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?
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?
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
Sort the houses in my street into different groups. Can you do it in any other ways?
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.
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?
"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 ...?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
A challenging activity focusing on finding all possible ways of stacking rods.
Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenge extends the Plants investigation so now four or more children are involved.
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?
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.
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
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?
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?
An investigation that gives you the opportunity to make and justify predictions.
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?
This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?
If the answer's 2010, what could the question be?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
I cut this square into two different shapes. What can you say about the relationship between them?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Can you find ways of joining cubes together so that 28 faces are visible?
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?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.
What is the largest cuboid you can wrap in an A3 sheet of paper?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Investigate what happens when you add house numbers along a street in different ways.
In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?
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?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.