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

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

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.

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?

Are these statements always true, sometimes true or never true?

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

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

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?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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?

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

Can you find any perfect numbers? Read this article to find out more...

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

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?

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

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 throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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

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?

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

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.

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?

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

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?

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.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

Can you work out some different ways to balance this equation?

Have a go at balancing this equation. Can you find different ways of doing it?

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?

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

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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

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

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

Number problems at primary level to work on with others.

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?

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

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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?

Number problems at primary level that may require determination.

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?