Topic: Factoring Quadratic Trinomials Using Algebra Tiles
Group: Howard, Maria, Raman
Intended Students: Grade 10 Fundamentals and Pre-calculus
Intended Students: Grade 10 Fundamentals and Pre-calculus
I. BRIDGE - (1 minute)
Give everyone a small sheet of paper. In 5 seconds, write as many factors of 60.
II. LEARNING OBJECTIVES: Using the algebra tiles, students will be able to:
2.1 factor quadratic trinomials, including perfect square trinomials
2.2 relate the dimensions of a rectangular area with finding the factors of a trinomial
2.3 experience three modes of factoring trinomials: algebraic method, concrete algebra
tiles, and virtual manipulatives
III. TEACHING OBJECTIVES
3.1 maximum engagement of all students
3.2 individual hands-on-learning using math manipulatives (algebra tiles)
3.3 demonstration of using virtual manipulatives in factoring trinomials
III. TEACHING OBJECTIVES
3.1 maximum engagement of all students
3.2 individual hands-on-learning using math manipulatives (algebra tiles)
3.3 demonstration of using virtual manipulatives in factoring trinomials
IV. PRE-TEST (Each student will be given a worksheet sheet (2 minutes)
4.1 Factor the trinomial: x2 + 5x + 6. Write answer in worksheet.
Show of hands who got the correct answer. Ask a student to briefly explain her answer.
V. PARTICIPATORY LEARNING (9 minutes)
5.1 State the learning objectives. Tie-up bridge and pre-test to objectives.
5.2 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?
5.3 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.
5.4 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 the equation #2: 2x2 + 5x + 2 = ( ) ( )
5.5 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 = ( ) ( ) = ( )2
5.6 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. = ( )( ).
VI. 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.
VII. SUMMARY/CLOSURE: Ask students what they have learned today, which should touch the following points: (3 minutes)
1. That to the concept of factoring is very much related to finding the dimensions of a rectangle
V. PARTICIPATORY LEARNING (9 minutes)
5.1 State the learning objectives. Tie-up bridge and pre-test to objectives.
5.2 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?
5.3 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.
5.4 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 the equation #2: 2x2 + 5x + 2 = ( ) ( )
5.5 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 = ( ) ( ) = ( )2
5.6 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. = ( )( ).
VI. 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.
VII. SUMMARY/CLOSURE: Ask students what they have learned today, which should touch the following points: (3 minutes)
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,
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.
4. Ask students to complete # 6 & 7 of their worksheet. Collect worksheets.
Student Worksheet :
Name: __________________ Topic: Factoring Quadratic Trinomials
1. Factor: x2 + 5x + 6
2. 2x2 + 5x + 2 = ( ) ( )
3. x2 + 6x + 9 = ( ) ( ) = ( )2
4. x2 + 7x + 12. = ( ) ( )
5. x2 + kx + 6 = ( )( ) or ( )( )
6. One thing I learned today is _____________________________________.
7. Algebra tiles do/do not help in understanding factoring trinomials because_______________________________________________________.
Name: __________________ Topic: Factoring Quadratic Trinomials
1. Factor: x2 + 5x + 6
2. 2x2 + 5x + 2 = ( ) ( )
3. x2 + 6x + 9 = ( ) ( ) = ( )2
4. x2 + 7x + 12. = ( ) ( )
5. x2 + 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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