Can you each work out the number on your card? What do you notice? How could you sort the cards?
Number problems at primary level that require careful consideration.
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
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?
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?
Given the products of adjacent cells, can you complete this Sudoku?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Can you find different ways of creating paths using these paving slabs?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?
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?
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.
56 406 is the product of two consecutive numbers. What are these two numbers?
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!
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?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
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!
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
If the answer's 2010, what could the question be?
Can you work out what a ziffle is on the planet Zargon?
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?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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 numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
This task combines spatial awareness with addition and multiplication.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?