Files from Alan Catley - Versions 3.0 and 3.2

Teaching mathematics with dynamic software has been shown to be more effective, more efficient, and above all more enjoyable for both teacher and learner.

The ability of Autograph to ‘select’ appropriate ‘dependent’ objects and then ‘animate’ mathematical concepts helps learners to better understand principles in many areas of the mathematics curriculum. This enables the teacher to adopt a more investigative approach than might otherwise be possible.

The following ‘resources’ are an (ever growing!) mixture of detailed Lesson Plans (LP) and student ‘Activity/Work’ Sheets (WS). They are all documented accounts of ideas that have been successfully trialled in the classroom with learners at all levels. Also included are some ideas to help understand examination questions (EX) as well as some ‘instruction sheets’ (IS) to help with project work.

For more information about these resources and training opportunities contact:

Alan Catley    alan@catley.org
Tel 0191 2590347      Mobile 07855431818

Version 3.0

All these files are for Version 3.0 and apart from some small changes can be used with version 3.2.  However if you would like the files for Version 3.2 hosted at Kangaroo Maths then - Click here

Help Sheets

IS Calculus Activities with Autograph – PowerPoint
IS Transformations with Autograph – PowerPoint
IS Uses of Autograph - PowerPoint showing scope
IS 45 Exercises in Autograph –  Right Click then Save As
IS Autograph Buttons v3.20
IS Dynamic Text Boxes Version 3.20

 

Circles

 

WS A line and a circle - investigation
WS The general equation of the circle

 

Transformations

 

LP An ‘interactive’ approach to teaching all four transformations
WS Translations - Paper based worksheet designed by students using the LP above
WS Reflections - Paper based worksheet designed by students using the LP above
WS Rotations - Paper based worksheet designed by students using the LP above
WS Enlargements - Paper based worksheet designed by students using the LP above
   

 

Linear Functions

 

LP Number Chains
WS Investigating the ‘c’ in y = mx + c
WS Investigating the ‘m’ in y = mx + c
WS Ways to define ‘gradient’ or ‘slope’
WS The distance, slope, mid-point of a line joining 2 points
WS The connection between the gradient of 2 perpendicular lines
WS The equation of a line through any two points
WS Finding the equation of a perpendicular bisector
WS Linear graphs ‘quiz’
EX A typical ‘examination question’
LP Mobile Phone Bills – a detailed investigation

 

 Linear Programming

 

WS Linear Programming Problem
WS The same problem on Autograph

 

 Quadratic Functions

 

LP Introducing the Quadratic Function
WS Investigating the ‘a’ in y = ax²
WS Investigating the ‘b’ in y = (x + b)²
WS Investigating the ‘c’ in y = x² + c
WS Investigating the ‘complete square’ form
WS Investigating ‘roots’ of quadratics
EX A typical examination question (equal roots)
EX Simultaneous Equations involving a quadratic function

 

Statistics and Data Handling

 

IS Analysing integer data
IS Analysing grouped data – histograms, box plots etc
IS Producing a frequency data table
IS Histograms and Frequency Density – unequal class intervals
IS Scatter graphs – analysing 2 variable data
LP Animating Least Squares Regression
IS Moving Averages (Time Series)
WS Binomial & Poisson Distributions

 

Calculus - The Basics of Differentiation

 

LP Pre-Calculus Activity
WS Numerical Gradient
WS Differentiation of a straight line
WS Introducing the Derivative
WS Differentiation of a quadratic
WS Differentiation of a cubic
WS Differentiation of a function in factorised form
WS Finding the equation of a tangent to a quadratic
EX A typical exam question

 

 Calculus - The Basics of Integration

 

WS The area under a straight line
WS The area under a curve1
WS The area under a curve 2
WS The area under a curve 3
WS Mid-Ordinate Rule
WS Trapezium Rule
WS Integration as the reverse of differentiation
WS Integration of a quadratic function

 

Trigonometric Functions

 

WS The graphs of y = asinx and y = cosx + d
WS The graphs of y = sinbx and y  = tan(x + c)
WS Solving basic trig equations

   

Functions

 

LP Composite functions
LP Translation of functions

 

Exponential and Logarithmic Functions

 

WS The ‘search’ for ‘e’
WS The Exponential Function
WS Transforming the graph of y = exp(x)

 

Numerical Methods

 

WS Iterations – instructions for the spreadsheet
WS Iterations 2
SS Iterations – the spreadsheet
WS Iterations - graphical interpretation using Autograph
WS Iterations on Autograph

 

More Topics

 

LP Parametric Equations
LP Differential Equations
LP Terminal Velocity – Differential Equations
LP Vector Equation of a line – lesson approach
WS Vector Equation of a line – setting up Autograph

 

Alan Catley    alan@catley.org     Tel +44 (0)191 2590347