Module 7 Transformations
Module Content Lesson Resources Lesson Plans Exam Questions Probing Questions

Transformations - Teacher Notes

Solvemymaths has produced pages like this for lots of topics

NRICH Tasks

NRICH: Reflecting Squarely
NRICH: ...on the Wall
NRICH: Orbiting Billiard Balls
NRICH: Transformation Game
NRICH: Transformation of Lines
NRICH: Hex
NRICH: Semi-regular tessellations
NRICH: Who is the Fairest of All?
NRICH: Zig Zag
NRICH: Square It
NRICH: Spotting the Loophole
NRICH: Square Coordinates
NRICH: Squirty
NRICH: Parabolic Patterns
NRICH: More Parabolic Patterns
NRICH: Families of Graphs
Extras

RoboCompass
YouTube: BBoys Symmetry Dancing
YouTube: Synchronised Swimming
YouTube: Maths in Nature
Creating Shapes order 4

Build a Pattern
Snowflake Maker
Similarity Proof by Transformations
Interactive Website
Range of Online Questions
Match Move Quad Graph Activity
Match Trig Graphs Activity

 

Symmetry - NRICH Task

Charlie created a symmetrical pattern by shading in four squares on a 3 by 3 square grid:

Alison created a symmetrical pattern by shading in two triangles on a 3 by 3 isometric grid:

Choose whether you would like to work on square grids or isometric grids.

 

Tessellations

This superb blog by Jo Morgan @mathsjem is her planning and thought process on teaching Tesellations - Click here

Paper Cut Method - Click here

This tessellation lesson is easy and foolproof

Alternative Method

Using a Square, Rectangle or Hexagon you can use the Cut and Add method

 

More Complex Tessellations - Click here

Toblerone Tessellations

Break off the corners and you get a hexagon.

Break off one corner and you get a trapezium.

Two triangles together makes a parallelogram … or it a rhombus? - Click here

 

 

Rotational Symmetry

Interactive: Rotational Symmetry Designs

Students complete the designs so that they have rotational symmetry of order 4. When they think they have finished, they can watch their design rotate to see if they are correct

 

Worksheet: Rotational Symmetry Designs

A paper based version of the interactivity above, where students must complete the designs to give them rotational symmetry of order 4.

 

Link: Interactive Rotational Symmetry Tool

An interactive tool that demonstrates the order of rotational symmetry of different shapes. From www.flashymaths.co.uk

 

Brilliant short video showing the development of a complex shape with line and rotational symmetry - Click here

Transformations With Pacman [@robertkaplinsky]

For detailed Explanation - Click here

 
Enlargements Using Vectors

Follow these Steps

Enlargements

Learners are asked to enlarge a given triangle with a scale factor of enlargement of 3 about a centre of enlargement of their choice. Having done this a few times, they may discover that sometimes the enlarged triangle goes off the edge of the paper. So a natural question for learners to ask, or one that can be posed to them, is ‘Where can the centre of enlargement be so that the image lies completely on the grid?’ Learners may conjecture that the locus of centres of enlargement such that the image just lies on the grid will be a triangle mathematically similar to the given one, or perhaps a circle, oval or (rounded) rectangle. Much practice of drawing enlargements ensues as learners seek to establish the permissible area in which the centre of enlargement may lie. At the same time, their attention is being drawn to the edges of the paper, and perhaps to working backwards from where they want the image to lie in order to construct a possible position for the centre of enlargement. Such analysis may help them to appreciate more deeply the details of how the enlargement method works.

There is scope for confident learners to extend the problem by trying a different starting shape, or placing it in a different position on the grid, and exploring the effect that this has on the boundary of possible positions for the centre of enlargement.

 

3D Enlargements

 

Interactive Environment: Transformations

Can you use this tool to make a symmetrical design? Can you find three different transformations that end up with the same image? What are your questions? Created by James Pearce.

 

Symmetry and Tessellation
[Thanks to Jo @mathsjam  http://www.resourceaholic.com/]

Stained glass tessellations - Teachit Maths

Rotational designs (& interactive activity) - MathsPad

Rotational symmetry demonstration - Flash Maths

Making symmetrical shapes - Teachit Maths

Add one square - Median Don Steward 

 

Transformation Game - http://www.flashymaths.co.uk/swf/transformations.swf

Transformation Golf - DESMOS - Click here

 

Mix of Transformations

State a pair of flags which have been translated, rotated ...
Describe a single Transformation which moves A to B.
Describe a pair of transformations which moves A to B.
Can you find more than one way?

 

Transformers

Draw the body parts and then Transform them to create a new shape. 

Body part

Transformation

(4,15), (8,15), (7,13), (5,13)

Rotate 90o anticlockwise about (11,16)

(4,13), (8,13), (8,9), (4,9)

Reflect in line x = 11

(2,13), (4,13), (4,11)

Rotate 180o about (11,12)

(8,13), 10,13),  (8,11)

  Translate vector

(4,9), (6,9), (4,6), (2,6)

Reflect in line y = 5, then translate vector

(6,9), (8,9), (10,6), (8,6)

Reflect in line x = 12

Pupil's can create their own problems by: Starting with a shape, split it into say 8 parts and transform each part so the shape is broken up.  Then present either a drawing, or co-ordinates of the broken parts and the reverse transformation for others to complete

 

 

Vectors
[Thanks to Jo @mathsjam  http://www.resourceaholic.com/]

Dancing vectors lesson - teachingmathematics.net

Vectors problem - The Chalk Face

Vectors worksheet - m4ths.com

Drawing Vectors 1 and Drawing Vectors 2 - teachingmaths.net

Vectors enrichment task - m4ths.com

Vectors assessment and exam questions - teachingmaths.net

A-Mazing Vectors competition - jensilvermath.com

 

Proving the Midpoints of any Quadrilateral makes a Parallelogram:

A Simple Proof of an interesting fact – Click here

Leap Frog Puzzle: Click here