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?

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?

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?

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?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.

How many different rectangles can you make using this set of rods?

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Can you make square numbers by adding two prime numbers together?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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?

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 find the chosen number from the grid using the clues?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Can you complete this jigsaw of the multiplication square?

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

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

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

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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

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?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Number problems at primary level that may require resilience.

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

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

How will you work out which numbers have been used to create this multiplication square?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Number problems at primary level to work on with others.

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.