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

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?

Can you find the chosen number from the grid using the clues?

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

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

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

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

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.

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

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

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

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

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

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?

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 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.

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

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

Can you complete this jigsaw of the multiplication square?

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?

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

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?

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.

Number problems at primary level to work on with others.

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?

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

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

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

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

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 interactivities to complete these Venn diagrams.

Number problems at primary level that may require determination.

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

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

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

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

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?

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?