In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
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?
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you replace the letters with numbers? Is there only one
solution in each case?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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.
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?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
56 406 is the product of two consecutive numbers. What are these
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Can you work out some different ways to balance this equation?
This activity focuses on doubling multiples of five.
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Find a great variety of ways of asking questions which make 8.
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?
What is the sum of all the three digit whole numbers?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Resources to support understanding of multiplication and division through playing with number.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you work out what a ziffle is on the planet Zargon?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
This number has 903 digits. What is the sum of all 903 digits?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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,. . . .
An old game but lots of arithmetic!