Robin Nagy - MANSW Conference 2016

Robin Nagy, Sep 12, 2016

This book contains all the worksheets and files used as activities in my MANSW Conference session on Sunday 18th September 2016

Table of Contents

  1. Introduction
    1. Nagy's Geogebra Crib Sheet
    2. MANSW Presentation Slides
  2. Navigating by the Southern Cross
    1. Navigating by the Southern Cross
  3. Transformation of Functions
    1. Transformation of Functions Assignment
  4. Reflection and Rotation
    1. Reflection and Rotation Activity - MANSW 2016 Conference
  5. Enlargement
    1. Enlargement Activity for MANSW Conference 2016
  6. Limiting Sums - introducing Integral Calculus
    1. Limiting Sums - The Squeeze Theorem
  7. Centres of a Triangle and the Euler Line
    1. Centres of a Triangle and the Euler Line
  8. Introduction to Differential Calculus
    1. Introduction to Calculus

1.

Introduction

Here is a page of my handy tips about Geogebra which you may not know, including useful shortcuts, menu options, notes about syntax etc. I am also including all my slides from my presentation.

  • 1. Nagy's Geogebra Crib Sheet
  • 2. MANSW Presentation Slides

1.1.

Nagy's Geogebra Crib Sheet

Nagy's Geogebra Crib Sheet
– Robin Nagy

1.2.

–

2.

Navigating by the Southern Cross

Print out the three different Geogebra Activity files and, using only a compass and straight edge, find out where South is on the horizon. You will need to be able to construct perpendicular bisectors and to be able to drop a perpendicular from a point to a line.

  • 1. Navigating by the Southern Cross

2.1.

Navigating by the Southern Cross

To find South with the Southern Cross and Pointer Stars - you will need a compass and straight edge.
Print out each of the three Geogebra Files below on separate pieces of paper.[br]1. Draw a line through the long diagonal of the Southern Cross.[br]2. Construct the perpendicular bisector of the pointer stars.[br]3. Where these two lines meet, mark the intersection point 'X'.[br]4. Construct a perpendicular line from X to the horizon.[br]5. Mark the point 'S' where this perpendicular joins the horizon. This is South.
Southern Cross Activity 1 (see below for the solution)
Southern Cross Activity 2 (see below for the solution)
Southern Cross Activity 3 (see below for the solution)
SOLUTION to Southern Cross Activity 1 (print out and overlay on your work - hold it up to a window to see how accurate your construction is)
SOLUTION to Southern Cross Activity 2 (print out and overlay on your work - hold it up to a window to see how accurate your construction is)
SOLUTION to Southern Cross Activity 3 (print out and overlay on your work - hold it up to a window to see how accurate your construction is)
– Robin Nagy

3.

Transformation of Functions

This assignment encourages students to investigate the transformation of function graphs by changing f(x) to other forms such as f(-x), -f(x), f(x-a), f(x)+a, kf(x) and f(x/k).

  • 1. Transformation of Functions Assignment

3.1.

Transformation of Functions Assignment

Transformation of Functions Assignment
Download the pdf Assignment below and ask students to complete. The solutions are also downloadable below that, and a summary transformations of functions Geogebra file.
Transformation of Functions Assignment
This Geogebra file allows you to look at different functions (select left hand side buttons or type in your own into the input box) and how the transformations effect the original function (select from the right hand side tick-boxes)
Transformation of Functions - Solutions
– Robin Nagy

4.

Reflection and Rotation

In this activity, you will discover the equivalence of rotation as the combination of two reflections.

  • 1. Reflection and Rotation Activity - MANSW 2016 Conference

4.1.

Reflection and Rotation Activity - MANSW 2016 Conference

Reflections and Rotation Activity
Download the pdf instructions below and follow the worksheet. The different stages of the activity are illustrated by the Geogebra files below.
Geogebra Transformations Worksheet 1 Reflection and Rotation
Stage 1 showing reflections
Stage 2 - showing rotation
Stage 1 - showing reflections
Stage 1b - showing double reflection - where is the centre of rotation?
Stage 2 - showing rotation
– Robin Nagy

5.

Enlargement

This activity investigates the scale factor of enlargement and the position of the image relative to the centre of enlargement. It also investigates negative scale factors and the ratio of distances away from the centre of enlargement.

  • 1. Enlargement Activity for MANSW Conference 2016

5.1.

Enlargement Activity for MANSW Conference 2016

Enlargement Activity
Download the pdf activity below and follow the instructions. The stages of the worksheet are illustrated by the Geogebra files which follow.
Geogebra Transformations Worksheet 2 Enlargement
Enlargement - showing first stage of worksheet activity
Enlargement - showing final stage of worksheet
– Robin Nagy

6.

Limiting Sums - introducing Integral Calculus

This investigation is from the Geogebra Manual (Creating Dynamic Worksheets page 2 of 6) and looks at the limiting sum of rectangular areas below and above a function as the value of the area under the graph.

  • 1. Limiting Sums - The Squeeze Theorem

6.1.

Limiting Sums - The Squeeze Theorem

Limiting Sums Worksheet - adapted from GeoGebra Manual (Creating Dynamic Worksheets page 2/6)
The following Geogebra file is the final output of the worksheet
– Robin Nagy

7.

Centres of a Triangle and the Euler Line

This activity is an investigation into four well-known centres of a triangle: the incentre, circumcentre, orthocentre and centroid, three of which form the Euler line. The worksheet allows you to discover the attributes of each centre and which three form the Euler line.

  • 1. Centres of a Triangle and the Euler Line

7.1.

Centres of a Triangle and the Euler Line

Centres of a Triangle Investigation
In this investigation, you will follow the instructions below to discover the attributes of four well-known centres of a triangle (the incentre, circumcentre, orthocentre and centroid) and find out that three of them always form a straight line (known as the Euler line). Download the pdf which follows and follow the instructions. If you get stuck, two versions of the final Geogebra files are produced below.
Geogebra Centres of a Triangle and the Euler Line
Centres of a Triangle and the Euler Line - final Geogebra file example 1
Centres of a Triangle and the Euler Line - final Geogebra file example 2
– Robin Nagy

8.

Introduction to Differential Calculus

This activity investigates the limiting value of the gradient of a chord drawn between two points on a function and its relation to the gradient of the tangent.

  • 1. Introduction to Calculus

8.1.

Introduction to Calculus

Investigating Gradients of Tangents as the Limit of Gradients of Chords
Download the pdf worksheet below and follow all instructions to create a Geogebra file which will enable you to investigate the gradient of a tangent as the limiting value of the gradient of a chord.[br]Examples of final Geogebra files are shown below.
Geogebra Introduction to Differential Calculus
Finished Geogebra file - example 1
Finished Geogebra file - example 2
– Robin Nagy

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