Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
This challenge extends the Plants investigation so now four or more children are involved.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
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
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
An investigation that gives you the opportunity to make and justify
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
What happens when you round these numbers to the nearest whole number?
Can you work out some different ways to balance this equation?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
What happens when you round these three-digit numbers to the nearest 100?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you draw a square in which the perimeter is numerically equal
to the area?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
The pages of my calendar have got mixed up. Can you sort them out?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
These practical challenges are all about making a 'tray' and covering it with paper.
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
In this matching game, you have to decide how long different events take.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
How many triangles can you make on the 3 by 3 pegboard?