.
The algebra tiles are made up of small squares, large squares, and rectangles. The number one is represented by the small square, which is also known as the unit tile. The rectangle represents the variable x and the large square represents x2. The length of the side of the large square is equal to the length of the rectangle, also known as the x tile. When visualizing these tiles it is important to remember that the area of a square is s2, which is the length of the sides squared. So if the length of the sides of the large square is x then it is understandable that the large square represents x2. The width of the x tile is the same length as the side length of the unit tile. The reason that the algebra tiles are made this way will become clear through understanding their use in factoring and multiplying polynomials.
What do they do?
•Manipulatives used to enhance student understanding of subject traditionally taught at symbolic level.
•Provide access to symbol manipulation for students with weak number sense.
•Provide geometric interpretation of symbol manipulation.
•Support cooperative learning, improve discourse in classroom by giving students objects to think with and talk about.
•Provide access to symbol manipulation for students with weak number sense.
•Provide geometric interpretation of symbol manipulation.
•Support cooperative learning, improve discourse in classroom by giving students objects to think with and talk about.
How to get them?
How to use algebra tiles?
Zero Pairs:
- called zero pairs because they are the additive inverse of each other
- when put together they cancel each other out to model zero
Adding/Subtracting Integers:
- Add or subtract positive and/or negative integers
- Addition can be viewed as “combining”. Combining involves the forming and removing of all zero pairs.
- Subtraction can be interpreted as “take-away.” Subtraction can also be thought of as “adding the opposite.”
Multiplication of Integers:
- Integer multiplication builds on whole number multiplication.
- Use concept that the multiplier serves as the “counter” of sets needed.
- The counter indicates how many rows to make. It has this meaning if it is positive
- If the counter is negative it will mean “take the opposite of.” (flip-over)
Modeling and Simplifying Algebraic Expressions:
- Introduce algebraic expressions with algebra tiles to help reinforce the concept in a concrete manner
Solving Linear Equations:
- Isolate a variable to solve the algebraic expression
Multiplying Polynomials
- Use a T-Chart to multiply polynomials. One part of the equation goes onto the vertical line while the second half goes onto the horizontal line.
![Picture](/uploads/6/6/7/2/6672522/4779317.png?250)
Factoring:
- Algebra tiles help to visualize how to break a polynomial into two factors
![Picture](/uploads/6/6/7/2/6672522/458344.gif)
Completing the Square:
- Completing the square is used for solving quadratic equations or getting certain equations such as the standard form of a parabola