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

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

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!!!!

Created by Robin McAteer for OAME 2008 Barriers: Comfort Zones

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

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

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

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

Created by Robin McAteer for OAME 2008 Factoring Practice

Created by Robin McAteer for OAME 2008 Factoring Practice

Created by Robin McAteer for OAME 2008 From Tiles to Diagrams

Created by Robin McAteer for OAME 2008 Student Work

Created by Robin McAteer for OAME 2008 Student Work

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

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

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

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

Created by Robin McAteer for OAME 2008 Student Work

Created by Robin McAteer for OAME 2008 Looking Forward…

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

Created by Robin McAteer for OAME 2008 Our Proof of Equivalence

Created by Robin McAteer for OAME 2008 Equivalence / Representations

Created by Robin McAteer for OAME 2008 Link to Transformations

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

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

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

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

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

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

Created by Robin McAteer for OAME 2008 Building Quadratic Relations

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

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

Created by Robin McAteer for OAME 2008 Actual Students!

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?

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

Created by Robin McAteer for OAME 2008 Similar Triangles

Created by Robin McAteer for OAME 2008 Modeling

Created by Robin McAteer for OAME 2008 MATH IS FUN!

Created by Robin McAteer for OAME 2008 Contact Info - for more information My Website: mrsmac.pbwiki.com - my courses, links, sequencing, handouts School Site: - manipulatives videos