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Manipulatives in Grade 10 Math Robin McAteer Head of Math and Computer Science Sir Robert Borden High School Ottawa, Ont

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Created by Robin McAteer for OAME 2008 WHY? Mathematical Processes Problem Solving : conduct investigations to help deepen their mathematical understanding Selecting Tools : select and use a variety of concrete, visual, and electronic learning tools…. to investigate mathematical ideas… Representing: create a variety of representations of mathematical ideas Commmunicate mathematical ideas using… a variety of appropriate representations and, and observing mathematical connections

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Created by Robin McAteer for OAME 2008 Why: Instructional Effectiveness Differentiated Instruction –Appeals to kinesthetic learners –Provides alternate access to concepts Cooperative Learning –Group investigations Enduring Understandings –Students forget rules, but REMEMBER concepts FUN!!!!

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Created by Robin McAteer for OAME 2008 Barriers: Comfort Zones

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Created by Robin McAteer for OAME 2008 Three Main Applications Algebraic Connections (tiles) Concrete Functions (cubalinks) General Modeling (ex. trig) Gun building

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Created by Robin McAteer for OAME 2008 Algebraic Connections Area Model Unit tile ( 1 x 1) Area=1 X tile ( X x 1) Area=X X 2 tile ( X x X) Area= X 2 Negative Tiles

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Created by Robin McAteer for OAME 2008 Multiply/Divide/Factor

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Created by Robin McAteer for OAME 2008 Factoring Make a Rectangle, and look at the dimensions!

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Created by Robin McAteer for OAME 2008 Factoring Practice

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Created by Robin McAteer for OAME 2008 Factoring Practice

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Created by Robin McAteer for OAME 2008 From Tiles to Diagrams

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Created by Robin McAteer for OAME 2008 Student Work

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Created by Robin McAteer for OAME 2008 Student Work

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Created by Robin McAteer for OAME 2008 Looking Back Grade 7/8/9 – concept of x as a variable - integer concepts - subtracting is adding the opposite - negative + positive pair makes zero - Evaluating expressions with x - Video 1 Evaluating Linear ExpressionsEvaluating Linear Expressions

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Created by Robin McAteer for OAME 2008 Completing the Square Make a SQUARE shape + Extras extras

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Created by Robin McAteer for OAME 2008 Practice: Completing the Square extras

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Created by Robin McAteer for OAME 2008 More Practice extras Add ZERO group

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Created by Robin McAteer for OAME 2008 Student Work

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Created by Robin McAteer for OAME 2008 Looking Forward…

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Created by Robin McAteer for OAME 2008 Looking Forward Algebra Blocks Calculus

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Created by Robin McAteer for OAME 2008 Our Proof of Equivalence

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Created by Robin McAteer for OAME 2008 Equivalence / Representations

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Created by Robin McAteer for OAME 2008 Link to Transformations

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Created by Robin McAteer for OAME 2008 What are First Differences?

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Created by Robin McAteer for OAME 2008 First Differences Linear? Yes / No Height Difference Between Stacks

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Created by Robin McAteer for OAME 2008 More Differences Linear? Yes / No Height Difference Between Stacks

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Created by Robin McAteer for OAME 2008 What are Second Differences?

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Created by Robin McAteer for OAME 2008 Second Differences Height Difference Between Stacks First Differences are Linear

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Created by Robin McAteer for OAME 2008 Exercise Exercise: In your groups, build a quadratic relation with a second difference of 1. DO NOT USE A TABLE OF VALUES! Hint: Could start like this

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Created by Robin McAteer for OAME 2008 Building Quadratic Relations

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Created by Robin McAteer for OAME 2008 Cubalink Parabola – Second Differences of 1

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Created by Robin McAteer for OAME 2008 Cubalinks Insights Very rich model Explore concavity Explore transformations Takes some time – give YOURSELF time to play

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Created by Robin McAteer for OAME 2008 Actual Students!

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Created by Robin McAteer for OAME 2008 General Modeling θ What is the tan ratio for θ ? What angle gives a tan ratio of 1? What angle gives a ratio of 1/8?

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Created by Robin McAteer for OAME 2008 Trig Ratios θ cos θ = 14/17 What is θ ?

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Created by Robin McAteer for OAME 2008 Similar Triangles

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Created by Robin McAteer for OAME 2008 Modeling

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Created by Robin McAteer for OAME 2008 MATH IS FUN!

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Created by Robin McAteer for OAME 2008 Contact Info E-mail: robin.mcateer@ocdsb.ca - for more information My Website: mrsmac.pbwiki.com - my courses, links, sequencing, handouts School Site: www.srbhs.ca - manipulatives videos

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