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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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!
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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 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.
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?
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
This Sudoku requires you to do some working backwards before working forwards.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
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?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
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?
Here is a chance to play a fractions version of the classic Countdown Game.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
A number game requiring a strategy.
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
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.
Number problems at primary level that require careful consideration.
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?
Here is a chance to play a version of the classic Countdown Game.
Can you put these four calculations into order of difficulty? How did you decide?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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.
Number problems at primary level that may require resilience.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
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.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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?
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!
This number has 903 digits. What is the sum of all 903 digits?
What is happening at each box in these machines?