1 CAS: A Perspective from North of the Border 2012 T 3 International Conference Chicago, IL Saturday, March 3rd Dwight Stead Paul Alves.

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CAS: A Perspective from North of the Border

2012 T3 International ConferenceChicago, ILSaturday, March 3rd Dwight Stead

Paul Alves

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Session Goals

• Understand the Ontario context in how CAS is used in our high school curriculum

• Experience some Nspire CAS activities for various grades in the Ontario curriculum

• Share CAS experiences

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What is CAS?

Computer Algebra System is software that allows students to manipulate algebraic expressions and equations

Nspire CAS has commands for:• solve• expand• factor• completing the square• Limits• derivatives• integrals

• and many more …

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The Ontario Context

• Ontario revised its High School Mathematics curriculum between 2005 and 2007

• Some grades 9 through 12 expectations explicitly reference the use of CAS

• CAS is used as a tool that allows students to • Develop patterns in algebra• investigate concepts in the general sense• solve problems

• CAS can be used as:• Black box: to provide the answer (checking)• White Box: to develop understanding (hypothesizing)

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CAS Self-Assessment

Please self assess your prior experience with CAS• 1 finger indicates no prior

experience with CAS• 2 fingers indicates only using it at

workshops• 3 fingers indicates using CAS in

your class• 4 fingers indicates downloading

and using pre-made activities in you class

• 5 fingers indicates creating your own activities in your class and being an expert at your school

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10 Escape(Undo)

9Scratchpad

(Save)

1Touchpad

2“Click”(Grab)

3Home(Off)

4Document

Tools(Add Page)

5NextPage

8Previous

Page

6Menu

(Context Menu)

7Tab

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CAS Concepts in Grade 9

• Ontario grade 9 students can use CAS to:• add & subtract polynomials• multiply monomial by polynomial• solve first degree equations

• Activities:• Develop the concept of an equation and the root of

an equation (white box approach)• Solving Linear Equations (create activity handout)

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CAS Concepts in Grade 10 and 11

• Ontario grades 10 and 11 students can use CAS to:• Solve first degree polynomials with fractional

coefficients (10 applied)• Expand and simplify second degree polynomials• Factor second degree polynomials (common,

trinomials, difference of squares and perfect squares) • Investigate properties of quadratic relations in

standard, vertex and factored forms• Explore the development of the quadratic formula

• Activities:• Factoring with CAS (TNS file and Student Activity

Handout)• Modeling Quadratic Relations (TNS file and Student

Activity Handout)

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CAS Concepts in Grade 12

• Ontario grade 12 students can use CAS to:• Develop the Factor and Remainder theorems• Explore the relationship between roots and zeroes of

polynomial functions• Solving polynomial equations to degree 4• Explore the relationship between roots and zeroes of

rational functions• Solve one variable rational equations• Solve optimization problems

• Activities:• The Box Problem (TBS File, explore numerically,

graphically and using black box CAS to confirm)

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For more information, please contact us:

• Dwight Stead – T3 Regional Instructor• [email protected]• Wiki: http://dpcdsb-nspire.wikispaces.com

• Click on the T3 Conference Page Link

• Paul Alves - T3 National Instructor• [email protected]

Google Search Terms:DPCDSBwikinspireT3