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?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
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.
This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Got It game for an adult and child. How can you play so that you know you will always win?
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
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?
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
If you have only four weights, where could you place them in order to balance this equaliser?
Number problems at primary level to work on with others.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Are these statements always true, sometimes true or never true?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Number problems at primary level that may require resilience.
Who said that adding couldn't be fun?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
How can we help students make sense of addition and subtraction of negative numbers?
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?
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
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?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
What is the sum of all the digits in all the integers from one to one million?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This is an adding game for two players.
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?