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.

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

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

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

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 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?

Can you complete this jigsaw of the multiplication square?

If you have only four weights, where could you place them in order to balance this equaliser?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

"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 ...?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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?

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

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?

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

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

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?

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

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

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

An environment which simulates working with Cuisenaire rods.

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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?

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?

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?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

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

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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?

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.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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?

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

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.