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CAS: A Perspective from North of the Border

CAS: A Perspective from North of the Border. 2012 T 3 International Conference Chicago, IL Saturday, March 3rd. Dwight Stead Paul Alves. Session Goals. Understand the Ontario context in how CAS is used in our high school curriculum

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CAS: A Perspective from North of the Border

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  1. CAS: A Perspective from North of the Border 2012 T3 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 • Share CAS experiences

  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 • 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)

  5. 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

  6. 10 2 3 1 9 4 8 5 7 6

  7. 10 Escape (Undo) 2 “Click” (Grab) 3 Home (Off) 1 Touchpad 9 Scratchpad (Save) 4 Document Tools (Add Page) 8 Previous Page 5 Next Page 7 Tab 6 Menu (Context Menu)

  8. 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)

  9. 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)

  10. 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)

  11. For more information, please contact us: • Dwight Stead – T3 Regional Instructor • Dwight.stead@rogers.com • Wiki: http://dpcdsb-nspire.wikispaces.com • Click on the T3 Conference Page Link • Paul Alves - T3 National Instructor • Paul.Alves@Peelsb.com Google Search Terms: DPCDSB wiki nspire T3

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