This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
Number problems at primary level that may require resilience.
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Can you work out what a ziffle is on the planet Zargon?
This task combines spatial awareness with addition and multiplication.
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?
Use the information to work out how many gifts there are in each pile.
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.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
What is happening at each box in these machines?
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!
How will you work out which numbers have been used to create this multiplication square?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that require careful consideration.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
What is the sum of all the three digit whole numbers?
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?