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?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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.
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?
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
Follow the directions for circling numbers in the matrix. Add all
the circled numbers together. Note your answer. Try again with a
different starting number. What do you notice?
How many models can you find which obey these rules?
This challenge extends the Plants investigation so now four or more children are involved.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
In how many ways can you stack these rods, following the rules?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
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 different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
An activity making various patterns with 2 x 1 rectangular tiles.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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 investigation that gives you the opportunity to make and justify
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!
Investigate the different ways you could split up these rooms so
that you have double the number.
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.
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
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?