Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What is the best way to shunt these carriages so that each train
can continue its journey?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Here are the six faces of a cube - in no particular order. Here are
three views of the cube. Can you deduce where the faces are in
relation to each other and record them on the net of this cube?
An extension of noughts and crosses in which the grid is enlarged
and the length of the winning line can to altered to 3, 4 or 5.
Can you fit the tangram pieces into the outline of the child walking home from school?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you fit the tangram pieces into the outlines of these clocks?
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
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 fit the tangram pieces into the outlines of these people?
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outline of Granma T?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Try this interactive strategy game for 2
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
I've made some cubes and some cubes with holes in. This challenge
invites you to explore the difference in the number of small cubes
I've used. Can you see any patterns?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you cut up a square in the way shown and make the pieces into a
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
Can you fit the tangram pieces into the outline of Mai Ling?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Which of these dice are right-handed and which are left-handed?
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
What is the greatest number of squares you can make by overlapping
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
Can you fit the tangram pieces into the outline of Little Ming?
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Can you fit the tangram pieces into the outline of the rocket?
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
Can you fit the tangram pieces into the outline of these convex shapes?