Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
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?
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these
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?
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.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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. . . .
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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.
This problem is designed to help children to learn, and to use, the two and three times tables.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
A game that tests your understanding of remainders.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Here is a picnic that Chris and Michael are going to share equally.
Can you tell us what each of them will have?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you replace the letters with numbers? Is there only one
solution in each case?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Can you complete this jigsaw of the multiplication square?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?
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
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What is happening at each box in these machines?
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!
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 describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?