During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
This article for teachers suggests ideas for activities built around 10 and 2010.
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 this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores 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?
Can you replace the letters with numbers? Is there only one
solution in each case?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
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!
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you complete this jigsaw of the multiplication square?
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 your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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?
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 challenge encourages you to explore dividing a three-digit number by a single-digit number.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
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,. . . .
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Choose a symbol to put into the number sentence.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
This problem is designed to help children to learn, and to use, the two and three times tables.
Here is a chance to play a version of the classic Countdown Game.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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?
Resources to support understanding of multiplication and division through playing with number.
A game that tests your understanding of remainders.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?