Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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.
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
An investigation that gives you the opportunity to make and justify
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
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?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
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.
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Can you draw a square in which the perimeter is numerically equal
to the area?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
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!
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you make square numbers by adding two prime numbers together?