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?
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.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Can you find any perfect numbers? Read this article to find out more...
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?
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?
Number problems at primary level that may require determination.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
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?
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you explain the strategy for winning this game with any target?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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?
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?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
Follow the clues to find the mystery number.
Number problems at primary level to work on with others.
An investigation that gives you the opportunity to make and justify predictions.
Can you make square numbers by adding two prime numbers together?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you work out what a ziffle is on the planet Zargon?
If you have only four weights, where could you place them in order to balance this equaliser?
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?