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.

What is the best way to shunt these carriages so that each train can continue its journey?

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 work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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?

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

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?

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?

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

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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?

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Given the products of diagonally opposite cells - can you complete this Sudoku?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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 if you have an ordered approach.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

This article for primary teachers suggests ways in which to help children become better at working systematically.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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

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?

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.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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?

How many possible necklaces can you find? And how do you know you've found them all?

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Two sudokus in one. Challenge yourself to make the necessary connections.

How many different triangles can you make on a circular pegboard that has nine pegs?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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?

Investigate the different ways you could split up these rooms so that you have double the number.