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?
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
How many different shapes can you make by putting four right-
angled isosceles triangles together?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
My coat has three buttons. How many ways can you find to do up all
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
Explore the different snakes that can be made using 5 cubes.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
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
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?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
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?
Can you find the chosen number from the grid using the clues?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
Can you find out in which order the children are standing in this
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This challenge is about finding the difference between numbers which have the same tens digit.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
This dice train has been made using specific rules. How many different trains can you make?
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?
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?