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?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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?

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?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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

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

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.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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?

This package will help introduce children to, and encourage a deep exploration of, multiples.

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?

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 find the chosen number from the grid using the clues?

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

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 order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

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?

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

A game that tests your understanding of remainders.

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

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?

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

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?

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

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

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

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

56 406 is the product of two consecutive numbers. What are these two numbers?

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

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?

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?

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.

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

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

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?

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

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

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?

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?

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