Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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 designed to help children to learn, and to use, the two and three times tables.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you replace the letters with numbers? Is there only one
solution in each case?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you work out some different ways to balance this equation?
56 406 is the product of two consecutive numbers. What are these
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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.
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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 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 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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
How would you count the number of fingers in these pictures?
Here is a chance to play a version of the classic Countdown Game.
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 complete this jigsaw of the multiplication square?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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,. . . .
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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 arrange 5 different digits (from 0 - 9) in the cross in the
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
A game that tests your understanding of remainders.
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?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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!
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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.
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?