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?
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 problem is designed to help children to learn, and to use, the two and three times tables.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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?
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?
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.
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
If the answer's 2010, what could the question be?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
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.
Number problems at primary level that require careful consideration.
What is happening at each box in these machines?
This number has 903 digits. What is the sum of all 903 digits?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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 this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Find the next number in this pattern: 3, 7, 19, 55 ...
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Use the information to work out how many gifts there are in each
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?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
This activity focuses on doubling multiples of five.
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?
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.
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?
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
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Find a great variety of ways of asking questions which make 8.
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.
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?
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?
Can you work out what a ziffle is on the planet Zargon?