Micro-teaching: Factoring Quadratic Trinomials with Algebra Tiles

Lesson Plan: 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	Sheets of paper/pen
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       1. Factor the trinomial: x2 + 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	whiteboard
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 x2 (green), x (white) and 1 (red).  Explain that x is a variable that can represent any positive number. 4. Assemble 2-green x2, 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?    (2x2 + 5x + 2)  How can we get the dimensions of this rectangle?  * In your worksheet, complete equation #2:  2x2 + 5x + 2 = (2x + 1)(x + 2) 5. Empty your tile board.  For our second rectangle, assemble 1- green x2, 6-white x and 9-red 1-tiles into a rectangle.  What expression represents the area of this rectangle?  (x2 + 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:  x2 + 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 x2 + 7x + 12.  (x + 4)(x+3).	9     Minutes	whiteboard  Algebra tiles  Virtual manipulatives
POSTTEST	Using your algebra tiles, find values of k, where x2 + 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

                                            Student Worksheet
Name:  __________________                      Topic:  Factoring Quadratic Trinomials
1.    Factor:    x²  +  5x  +  6
2.    2x² + 5x + 2 = (                )(                  )
3.    x² + 6x + 9   = (                 )(                  )  =  (                )²
4.    x² + 7x +  2  = (                  )(                  )
5.    x² + kx + 6   = (                   )(                    ) or (                   )(                   )
6.    One thing I learned today is _____________________________________.
7.    Algebra tiles do/do not help in understanding factoring trinomials

       because_______________________________________________________.