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?

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

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

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?

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?

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?

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 find the chosen number from the grid using the clues?

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?

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

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.

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 complete this jigsaw of the multiplication square?

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.

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.

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

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?

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

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?

Use the interactivities to complete these Venn diagrams.

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

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

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?

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

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?

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

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

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?

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

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

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?

Number problems at primary level that may require determination.

Number problems at primary level to work on with others.

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

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

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

An environment which simulates working with Cuisenaire rods.

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

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

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.

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