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

Ben and his mum are planting garlic. Use the interactivity to help 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.

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?

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

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!

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

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

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?

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

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?

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

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

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

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?

Can you complete this jigsaw of the multiplication square?

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

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?

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?

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

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

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

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.

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

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

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 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 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?

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?

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

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?

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

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

Use the interactivities to complete these Venn diagrams.

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.

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

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.

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?

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

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?

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.

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?

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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

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

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

A game that tests your understanding of remainders.