How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you find all the different triangles on these peg boards, and
find their angles?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
What happens when you try and fit the triomino pieces into these
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?
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
Can you cover the camel with these pieces?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
A game for 2 people. Take turns placing a counter on the star. You
win when you have completed a line of 3 in your colour.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Use the clues to colour each square.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many triangles can you make on the 3 by 3 pegboard?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many different rhythms can you make by putting two drums on the
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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.
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?
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.
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?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
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?
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
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?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
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
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
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?