How many models can you find which obey these rules?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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 ...?

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.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

An investigation that gives you the opportunity to make and justify predictions.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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.

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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?

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.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

What happens when you round these three-digit numbers to the nearest 100?

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 practical challenges are all about making a 'tray' and covering it with paper.

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Can you find all the ways to get 15 at the top of this triangle of numbers?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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?

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.

What happens when you round these numbers to the nearest whole number?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

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?