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

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

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

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.

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

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

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

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

Use the interactivities to complete these Venn diagrams.

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

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?

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

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.

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 complete this jigsaw of the multiplication square?

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?

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

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

A game that tests your understanding of remainders.

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!

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?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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?

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.

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

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

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 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?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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?

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?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

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?

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?

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

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?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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

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

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

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