Number problems at primary level that require careful consideration.
What is the sum of all the three digit whole numbers?
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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?
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.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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!
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
Use the information to work out how many gifts there are in each pile.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
If the answer's 2010, what could the question be?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that may require resilience.
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?
An old game but lots of arithmetic!
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Can you find different ways of creating paths using these paving slabs?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
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?
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.