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.
An investigation that gives you the opportunity to make and justify
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.
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 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?
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
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?
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?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
An activity making various patterns with 2 x 1 rectangular tiles.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
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?
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 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!
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 draw a square in which the perimeter is numerically equal
to the area?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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 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?