How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Use the clues to colour each square.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
How many trains can you make which are the same length as Matt's, using rods that are identical?
What happens when you try and fit the triomino pieces into these
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a 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
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
Can you cover the camel with these pieces?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many different rhythms can you make by putting two drums on the
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
How many triangles can you make on the 3 by 3 pegboard?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?