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?
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
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?
Use the information to work out how many gifts there are in each pile.
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?
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?
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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?
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.
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!
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
What is happening at each box in these machines?
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?
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!
Number problems at primary level that require careful consideration.
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?
How would you count the number of fingers in these pictures?
This article for teachers suggests ideas for activities built around 10 and 2010.
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.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Number problems at primary level that may require resilience.
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you find different ways of creating paths using these paving slabs?
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
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.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?