In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
Can you match these calculation methods to their visual representations?
Can you put these four calculations into order of difficulty? How did you decide?
In this article for primary teachers, Ems outlines how we can encourage learners to be flexible in their approach to calculation, and why this is crucial.
How many ways can you find to put in operation signs (+ - x ÷) to make 100?
More resources to support understanding multiplication and division through playing with numbers
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.
Resources to support understanding of multiplication and division through playing with number.
Related resources supporting pupils' understanding of multiplication and division through playing with numbers.
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 find different ways of creating paths using these paving slabs?
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.
Number problems at primary level that require careful consideration.
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?
Number problems at primary level that may require resilience.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Given the products of adjacent cells, can you complete this Sudoku?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This Sudoku requires you to do some working backwards before working forwards.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
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?
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?
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 largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Play this game and see if you can figure out the computer's chosen number.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house 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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Can you work out what a ziffle is on the planet Zargon?
A number game requiring a strategy.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Here is a chance to play a version of the classic Countdown Game.
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?
Choose a symbol to put into the number sentence.
Find the next number in this pattern: 3, 7, 19, 55 ...
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?