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?
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.
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.
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?
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 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 we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
This article for primary teachers suggests ways in which to help children become better at working systematically.
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
How many triangles can you make on the 3 by 3 pegboard?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Can you use this information to work out Charlie's house number?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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.
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
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?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
What is the best way to shunt these carriages so that each train can continue its journey?
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?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
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 models can you find which obey these rules?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
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?
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?