1. 1 Integrating CAS casmusings.wordpress.com Chris Harrow Atlanta, GA casmusings@gmail.com

2. 2 Why CAS? Levels the playing field/scaffolding; you focus on how to ask good questions and interpret the answers. Keeps the focus on student THINKING Has forced me to rethink assessment – what is my goal for each question? Output form is sometimes unpredictable. Lesson = just because an answer LOOKS different doesn’t mean it IS different. Teacher isn’t the sole expert – instant/pressure-free confirmation & sometimes new math is motivated.

3. 3 In my classes All students own a TI-Nspire CAS & many bring a laptop ◦ Implication = Full-time CAS access & free computer software. ◦ Encourage use of Nspire CAS, Wolfram Alpha, & Geogebra CAS is assumed, but isn’t the focus It’s about asking good questions in 3 languages: English, Math, & CAS Split assessments

4. 4 Sources PreCalculus Transformed http://bit.ly/ypCgft http://bit.ly/ypCg Precalculus with Trigonometry, 3 rd ed, Foerster, (TE & Instructor’s Resources) http://bit.ly/yjplJP http://bit.ly/yjpl http://casmusings.wordpress.com

5. 5 Quadratics In Foerster Instructor’s Resource Book (CAS Activity 1-3a) plus extensions TI Nspire CAS file: Quadratics Form is no longer a boundary. ◦ Vertex, intercept, standard form are all equally accessible (plus others) CAS Lesson: Different forms tell different stories about the underlying function/data. CAS makes most forms equally accessible.

6. 6 Quadratics II In PreCalculus Transformed TI Nspire CAS file: QuadSurprises Unexpected formatting sometimes leads to additional math What do each of the coefficients of a standard form quadratic equation do to the corresponding graph?

7. 7 Quadratics III Evolved from a student’s exploration that was published in the Mathematics Teacher TI Nspire CAS file: QuadSurprises What pattern emerges when you compute the areas of quadratic sectors of equal width?

8. 8 Probability From http://casmusings.wordpress.com/ TI Nspire CAS file: Probability Find the probability of exactly 3 heads in 10 tosses of a coin. Proportions of colors when P(same color) = P(different colors)

9. 9 Linear Regressions In Foerster Instructor’s Resource Book (CAS Activities 3-2a & 3-2b) TI Nspire CAS file: LinReg What does a linear regression do? This is 100% understandable by any algebra student.

10. 10 Straightening Data In Foerster Instructor’s Resource Book (CAS Activities 3-4a) TI Nspire CAS file: Straightening What do Power & other Regressions really do?

11. 11 Graphing in Cartesian & Polar New Idea we’re planning to incorporate into the next edition of PreCalculus Transformed. TI Nspire CAS file: CeilingsFloors Trig function centers, ceilings, & floors Polar function centers, ceilings, & floors

12. 12 Transformations II Trig identities via the SQ transformation

13. 13 Misc Number of zeros in 200! ? One term of (Ax+By)^n is 27869184x^5y^3. Define A, B, & n.