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?

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

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.

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

Can you complete this jigsaw of the multiplication square?

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?

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.

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

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?

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

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?

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

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.

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

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?

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

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

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

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.

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

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.

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

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

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.

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?

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?

An environment which simulates working with Cuisenaire rods.

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

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?

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

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?

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

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?

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?

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

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.

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

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

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