Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Can you find out in which order the children are standing in this
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 lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
My coat has three buttons. How many ways can you find to do up all
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
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.
This challenge extends the Plants investigation so now four or more children are involved.
Can you replace the letters with numbers? Is there only one
solution in each case?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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?
Can you find the chosen number from the grid using the clues?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
An investigation that gives you the opportunity to make and justify
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Find out what a "fault-free" rectangle is and try to make some of
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.