7/08/2001 Prepared & Presented by Jim Claffey1

Autograph

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

7/08/2001 Prepared & Presented by Jim Claffey2

Autograph

Autograph The 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!

7/08/2001 Prepared & Presented by Jim Claffey3

Autograph Some Options With Points

7/08/2001 Prepared & Presented by Jim Claffey4

Autograph 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

7/08/2001 Prepared & Presented by Jim Claffey5

Autograph Some Geometry

7/08/2001 Prepared & Presented by Jim Claffey6

Autograph Investigations 1

The nine-Point Circle (or Euler Circle)

7/08/2001 Prepared & Presented by Jim Claffey7

Autograph 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.

7/08/2001 Prepared & Presented by Jim Claffey8

AutographFrequency Diagrams

and Box and Whisker Plots

7/08/2001 Prepared & Presented by Jim Claffey9

Autograph Regression Lines

The 4-minute Mile: Predicting and Potential Problems with Extrapolating

7/08/2001 Prepared & Presented by Jim Claffey10

Autograph The Least Squares Line

Least Squares Line -animation Least Squares: Best fit Polynomials

7/08/2001 Prepared & Presented by Jim Claffey11

AutographThe 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.

7/08/2001 Prepared & Presented by Jim Claffey12

Autograph 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 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.

7/08/2001 Prepared & Presented by Jim Claffey13

AutographLimits - Continuity and

Differentibility

Composite functions Differentiability over an Interval

7/08/2001 Prepared & Presented by Jim Claffey14

Autograph The Chain Rule

7/08/2001 Prepared & Presented by Jim Claffey15

Autograph Piecewise Functions

7/08/2001 Prepared & Presented by Jim Claffey16

Autograph Transformation of Functions

Translation of Linear Functions Translation of Quadratic Functions

7/08/2001 Prepared & Presented by Jim Claffey17

Autograph Geometric Transformations 1

Enlargement Rotation

7/08/2001 Prepared & Presented by Jim Claffey18

Autograph Geometric Transformations 2

Translation Shear Along the x-axis

7/08/2001 Prepared & Presented by Jim Claffey19

Autograph Optimisation 1

Feasible RegionsTesting 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)

7/08/2001 Prepared & Presented by Jim Claffey20

AutographOptimisation Involving Additional Constraints

Optimise p where p= x + 3y Subject to the constraints

x + y < 5and x+2y < 8 where

x & y Positive Integers ***********************************************

Test by ExhaustionPoint 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) 6Points on the boundary are excluded.

Linear Programming

7/08/2001 Prepared & Presented by Jim Claffey21

AutographArea &

Probability Distributions

Working in the Graph Plotter page Working in the Statistics Page

7/08/2001 Prepared & Presented by Jim Claffey22

Autograph Conics: The Parabola

Two aspects studying various Locii relating to the parabola

7/08/2001 Prepared & Presented by Jim Claffey23

Autograph Polar Co-ordinates

7/08/2001 Prepared & Presented by Jim Claffey24

Autograph Probability Distributions

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Autograph Statistics

The Central Limit Theorem Frequency Histogram from Raw Data

7/08/2001 Prepared & Presented by Jim Claffey26

Autograph Vectors 1

Addition and subtraction of vectors; Multiplication by a scalar; Unit Vectors

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Autograph 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.