Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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,. . . .
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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 shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train
can continue its journey?
A game for two players on a large squared space.
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
Exchange the positions of the two sets of counters in the least possible number of moves
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
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Can you make a 3x3 cube with these shapes made from small cubes?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
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.
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!
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Can you fit the tangram pieces into the outline of the telescope and microscope?
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.
What is the greatest number of squares you can make by overlapping
Can you find ways of joining cubes together so that 28 faces are
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you fit the tangram pieces into the outline of this junk?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Try this interactive strategy game for 2
Can you cut up a square in the way shown and make the pieces into a
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Granma T?
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 this plaque design?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of Little Ming?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of these rabbits?