Transformations - Teacher Notes
Solvemymaths has produced pages like this for lots of topics
NRICH: ...on the Wall
NRICH: Orbiting Billiard Balls
NRICH: Transformation Game
NRICH: Transformation of Lines
NRICH: Semi-regular tessellations
NRICH: Who is the Fairest of All?
NRICH: Zig Zag
NRICH: Spotting the Loophole
NRICH: Square Coordinates
NRICH: Parabolic Patterns
NRICH: More Parabolic Patterns
NRICH: Families of Graphs
Build a Pattern
Similarity Proof by Transformations
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:
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
Using a Square, Rectangle or Hexagon you can use the Cut and Add method
More Complex 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
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
A paper based version of the interactivity above, where students must complete the designs to give them rotational symmetry of order 4.
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 -
Transformations With Pacman [@
For detailed Explanation - Click here
Enlargements Using Vectors
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.
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
Stained glass tessellations - Teachit Maths
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
Draw the body parts and then Transform them to create a new shape.
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
Transformation of Graphs
Dancing vectors lesson - teachingmathematics.net
Vectors problem - The Chalk Face
Vectors worksheet - m4ths.com
Vectors enrichment task - m4ths.com
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