When a new technology rolls up - you are either: Part of the Steamroller, -or- Part of the Road . The choi

1. An Indispensable Teaching tool When a new technology rolls up - you are either: • Part of the Steamroller, -or- • Part of the Road.The choice is yours alone Prepared & Presented by Jim Claffey

2. AutographThe Teaching Tool Leading Into the 21st CenturyAn aid to learning in the 21st Century A Potpourri of ideas. If you don’t see anything that could be of help to you I’m sure we will find something for you! Prepared & Presented by Jim Claffey

3. Some Options With Points Prepared & Presented by Jim Claffey

4. Three Points: Options Autograph works in two modes:(i) Graphs and Co-ordinate Geometry.(ii) Single variable Statistics and Probability. To work with you will need to understand how objects are placed on the screen and how they are related (father-son relation). All equation entries are input as you see them in any textbook. Menus, toolbars, & Help are almost self explanatory Prepared & Presented by Jim Claffey

5. Some Geometry Prepared & Presented by Jim Claffey

6. Investigations 1 The nine-Point Circle (or Euler Circle) Prepared & Presented by Jim Claffey

7. Designing Investigations • You can design your own investigations. • Present on disc or hard copy the problem to be investigated and pose questions or extensions that can be considered. • Provide hints if considered desirable or necessary. • Have students demonstrate their solutions. • Provide the solutions. • Store exchange and improve. Prepared & Presented by Jim Claffey

8. Frequency Diagrams and Box and Whisker Plots Prepared & Presented by Jim Claffey

9. Regression Lines The 4-minute Mile: Predicting and Potential Problems with Extrapolating Prepared & Presented by Jim Claffey

10. The Least Squares Line Least Squares Line -animation Least Squares: Best fit Polynomials Prepared & Presented by Jim Claffey

11. The Tangent As the Limiting Position of the Secant • Insert a cursor point on the curve at P then draw the tangent at P. Insert a second point at Q. • While holding down the shift key select both P and Q. • Right click the mouse. Select line from the menu. This draws a line through P and Q. • Again with both P and Q selected right click on the Mouse. Select Gradient from the menu. • Select the point Q and move the point Q towards point P. Prepared & Presented by Jim Claffey

12. The Gradient Function f(x) Defined As a Special Limit • Click on the toolbar button. • Enter a function: eg f(x) =x²-4x-3 • On the toolbar click on the gradient button to draw the gradient function. • Press <ENTER> and input the equationy=(f(x+h)-f(x))/h(The starting value for h is taken to be 1). • Click on the graph just drawn in the last step. • On the toolbar click on the Constant controller Button • Study what happens as h approaches zero. The step size can be changed. Prepared & Presented by Jim Claffey

13. Limits - Continuity and Differentibility Composite functions Differentiability over an Interval Prepared & Presented by Jim Claffey

14. The Chain Rule Prepared & Presented by Jim Claffey

15. Piecewise Functions Prepared & Presented by Jim Claffey

16. Transformation of Functions Translation of Linear Functions Translation of Quadratic Functions Prepared & Presented by Jim Claffey

17. Geometric Transformations 1 Enlargement Rotation Prepared & Presented by Jim Claffey

18. Geometric Transformations 2 Translation Shear Along the x-axis Prepared & Presented by Jim Claffey

19. Optimisation 1 Subject to the given constraints: give all the possible (x,y) and the optimal value ofpsuch thatpis a maximum where p = 4x+3y*************************************************** Constraints: • x Integers: 0≤ x ≤ 10y Integers: 0≤ y ≤ 10 • The given line is below the point (5,6) Feasible RegionsTesting by EXHAUSTION What happens if the line is not permitted to pass beyond (5,6)? (try other points) Prepared & Presented by Jim Claffey

20. Optimisation Involving Additional Constraints Linear Programming Optimise p wherep= x + 3y Subject to the constraints x + y < 5and x+2y < 8where x & y Positive Integers*********************************************** Test by Exhaustion Point P= x+3y k (1,1) 1+3(1) 4 (1,2) 1+3(2) 7 (1,3) 1+3(3) 10 optimum (2,1) 2+3(1) 5 (2,2) 2+3(2) 8 (3,1) 3+3(1) 6 Points on the boundary are excluded. Prepared & Presented by Jim Claffey

21. Area & Probability Distributions Working in the Graph Plotter page Working in the Statistics Page Prepared & Presented by Jim Claffey

22. Conics: The Parabola Two aspects studying various Locii relating to the parabola Prepared & Presented by Jim Claffey

23. Polar Co-ordinates Prepared & Presented by Jim Claffey

24. Probability Distributions Prepared & Presented by Jim Claffey

25. Statistics The Central Limit Theorem Frequency Histogram from Raw Data Prepared & Presented by Jim Claffey

26. Vectors 1 Addition and subtraction of vectors; Multiplication by a scalar; Unit Vectors Prepared & Presented by Jim Claffey

27. Vector Equation of a Line • Select the point P. • Use the cursors to move P along the line. • Note the information provided in the status bar below the graph. • The original line was entered in its parametric form. This activity shows the relationship between the two forms. Prepared & Presented by Jim Claffey