Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
We can cut a small triangle off the corner of a square and then fit
the two pieces together. Can you work out how these shapes are made
from the two pieces?
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Explore the effect of reflecting in two parallel mirror lines.
Explore the effect of reflecting in two intersecting mirror lines.
Explore the effect of combining enlargements.
The first part of an investigation into how to represent numbers
using geometric transformations that ultimately leads us to
discover numbers not on the number line.
Introduces the idea of a twizzle to represent number and asks how
one can use this representation to add and subtract geometrically.
How can you use twizzles to multiply and divide?
Track the roots of quadratic equations as you move the corresponding graphs and discover the transitions from real to complex roots.
Make a conjecture about the curved track taken by the complex roots of a quadratic equation and use complex conjugates to prove your conjecture.
Sam and Rajul each had good strategies to help them solve this
Working systematically and introducing some algebra led to some excellent solutions to this problem.
Andrei sent in a brilliant table, organising the data so that a
hard problem reduced to a sequence of manageable steps.
See eight different methods of solving this problem and a
generalisation from 3 by 1 to n by 1.
This article describes the scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over.
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on the
intersections between two diagonally adjacent squares.
Why not challenge a friend to play this transformation game?
This article introduces complex numbers, brings together into one
bigger 'picture' some closely related elementary ideas like vectors
and the exponential and trigonometric functions and their
derivatives and proves that e^(i pi)= -1.