Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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.
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?
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
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
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?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
If you had 36 cubes, what different cuboids could you make?
How many models can you find which obey these rules?
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.
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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.
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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.
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!
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Can you draw a square in which the perimeter is numerically equal
to the area?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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!
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?