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.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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.
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?
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 triangle.
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?
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 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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Investigate the different ways you could split up these rooms so that you have double the number.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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.
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.
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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?
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 is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In how many ways can you stack these rods, following the rules?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
A challenging activity focusing on finding all possible ways of stacking rods.
How many models can you find which obey these rules?
Have a go at this 3D extension to the Pebbles problem.
An investigation that gives you the opportunity to make and justify predictions.
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?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
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?
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?
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?
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?
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 make?
Ben has five coins in his pocket. How much money might he have?