Activities to Teach Students to Factor Quadratics Using Algebra Tiles
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As a math teacher, you might have realized that teaching students to factor quadratics using algebra tiles is a challenging task. Some students find factoring a daunting task, especially when they encounter quadratic expressions with no apparent factor pairs. However, with hands-on activities and exercises, you can make factoring less intimidating and more enjoyable for your students. In this article, we will explore some activities that you can use to teach your students to factor quadratics using algebra tiles.
1. Introduction to Algebra Tiles
Before you introduce students to factoring using algebra tiles, start by teaching them the primary algebra tiles. Utilize kits of algebra tiles during this activity, and distribute tiles to each student in the class and have them place them in front of them. Make sure each student has the same set of tiles, and that they understand the types of tiles they have.
With the tiles in front of them, give the students quadratic expressions that are already factored, and have them model the expressions using their tiles. Alternatively, you could display the expression on the board and have the students model it on their tiles. As they place the tiles, have them verbalize the factors that they see. After every student has done it, ask for their observations and share the different forms that the algebra tiles can take.
2. Factoring Square Trinomials
After students have an understanding of algebra tiles, you can introduce them to the next activity, which is factoring square trinomials. Square trinomials or quadratic expressions are polynomials that look like ax² + bx + c.
To start, display a square trinomial on the board and have students model it using their tiles. As they model, have them group the tiles to form a square. Tell them that the square represents both a missing expression and a substitute variable that they can use to determine the square’s dimensions.
Now have students try to find the dimensions of the square and have them verbalize what they see. Next, distribute a worksheet that contains different square trinomials, and have students use their tiles to model and factor the expressions. This helps them understand the idea of factoring quadratics better.
3. Factoring General Quadratics
After students have gained a mastery of factoring square trinomials, challenge them to try and factor general quadratics by themselves. General quadratics are quadratic expressions that don’t have the form of a square trinomial. With this activity, students must come up with new factoring techniques to determine the factors of the quadratic expressions.
To start, model a general quadratic using the algebra tiles, but don’t show the students that it’s a quadratic yet. Instead, have them work together in small groups to determine which tiles belong together and convert the tiles into area models. Afterward, have them work together to determine whether their area models can form a square.
After they have figured that out, have them find the dimensions of the square, and voila – they now have the factors of the general quadratic. They can then rewrite the expression in its factored form.
Conclusion
Factoring quadratics using algebra tiles exercises students to think critically, observe patterns and encourages an environment of solving problems creatively. These activities provide the students with a much deeper understanding of what factors are and how they work. As the teacher, your role is to guide and motivate the students throughout the exercises and activities. With time and practice, factoring quadratics will not be such a daunting task for your students, and they can apply the concepts learned in algebra to other mathematical problems that require factoring.