10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Explore the different snakes that can be made using 5 cubes.
How many models can you find which obey these rules?
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?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Use the clues to colour each square.
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
How many different shapes can you make by putting four right-
angled isosceles triangles together?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
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
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
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
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?
My coat has three buttons. How many ways can you find to do up all
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
This challenge is about finding the difference between numbers which have the same tens digit.
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?
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?
Can you cover the camel with these pieces?