Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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'.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these
Can you work out what a ziffle is on the planet Zargon?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
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?
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.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
This problem is designed to help children to learn, and to use, the two and three times tables.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Resources to support understanding of multiplication and division through playing with number.
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Number problems at primary level that may require determination.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
What is the sum of all the three digit whole numbers?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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.
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 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
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?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
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!
If the answer's 2010, what could the question be?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Use the information to work out how many gifts there are in each
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
How would you count the number of fingers in these pictures?