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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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.
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you complete this jigsaw of the multiplication square?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
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 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.
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 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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
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,. . . .
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Resources to support understanding of multiplication and division through playing with number.
Can you work out what a ziffle is on the planet Zargon?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
This challenge combines addition, multiplication, perseverance and even proof.