This problem is designed to help children to learn, and to use, the two and three times tables.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Can you replace the letters with numbers? Is there only one
solution in each case?
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In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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.
A game that tests your understanding of remainders.
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?
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 Chris and Michael are going to share equally.
Can you tell us what each of them will have?
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?
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?
Resources to support understanding of multiplication and division through playing with number.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Here is a chance to play a version of the classic Countdown Game.
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?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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!
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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,. . . .
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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Imagine a pyramid which is built in square layers of small cubes.
If we number the cubes from the top, starting with 1, can you
picture which cubes are directly below this first cube?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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?
What is the sum of all the three digit whole numbers?