Draft: this lesson was written with AI help and has not yet been read by a human editor.
1 What your class asks
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
Curriculum expectations, with their official codes
- B1.1 read, represent, compose, and decompose whole numbers up to and including 1000, using a variety of tools and strategies, and describe various ways they are used in everyday life
- B1.5 use place value when describing and representing multi-digit numbers in a variety of ways, including with base ten materials
- B2.4 demonstrate an understanding of algorithms for adding and subtracting whole numbers by making connections to and describing the way other tools and strategies are used to add and subtract
- B2.5 represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 1000, using various tools and algorithms
2 Before you start
A thought to carry into the lesson.
3 The lesson
What does the place of a digit tell you?
Take 305 and 350. Which digits are the same? What changes, and why? Say how you know.
Why write the steps in order?
Add two numbers in writing and tell a partner what you did first, next and last. Could someone else follow your steps?
Go deeper
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.
Think about it
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?
Into the museum
- 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.
Try this
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.
4 Check yourself
Nothing here is marked or sent anywhere. It is for you.
In your own words: what does Algorism (reckoning with Indian decimal numerals in al-Khwarizmi's book of arithmetic) have to do with this lesson?
Compare with the card
Reckoning with nine numerals and zero. Algorism is a way of writing and working numbers with nine numerals and a zero, in which each place takes its value from its position: units, then tens, then hundreds, then thousands. Al-Khwarizmi wrote a book on it in Baghdad, and a Latin translation survives that opens "Dixit Algorizmi", "al-Khwarizmi said". Numbers are added, subtracted, multiplied and divided in writing by ordered steps. How does the place of a digit change its value?
I can now
Notes
- 1. Ontario Ministry of Education, The Ontario Curriculum: Mathematics
- 2. HÂRİZMÎ, Muhammed b. Mûsâ — TDV İslâm Ansiklopedisi (İhsan Fazlıoğlu), pp. 224–227
- 3. Wikimedia Commons (file pages, CC BY-SA and CC BY licences)
- 4. al-Khwarizmi, Kitab al-Jabr wal-Muqabala, ed. Mosharafa and Ahmad (Cairo, 1939), p. 25