Explore the different snakes that can be made using 5 cubes.
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
The brown frog and green frog want to swap places without getting
wet. They can hop onto a lily pad next to them, or hop over each
other. How could they do it?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
My coat has three buttons. How many ways can you find to do up all
How many different shapes can you make by putting four right-
angled isosceles triangles together?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Can you find out in which order the children are standing in this
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?
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.
This challenge is about finding the difference between numbers which have the same tens digit.
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 the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Can you find all the ways to get 15 at the top of this triangle of numbers?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
This task follows on from Build it Up and takes the ideas into three dimensions!
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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.
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?
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?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you find the chosen number from the grid using the clues?