autograph 7/08/2001 prepared & presented by jim claffey 1 when a new technology rolls up - you...
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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 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
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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.
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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
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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.
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AutographLimits - Continuity and
Differentibility
Composite functions Differentiability over an Interval
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
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Autograph Geometric Transformations 2
Translation Shear Along the x-axis
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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
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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
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Autograph Statistics
The Central Limit Theorem Frequency Histogram from Raw Data
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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.