In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What is happening at each box in these machines?
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Use the information to work out how many gifts there are in each pile.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
How would you count the number of fingers in these pictures?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
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?
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require resilience.
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
What is the sum of all the three digit whole numbers?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
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?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?