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?
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?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
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?
Can you find the chosen number from the grid using the clues?
Explore the different snakes that can be made using 5 cubes.
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
How many different shapes can you make by putting four right-
angled isosceles triangles together?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
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?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
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.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
My coat has three buttons. How many ways can you find to do up all
Try this matching game which will help you recognise different ways of saying the same time interval.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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?
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....?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
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?
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?
In this matching game, you have to decide how long different events take.
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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 try and fit the triomino pieces into these
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'?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Can you cover the camel with these pieces?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.