Download Gr10_PPQ_FactoringSimpleTrinomials

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
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BLM 1: Quadratic Models (1/6)
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BLM 1: Quadratic Models (2/6)
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BLM 1: Quadratic Models (3/6)
x  3x  2
2
x  5x  6
2
x  6 x  8 x  8 x  15
2
2
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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
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BLM 1: Quadratic Models (5/6)
( x  2)( x  1)
( x  2)( x  3)
( x  2)( x  4) ( x  3)( x  5)
Effective Questioning
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BLM 1: Quadratic Models (6/6)
( x  2)( x  6) ( x  4)( x  3)
( x  2)( x  5) ( x  3)( x  3)
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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
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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)
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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
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Artefact WCDSB
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