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

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?

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?

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

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

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?

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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

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?

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?

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

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?

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

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

This article for teachers describes how number arrays can be a useful representation 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?

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

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

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?

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

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

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?

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

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.

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

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

Number problems at primary level that may require resilience.

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

Can you sort numbers into sets? Can you give each set a name?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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

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?

How many different rectangles can you make using this set of rods?

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

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.

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?

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?

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 different ways of creating paths using these paving slabs?

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?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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.