In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Choose a symbol to put into the number sentence.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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 is a chance to play a version of the classic Countdown Game.
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
An old game but lots of arithmetic!
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
Annie and Ben are playing a game with a calculator. What was
Annie's secret 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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you complete this jigsaw of the multiplication square?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
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?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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 describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Here is a picnic that Chris and Michael are going to share equally.
Can you tell us what each of them will have?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Unmultiply is a game of quick estimation. You need to find two
numbers that multiply together to something close to the given
target - fast! 10 levels with a high scores table.
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?