Design an arrangement of display boards in the school hall which fits the requirements of different people.
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
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?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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 it up?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
In this matching game, you have to decide how long different events take.
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?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
This article for primary teachers suggests ways in which to help children become better at working systematically.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
These practical challenges are all about making a 'tray' and covering it with paper.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
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.
What could the half time scores have been in these Olympic hockey matches?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?