The four operations, step by step

This lesson asks you to represent and solve problems that add, subtract, multiply and divide whole numbers and decimal tenths, using tools and strategies that include algorithms and arrays. The museum offers the history of how such written steps reached the Islamic world and where the word "algorithm" comes from; the problems, the arrays and the practice are your class's. ¹

Read each problem and decide whether it joins, separates, joins equal groups or shares equally. Then write your steps in order so that someone else could follow them.

Ibn Khaldun counts four jobs in arithmetic. Joining one by one is adding, he says, and joining by multiples is multiplying; separating one by one is taking away, and separating into equal parts is dividing ². The record on algorism says that with the Indian numerals these four operations become steps repeated place by place ². From al-Khwarizmi's name comes the word "algorithm", for an ordered way of solving problems ³.

Ibn Khaldun describes multiplying as joining by multiples and dividing as separating into equal parts. Why might it help to see multiplying as a kind of joining and dividing as a kind of separating when you decide which operation a problem asks for?

• Algorism: the numerals, the steps and the word "algorithm".
• Ibn Khaldun: the author of the Muqaddima, where the passage on arithmetic comes from.
• al-Khwarizmi's Book of Arithmetic: the words that came from his name.

Read the record Algorism. Choose one addition and one division problem from your class, solve each in ordered written steps, and name the operation each step does.