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 use symbols as variables in expressions and equations, and to solve equations with whole numbers up to 50 and check the solutions. The museum offers the history of one early book on solving for an unknown; the equations and the checking are your class's. 1
Curriculum expectations, with their official codes
- C2.1 identify and use symbols as variables in expressions and equations
- C2.2 solve equations that involve whole numbers up to 50 in various contexts, and verify solutions
2 The lesson
What does the symbol stand for, and how do you know your answer is right?
Write a problem as an equation with a symbol for the unknown. Solve it, then put your answer back into the equation to see whether both sides are equal.
Go deeper
A copy of al-Khwarizmi's book on algebra survives in the Bodleian Library at Oxford, written in Cairo 2. The museum's record shows two pages of such a manuscript, with the proofs drawn as squares in red ink 3. Al-Khwarizmi wrote the book for what people need, in inheritance, bequests, trade and land measurement 4.
Think about it
Al-Khwarizmi drew his proofs as squares in red ink, as well as writing his rules in words. When you check an answer, which helps you more, the words of the rule or a drawing, and why?
Into the museum
- Algebra: the book, who wrote it, and what it was for.
- The Book of al-Jabr and al-Muqabala: how the book is arranged, chapter by chapter.
- al-Khwarizmi: the scholar who wrote it.
Try this
Read the record Algebra. Make up a story problem with an unknown number up to 50, write it as an equation, solve it and check it.
3 Carry it further
Where this lesson leads in the museum.
4 Check yourself
Nothing here is marked or sent anywhere. It is for you.
In your own words: what does Algebra (al-jabr wal-muqabala as a discipline in al-Khwarizmi's work) have to do with this lesson?
Compare with the card
A book for people's needs. The record says algebra, al-jabr wal-muqabala, is the art of finding an unknown number from known ones through an equation. Al-Khwarizmi set it out in Baghdad, in a concise book, for people's needs in inheritance, bequests, trade and land measurement. TDV adds that his algebra was wholly in words, with no symbols. What symbol could stand for the unknown number in a problem of your own?
In your own words: what does Algebra (al-jabr wal-muqabala as a discipline in al-Khwarizmi's work) have to do with this lesson?
Compare with the card
Restoring and balancing. Two operations give algebra its name, the record explains. Al-jabr, "restoring", removes a subtracted quantity from one side by adding it to both; al-muqabala, "balancing", cancels like terms that appear on both sides. How does doing the same thing to both sides keep an equation true, and how can you check your answer?
I can now
Notes
- 1. Ontario Ministry of Education, The Ontario Curriculum: Mathematics
- 2. al-Khwarizmi, Kitab al-Jabr wal-Muqabala, ed. Mosharafa and Ahmad (Cairo, 1939), p. 26
- 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), pp. 29–30