What two-digit numbers can you make with these two dice? What can't you make?

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

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 numbers to the nearest whole number?

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

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?

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?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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?

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

Can you find the chosen number from the grid using the clues?

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?

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there 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 ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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?

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.

Can you find out in which order the children are standing in this line?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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

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?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

My coat has three buttons. How many ways can you find to do up all the buttons?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

Have a go at balancing this equation. Can you find different ways of doing it?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

This challenge is about finding the difference between numbers which have the same tens digit.

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Can you work out some different ways to balance this equation?