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TIPS 2.0 – MPM2D: Quadratic Functions 1

Quadratic Functions

75 min

Math Learning GoalsEstablish connections between roots of quadratic equations and factors of quadratic •functions.Identify roots and factors from a variety of representations of quadratics (graphical, •algebraic, pictorial, table of values).Refinereasoningandprovingskills.•

MaterialsBLM 1.1.1 (copy •each representation on a different colour of paper)BLM 1.1.2, 1.1.3 •algebra tiles•Notebookfiles:• Quadratics - Activity Quadratic Survey -

Response Units•

Groups of Three Four Corners Variation Distribute one card to each student (BLM 1.1.1). Students locate the other two students with representations that model the same quadratic function as their cardandformagroup.Eachgrouplocatestheirworkingareabymatchingtheirrepresentations to the correct algebra tile representation (BLM 1.1.2).

Whole Class DiscussionEngagestudentsbyasking:Whatstrategiesdidyouusetofindyourgroupmates?•Was one model easier to connect to for your model (e.g., the table of values given •agraph)?

Develop mathematical language throughout the discussion (roots, factors, x-intercepts,…)

Minds On…

Groups of Three ActivityProvideeachstudentwithacopyofBLM1.1.3.UsingthecorrespondingNotebookfile:QuadraticsActivity,extendthelessontoincludefractionalroots.

Curriculum Expectation/Questioning/Mental Note: Observe students as they complete the questions using the manipulatives and assess their understanding of roots and factors.

If the majority of the students are not prepared to identify factors, go to Notebook p. 2 and discuss roots. Continue to p. 3, where they will likely connect to factors and then return to p. 1.

Action!

Individual Response Unit QuestionsDisplayeachquestion(NotebookfileQuadraticSurvey).Studentsindividuallyentertheir response.

Whole Class DiscussionReferringtotheclassscoreoneachquestion,havestudentsexplaintheirthinkingforselecting the correct response. Discuss only misunderstandings that are resulting in incorrect responses.

Consolidate Debrief

Concept PracticeSkill Drill

Home Activity or Further Classroom ConsolidationCompleteworksheet1.1.4.•In your journal, communicate your understanding of roots in as many ways as you •can.Inyourjournal,developatableorothergraphicorganizerthatidentifiestechniques•for determining roots, when it is appropriate to use each technique, and any other information you wish to include.

Teacher or students select the task to complete.

TIPS 2.0 – MPM2D: Quadratic Functions 2

1.1.1: Minds On Cards

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1.1.1: Minds On Cards (continued)

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1.1.1: Minds On Cards (continued)

y = (x + 3)(x + 6) y = (x + 2)(x + 5)

y = (x + 1)(x + 6) y = (x + 1)(x + 3)

y = (x + 4)(x + 7) y = x(x + 5)

TIPS 2.0 – MPM2D: Quadratic Functions 5

1.1.1: Minds On Cards (continued)

y = (x + 2)(x + 8) y = x(x + 3)

y = (x + 4)(x + 4) y = (x + 1)(x + 4)

TIPS 2.0 – MPM2D: Quadratic Functions 6

1.1.1: Minds On Cards (continued)

x y x y

-10 28 -10 40

-9 18 -9 28

-8 10 -8 18

-7 4 -7 10

-6 0 -6 4

-5 -2 -5 0

-4 -2 -4 -2

-3 0 -3 -2

-2 4 -2 0

-1 10 -1 4

0 18 0 10

1 28 1 18

x y x y

-10 36 -10 63

-9 24 -9 48

-8 14 -8 35

-7 6 -7 24

-6 0 -6 15

-5 -4 -5 8

-4 -6 -4 3

-3 -6 -3 0

-2 -4 -2 -1

-1 0 -1 0

0 6 0 3

1 14 1 8

TIPS 2.0 – MPM2D: Quadratic Functions 7

1.1.1: Minds On Cards (continued)

x y x y

-10 18 -10 50

-9 10 -9 36

-8 4 -8 24

-7 0 -7 14

-6 -2 -6 6

-5 -2 -5 0

-4 0 -4 -4

-3 4 -3 -6

-2 10 -2 -6

-1 18 -1 -4

0 28 0 0

1 40 1 6

x y x y

-10 16 -10 70

-9 7 -9 54

-8 0 -8 40

-7 -5 -7 28

-6 -8 -6 18

-5 -9 -5 10

-4 -8 -4 4

-3 -5 -3 0

-2 0 -2 -2

-1 7 -1 -2

0 16 0 0

1 27 1 4

TIPS 2.0 – MPM2D: Quadratic Functions 8

1.1.1: Minds On Cards (continued)

x y x y

-10 36 -10 54

-9 25 -9 40

-8 16 -8 28

-7 9 -7 18

-6 4 -6 10

-5 1 -5 4

-4 0 -4 0

-3 1 -3 -2

-2 4 -2 -2

-1 9 -1 0

0 16 0 4

1 25 1 10

TIPS 2.0 – MPM2D: Quadratic Functions 9

1.1.2: Algebra Tile Representations

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1.1.2: Algebra Tile Representations (continued)

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1.1.2: Algebra Tile Representations (continued)

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1.1.2: Algebra Tile Representations (continued)

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1.1.2: Algebra Tile Representations (continued)

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1.1.3: Quadratic Activity

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1.1.3: Quadratic Activity (continued)

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1.1.4: Worksheet

Part A:Write the roots. Write the equation in factored form.

TIPS 2.0 – MPM2D: Quadratic Functions 17

1.1.4: Worksheet (continued)

Part B:

x y x y

4 3 -6 9

5 0 -5 4

6 -1 -4 1

7 0 -3 0

8 3 -2 1

9 8 -1 4

10 15 0 9

11 24 1 16

x y x y

-2 5 -4 -6

-1 2 -3 0

0 1 -2 4

1 2 -1 6

2 5 0 6

3 10 1 4

4 17 2 0

5 26 3 -6

TIPS 2.0 – MPM2D: Quadratic Functions 18

1.1.4: Worksheet (continued)

Part CWhat are the dimensions of the following rectangle? What is the factored form of the quadratic expression represented by the algebra tile diagram?

Factor the following expressions

1.

2. 3x2 + 20x – 7

3. Make your own expression and factor it.

+ +