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Posing Powerful Questions Lesson Title: Factoring Quadratics (Simple Trinomials) Grade 10 Academic Goals(s) for a Specific Lesson Students are learning about making connections between algebraic, pictorial and graphical representations of quadratic relationships; factoring quadratics (simple trinomials) with and without the use of manipulatives. Curriculum Expectations Factor polynomial expressions involving trinomials. Big Idea(s) Addressed by the Expectations Many equivalent representations can describe the same situation or generalization. Each representation may give a different insight into certain characteristics of the situation or generalization. Minds On… Distribute cards representing factored expressions, standard expressions and diagrams of algebra tiles in factored form to students (BLM1) to form groups of three. Ask students to discuss/justify they belong to the group. Post graphs to represent each of the quadratic functions around the room. Tell groups to locate the graph that corresponds to their function group. (Open Questions) Groups discuss: - How do you know the graph matches each representation? - What do the four representations have in common? What do they represent? - What did you find to be easy/challenging throughout this activity? Whole group present answers to group discussions Action! In their groups of three students rearrange algebra tiles to represent the area of a rectangle whose dimensions are the factors of the expression. (BLM 2). To encourage group work and a math talk learning community instruct students to take turns with the algetiles while the other two members of the group coach how the tiles should be arranged. Switch roles. Scaffolding Questions (posed to individuals as needed) How can the tiles be arranged to form a rectangle? How do the tiles line up? What are the lengths of your model (the algetiles)? How do you know your answer is correct? Q 4: Can you use your answers to #1 & 2 to help you Are there other possible answers? Can you use negative numbers? Other types of numbers? How do you know your answer is correct? Q 4: Student Samples Consolidate/Debrief (Parallel Tasks) Pose two sets of questions: (BLM 3) Students choose one of two tasks to complete individually to consolidate their understanding of factoring simple trinomials. When done instruct students to discuss their solutions with someone who choose the same set of questions. Homework (Open Questions) Students create their own simple trinomial and determine the factors. These trinomials will be exchanged with a partner the following day for the Minds On… activity: In pairs factor the trinomial your partner created. This is repeated several times. Assign textbook questions for practice. Effective Questioning Artefact WCDSB May 2011 1/10 BLM 1: Quadratic Models (1/6) Effective Questioning Artefact WCDSB May 2011 2/10 BLM 1: Quadratic Models (2/6) Effective Questioning Artefact WCDSB May 2011 3/10 BLM 1: Quadratic Models (3/6) x 3x 2 2 x 5x 6 2 x 6 x 8 x 8 x 15 2 2 Effective Questioning Artefact WCDSB May 2011 4/10 BLM 1: Quadratic Models (4/6) x 8 x 12 x 7 x 12 2 2 x 7 x 10 x 6 x 9 2 Effective Questioning 2 Artefact WCDSB May 2011 5/10 BLM 1: Quadratic Models (5/6) ( x 2)( x 1) ( x 2)( x 3) ( x 2)( x 4) ( x 3)( x 5) Effective Questioning Artefact WCDSB May 2011 6/10 BLM 1: Quadratic Models (6/6) ( x 2)( x 6) ( x 4)( x 3) ( x 2)( x 5) ( x 3)( x 3) Effective Questioning Artefact WCDSB May 2011 7/10 BLM 2: Area with Algebra Tiles Name: 1. Using algebra tiles create the rectangles for the following areas. Complete the following chart. Area of Rectangle Number Number Number Use Algebra Tiles to Build and of x2 of x of Unit Length Width Sketch a Rectangle Tiles Tiles Tiles x2 + 4x + 3 x2 + 5x + 6 x2 + 6x + 8 x2 + 7x + 12 Effective Questioning Artefact WCDSB May 2011 8/10 BLM 2: Area with Algebra Tiles (Continued) 2. Find a relationship between the number of x tiles and the numbers in the expressions for the length and width. 3. Find a relationship between the number of unit tiles and the numbers in the expressions for the length and width. 4. Determine the missing value ” “ to complete the standard form of the equation and then express the quadratic expression in factored form. a) b) Effective Questioning Artefact WCDSB May 2011 9/10 x2 6 x 8 BLM 3: Factoring Quadratics Complete all of the questions from either Part A or Part B. Part A Part B Factor each of the following expressions, using Factor each of the following expressions, using the patterns found in the previous investigation. the patterns found in the previous investigation. 1. x2 + 18 x + 32 1. x2 - 14x + 45 2 2. x + 65x + 64 2. x2 -4x – 32 3. x2 - 13x + 42 3. x2 + 34x - 72 1. Which expression(s) did you find easiest to factor? Why? 2. Which expression(s) did you find hardest to factor? Why? 3. Factor the following expression: x2 - x + 12 Homework: Create your own quadratic trinomial and determine the factors. Effective Questioning 10/10 Artefact WCDSB May 2011