This task combines spatial awareness with addition and multiplication.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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?
This challenge combines addition, multiplication, perseverance and even proof.
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?
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?
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?
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
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?
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?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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.
Use the information to work out how many gifts there are in each pile.
What is happening at each box in these machines?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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!
Using the statements, can you work out how many of each type of rabbit there are in these pens?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
If the answer's 2010, what could the question be?
Here is a chance to play a version of the classic Countdown Game.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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 article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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.
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?
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.