Wednesday, October 13, 2010

Lesson Plan: Factoring Quadratic Trinomials Using Algebra Tiles

Lesson Plan: Factoring Quadratic Trinomials Using Algebra Tiles
EDCP 342:  Lesson Plan
Topic:  Factoring Quadratic Trinomials Using Algebra Tiles
Group:  Howard, Maria, Raman

Intended Students:    Grade 10  Fundamentals and Pre-calculus


WHAT
HOW LONG
MATERIALS
BRIDGE
Give everyone a small  sheet of paper.   In 5 seconds, write as many factors of 60.
1 minute


LEARNING OBJECTIVES
Using the algebra tiles, students will be able to:
1. Factor quadratic trinomials, including perfect square trinomials
2. Relate the dimensions of a rectangular area with finding the factors of a trinomial
3. Experience three modes of factoring trinomials:  algebraic method, concrete algebra tiles, and virtual  manipulatives


TEACHING OBJECTIVES
1. Maximum engagement of all students
2. Individual hands-on-learning using math manipulatives  (algebra tiles)
3. Demonstration of using virtual manipulatives in factoring trinomials


PRETEST
Each student will be given a worksheet sheet     
1. Factor the trinomial: x^2 + 5x + 6.  Write answer in worksheet. Ask for answer.  Show of hands who got the correct answer.  Ask a student to briefly explain his/her answer.

2 minutes


PARTICIPATORY LEARNING
1. State the learning objectives.  Tie-up bridge and pre-test to objectives.
2. What are the factors of 6? (3 and 2)  How can we illustrate this geometrically? (Draw a 3 by 2 rectangle, divided into 6 squares).  How are factors related to dimensions (of length and width), and product related to area?  (Finding the factors of a number is the same as finding the dimensions of a rectangle whose area is the number).  Will this geometric representation work for finding factors of a trinomial?
3. Distribute/introduce the algebra tiles, as a geometric method of finding factors of trinomials.  Each student will be given a complete set of tiles, with a transparent tile board.  Walk the students through the 3 different tile sizes representing x^2 (green), x (white) and 1 (red).  Explain that x is a variable that can represent any positive number.
4. Assemble 2-green x^2, 5-white x tiles and 2-red 1-tiles.  If all the 9 pieces represent the area of a rectangle, what algebraic expression represents this area?   
(2x^2 + 5x + 2)  How can we get the dimensions of this rectangle? 
* In your worksheet, complete equation #2:  2x^2 + 5x + 2 = (2x + 1)(x + 2)
5. Empty your tile board.  For our second rectangle, assemble 1- green x^2, 6-white x and 9-red 1-tiles into a rectangle.  What expression represents the area of this rectangle? 
(x^2 + 6x + 9).  What are the factors? 
(x + 3) and (x + 3).  What do you notice with our rectangle?  (It is a square).  Introduce the perfect square trinomial (PST). 
* In your worksheet, complete equation #3: 
x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2
6. Virtual Manipulatives:   
Reiterate that finding the linear factors of a quadratic trinomial is very much related to finding the dimensions of a rectangle that contain the trinomial.  The internet is full of virtual manipulatives that offer fun, creative, and interactive ways of factoring trinomial, which may appeal to today’s technology-savvy students. 
Factor x^2 + 7x + 12.  (x + 4)(x+3).





9 minutes





* Algebra tiles

* Virtual manipulatives

POST-TEST
Using your algebra tiles, find values of k, where x^2 + kx + 6 factors into 2 binomials. (k = 5, 7).  Write answer in #5 of your worksheet.



* Algebra tiles
SUMMARY & WRAP-UP
Ask students what they have learned today, which should touch the following points:
1. That to the concept of factoring is very much related to finding the dimensions of a rectangle of a given area.
2. That a quadratic trinomial factors only if one can arrange it into a rectangle.
3. That we know that a trinomial is a perfect square if the tiles neatly arranges into a square, with 2 equal dimensions.
4. Ask students to complete # 6 & 7 of their worksheet.  Collect worksheets.




3
minutes




Suggested student worksheet format:
Name:  __________________                                                                                    Topic:  Factoring Quadratic Trinomials
1.    Factor:    x^2  +  5x  +  6
2.    2x^2 + 5x + 2 = (                )(                  )
3.    x^2 + 6x + 9   = (                 )(                  )  =  (                )
4.    x^2 + 7x +  2  = (                  )(                  )
5.    x^2 + kx + 6   = (                   )(                    ) or (                   )(                   )
6.    One thing I learned today is _____________________________________.
7.    Algebra tiles do/do not help in understanding factoring trinomials because_______________________________________________________.

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