1. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 1 When a new technology rolls up - you are either: Part of the Steamroller, -or- Part of the Road. The choice is yours alone An Indispensable Teaching tool

2. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 2 Autograph The Teaching Tool Leading Into the 21 st Century An aid to learning in the 21 st 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!

3. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 3 Some Options With Points

4. Autograph 7/08/2001 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

5. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 5 Some Geometry

6. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 6 Investigations 1 The nine-Point Circle (or Euler Circle)

7. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 7 Designing Investigations 1.You can design your own investigations. 2.Present on disc or hard copy the problem to be investigated and pose questions or extensions that can be considered. 3.Provide hints if considered desirable or necessary. 4.Have students demonstrate their solutions. 5.Provide the solutions. 6.Store exchange and improve.

8. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 8 Frequency Diagrams and Box and Whisker Plots

9. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 9 Regression Lines The 4-minute Mile: Predicting and Potential Problems with Extrapolating

10. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 10 The Least Squares Line Least Squares Line -animationLeast Squares: Best fit Polynomials

11. Autograph 7/08/2001 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.

12. Autograph 7/08/2001 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 and input the equation y=(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.

13. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 13 Limits - Continuity and Differentibility Composite functionsDifferentiability over an Interval

14. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 14 The Chain Rule

15. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 15 Piecewise Functions

16. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 16 Transformation of Functions Translation of Linear FunctionsTranslation of Quadratic Functions

17. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 17 Geometric Transformations 1 EnlargementRotation

18. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 18 Geometric Transformations 2 TranslationShear Along the x-axis

19. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 19 Optimisation 1 Feasible Regions Testing by EXHAUSTION Subject to the given constraints: give all the possible (x,y) and the optimal value of p such that p is a maximum where p = 4x+3y *************************************************** Constraints: x  Integers: 0≤ x ≤ 10 y  Integers: 0≤ y ≤ 10 The given line is below the point (5,6) What happens if the line is not permitted to pass beyond (5,6)? (try other points)

20. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 20 Optimisation Involving Additional Constraints Optimise p where p= x + 3y Subject to the constraints x + y < 5 and x+2y < 8 where 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. Linear Programming

21. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 21 Area & Probability Distributions Working in the Graph Plotter pageWorking in the Statistics Page

22. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 22 Conics: The Parabola Two aspects studying various Locii relating to the parabola

23. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 23 Polar Co-ordinates

24. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 24 Probability Distributions

25. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 25 Statistics The Central Limit TheoremFrequency Histogram from Raw Data

26. Autograph 7/08/2001 Prepared & Presented by Jim Claffey 26 Vectors 1 Addition and subtraction of vectors; Multiplication by a scalar; Unit Vectors

27. Autograph 7/08/2001 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.