Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
56 406 is the product of two consecutive numbers. What are these
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
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.
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.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you work out what a ziffle is on the planet Zargon?
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
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 is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Use the information to work out how many gifts there are in each
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
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?
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?
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
This problem is designed to help children to learn, and to use, the two and three times tables.
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 group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Find the next number in this pattern: 3, 7, 19, 55 ...
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
This task combines spatial awareness with addition and multiplication.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?