Number problems at primary level that may require determination.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Number problems at primary level that require careful consideration.
On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?
This number has 903 digits. What is the sum of all 903 digits?
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?
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?
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 score 100 by throwing rings on this board? Is there more than way to do it?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
If the answer's 2010, what could the question be?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use the information to work out how many gifts there are in each pile.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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 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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
What is happening at each box in these machines?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
What is the sum of all the three digit whole 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?
This problem is designed to help children to learn, and to use, the two and three times tables.
Resources to support understanding of multiplication and division through playing with number.
Can you work out what a ziffle is on the planet Zargon?
This activity focuses on doubling multiples of five.
This task combines spatial awareness with addition and multiplication.
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
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?
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?