This problem is designed to help children to learn, and to use, the two and three times tables.
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?
A game that tests your understanding of remainders.
Find a great variety of ways of asking questions which make 8.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
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 is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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 number has 903 digits. What is the sum of all 903 digits?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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 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?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
56 406 is the product of two consecutive numbers. What are these
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Resources to support understanding of multiplication and division through playing with number.
Can you work out what a ziffle is on the planet Zargon?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Can you work out some different ways to balance this equation?
This activity focuses on doubling multiples of five.
What is the sum of all the three digit whole numbers?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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?
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?
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?
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?