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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