This activity focuses on doubling multiples of five.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
What is the sum of all the three digit whole numbers?
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?
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.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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 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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
What is happening at each box in these machines?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
This problem is designed to help children to learn, and to use, the two and three times tables.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This task combines spatial awareness with addition and multiplication.
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Can you work out what a ziffle is on the planet Zargon?
Resources to support understanding of multiplication and division through playing with number.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates