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

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

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?

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?

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

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?

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

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

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.

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

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?

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?

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?

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 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?

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

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

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

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

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

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

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

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?

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?

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?

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

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?

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

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

Can you find different ways of creating paths using these paving slabs?

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

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.

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

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?

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

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

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

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?

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?

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