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?

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.

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?

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

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?

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

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

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?

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

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

How many different sets of numbers with at least four members can you find in the numbers in this box?

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?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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?

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?

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.

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 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?

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

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Can you sort numbers into sets? Can you give each set a name?

Can you complete this jigsaw of the multiplication square?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

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?

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

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

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.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

An environment which simulates working with Cuisenaire rods.

Got It game for an adult and child. How can you play so that you know you will always win?

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.

A game in which players take it in turns to choose a number. Can you block your opponent?

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