These activities lend themselves to systematic working in the sense that it helps to 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 ...?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
An investigation that gives you the opportunity to make and justify predictions.
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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?
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found 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.
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?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
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?
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.
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
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....?
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!
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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.
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you find all the different ways of lining up these Cuisenaire rods?