Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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
Can you find out in which order the children are standing in this
Explore the different snakes that can be made using 5 cubes.
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?
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
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
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?
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 are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
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
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?
My coat has three buttons. How many ways can you find to do up all
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
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?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
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!
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.
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
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.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.