Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Help share out the biscuits the children have made.
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?
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.
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?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Can you find any perfect numbers? Read this article to find out more...
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Can you place the numbers from 1 to 10 in the grid?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Can you work out what a ziffle is on the planet Zargon?
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?
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
This activity focuses on doubling multiples of five.
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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 can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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 the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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?
Follow the clues to find the mystery number.
Got It game for an adult and child. How can you play so that you know you will always win?
Can you work out some different ways to balance this equation?
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.
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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?
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?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
An investigation that gives you the opportunity to make and justify predictions.
"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 ...?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Number problems at primary level to work on with others.
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Ben’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?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Can you find the chosen number from the grid using the clues?
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?