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.
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?
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?
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
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
An activity making various patterns with 2 x 1 rectangular tiles.
Use the clues to colour each square.
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?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many models can you find which obey these rules?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
What happens when you try and fit the triomino pieces into these
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
These practical challenges are all about making a 'tray' and covering it with paper.
Can you cover the camel with these pieces?
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?
How many different rhythms can you make by putting two drums on the
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
My coat has three buttons. How many ways can you find to do up all
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.