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?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
This article for teachers suggests ideas for activities built around 10 and 2010.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
56 406 is the product of two consecutive numbers. What are these
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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 each work out the number on your card? What do you notice?
How could you sort the cards?
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?
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?
What is the sum of all the three digit whole numbers?
Can you complete this jigsaw of the multiplication square?
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?
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?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
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?
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. . . .
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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 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?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
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.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
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?
What is happening at each box in these machines?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?