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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Number problems at primary level that require careful consideration.

How many trains can you make which are the same length as Matt's, using rods that are identical?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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

Can you replace the letters with numbers? Is there only one solution in each case?

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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.

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?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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?

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?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

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 challenging activity focusing on finding all possible ways of stacking rods.