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?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Investigate the different ways you could split up these rooms so
that you have double the number.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
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?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
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!
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
How many models can you find which obey these rules?
In how many ways can you stack these rods, following the rules?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate what happens when you add house numbers along a street
in different ways.
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?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
How many triangles can you make on the 3 by 3 pegboard?
Sort the houses in my street into different groups. Can you do it in any other ways?
Ben has five coins in his pocket. How much money might he have?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
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?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?