What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
What statements can you make about the car that passes the school
gates at 11am on Monday? How will you come up with statements and
test your ideas?
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?
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?
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This challenge extends the Plants investigation so now four or more children are involved.
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?
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.
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
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?
An investigation that gives you the opportunity to make and justify
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
What is the largest cuboid you can wrap in an A3 sheet of paper?
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Explore ways of colouring this set of triangles. Can you make
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?
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?
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?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
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 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?
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?
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!
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Here is your chance to investigate the number 28 using shapes,
cubes ... in fact anything at all.
Why does the tower look a different size in each of these pictures?
This problem is intended to get children to look really hard at something they will see many times in the next few months.
How many models can you find which obey these rules?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
These pictures were made by starting with a square, finding the
half-way point on each side and joining those points up. You could
investigate your own starting shape.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
How many tiles do we need to tile these patios?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
A challenging activity focusing on finding all possible ways of stacking rods.
In how many ways can you stack these rods, following the rules?
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.