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.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
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?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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?
Explore the different snakes that can be made using 5 cubes.
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
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.
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?
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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?
Find all the numbers that can be made by adding the dots on two dice.
My coat has three buttons. How many ways can you find to do up all
How many models can you find which obey these rules?
This challenge is about finding the difference between numbers which have the same tens digit.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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?
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?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
What happens when you try and fit the triomino pieces into these
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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.
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?
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 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Can you cover the camel with these pieces?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.