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?

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

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?

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

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

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

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

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

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

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?

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

Can you complete this jigsaw of the multiplication square?

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

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.

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.

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?

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?

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?

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

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

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

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

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.

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

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

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?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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

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?

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?

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

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?

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

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

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 are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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

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

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?

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

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.

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

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

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?