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 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.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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!
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.
This challenge extends the Plants investigation so now four or more children are involved.
Sort the houses in my street into different groups. Can you do it in any other ways?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
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?
How many models can you find which obey these rules?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
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.
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.
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?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Have a go at this 3D extension to the Pebbles problem.
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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.
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?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
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