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

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

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

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.

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.

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

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.

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

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

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?

Can you complete this jigsaw of the multiplication square?

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

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

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!

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?

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?

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?

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?

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?

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?

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?

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 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?

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?

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’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

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?

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.

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?

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?

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

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

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?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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?

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

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

Use the interactivities to complete these Venn diagrams.

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

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

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