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.

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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?

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

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

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!

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.

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?

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?

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

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

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.

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.

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?

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?

Can you complete this jigsaw of the multiplication square?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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?

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

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?

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

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

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?

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

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

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.

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?

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

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

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

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

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

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

An environment which simulates working with Cuisenaire rods.

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.

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 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.

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

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

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