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?
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?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
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.
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?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
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?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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 to have an ordered approach.
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
These practical challenges are all about making a 'tray' and covering it with paper.
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
This activity investigates how you might make squares and pentominoes from Polydron.
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
What happens when you round these three-digit numbers to the nearest 100?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.