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

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.

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.

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.

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

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?

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?

Can you complete this jigsaw of the multiplication square?

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.

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

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

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

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?

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?

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?

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?

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

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?

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

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?

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

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 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?

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

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

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.

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?

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?

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?

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

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

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

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

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.

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

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

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

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

Use the interactivities to complete these Venn diagrams.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?