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.

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?

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

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?

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?

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

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?

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?

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?

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 find the chosen number from the grid using the clues?

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

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

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

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?

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

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?

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

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

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?

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

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

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?

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

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

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

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

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

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

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

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?

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?

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

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?

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

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?

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 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?

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?

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.

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

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