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

2 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 Discuss how CAS could be used to implement the CCSS

3 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 …

4 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 (exponent rules, binomial theorem, …) 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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6 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 CAS activities in you class 5 fingers indicates creating your own CAS activities in your class and being an expert at your school

8 Escape (Undo) 9 Scratchpad (Save) 1 Touchpad 2 “Click” (Grab) 3 Home (Off) 4 Document Tools (Add Page) 5 Next Page 8 Previous Page 6 Menu (Context Menu) 7 Tab

9 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)

10 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)

11 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)

12 CAS in Common Core State Standards Most states are in the process of implementing the CCSS Form a group of teachers for one of: Algebra 1 Algebra 2 Pre-Calculus Calculus Task: How could CAS help you meet some of the CCSS for your course? Be prepared to share.

13 For more information, please contact us: Dwight Stead – T 3 Regional Instructor Wiki: Click on the T3 Conference Page Link Paul Alves - T 3 National Instructor Google Search Terms: DPCDSB wiki nspire T3