Some children were playing a game. Make a graph or picture to show
how many ladybirds each child had.
A hundred square has been printed on both sides of a piece of
paper. What is on the back of 100? 58? 23? 19?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Charlie thinks that a six comes up less often than the other
numbers on the dice. Have a look at the results of the test his
class did to see if he was right.
Use the two sets of data to find out how many children there are in
Classes 5, 6 and 7.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Here are four tiles. They can be arranged in a 2 by 2 square so
that this large square has a green edge. If the tiles are moved
around, we can make a 2 by 2 square with a blue edge... Now try. . . .
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .
Sketch the graphs of y = sin x and y = tan x and some straight
lines. Prove some inequalities.
Draw the graph of a continuous increasing function in the first
quadrant and horizontal and vertical lines through two points. The
areas in your sketch lead to a useful formula for finding
Here the diagram says it all. Can you find the diagram?
Harry and Chiu both reasoned through their solutions clearly, and Chiu demonstrates the power of diagrams.
A number of contributions shed light on this problem.
Derek offered some interesting insights into this problem and explained it nicely too. Chen and Andrei took a slightly different approach.
Angus gives a very good account of how matrices, probability and graph theory are used in his solution.
Written for teachers, this article discusses mathematical
representations and takes, in the second part of the article,
examples of reception children's own representations.
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.