Numbers written in places

This lesson asks you to read and show numbers up to 1000 by the value of each place, and to add and subtract them in writing, explaining the steps. The museum offers one method of writing numbers in places and reckoning with them in ordered steps; counting with base ten materials and solving problems is the class's own work. ¹

Take 305 and 350. Which digits are the same? What changes, and why? Say how you know.

Add two numbers in writing and tell a partner what you did first, next and last. Could someone else follow your steps?

Look at a very old page. Al-Khwarizmi's Arabic book of arithmetic is lost, but a Latin translation of the twelfth century survives in the Cambridge library ². The picture in the record on algorism is the opening page of that copy, and it begins "DIXIT algorizmi" ³. The words mean "al-Khwarizmi said" ². People in the West learned arithmetic from this book, and his Latin name, Algorismus, became a name for the numerals themselves ⁴.

The first book is lost, and only a copy in another language is left. Why should we be careful when we say what the first book was like?

• Algorism: the numerals, the lost book and its Latin translation.
• al-Khwarizmi's Book of Arithmetic: what the Cairo editors say about its effect in the West.
• al-Khwarizmi: what is known of his life, and what is not.

Read the record on algorism. Choose a number below 1000, write what each digit stands for, then add 128 to it in writing, step by step, and explain each step to a partner.