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, compare and order decimal tenths, and to show how tenths and fractions match. The museum offers one record on early work with decimal fractions; your class brings the number lines, models and practice. 1
Curriculum expectations, with their official codes
- B1.7 read, represent, compare, and order decimal tenths, in various contexts
- B1.9 describe relationships and show equivalences among fractions and decimal tenths, in various contexts
2 The lesson
How can one number be written in two ways?
Look for a fraction and a decimal tenth that name the same amount. Explain how you know they are equal.
Go deeper
Picture a strip of paper cut into ten equal pieces: five of them make a half. Cut it into a hundred pieces and twenty-five make a quarter. Today we write 0.5 and 0.25, but our signs are modern, not a manuscript imitation 2. Al-Uqlidisi wrote a book at Damascus with an early, direct treatment of such fractions 3 2. The idea that matters is that a digit's position tells us which part we count, and a mark for the units place protects that reading 2.
Think about it
On a strip cut into ten pieces, a half is five tenths. Why can the same strip not show a quarter as a whole number of tenths, and what would you do to show it?
Into the museum
- al-Uqlidisi's decimal-fraction methods: how halving and a mark for the units place work.
- al-Uqlidisi: what is known of the author, and what is not.
- Algorism: the Indian place-value arithmetic his book builds on.
Try this
Read the record Al-Uqlidisi's decimal-fraction methods. Write a half and half of a half as tenths and hundredths.
3 Check yourself
Nothing here is marked or sent anywhere. It is for you.
In your own words: what does Al-Uqlidisi's decimal-fraction methods have to do with this lesson?
Compare with the card
A half as five tenths. A half can be written as five tenths, and half of that as twenty-five hundredths. The record says a book composed at Damascus by al-Uqlidisi has an early direct treatment of such fractions within Indian place-value arithmetic. It adds that this is not the invention of the Indian numerals or of today's decimal point, and that historians disagree about how complete the idea was. How would you write five tenths as a decimal?
I can now
Notes
- 1. Ontario Ministry of Education, The Ontario Curriculum: Mathematics
- 2. Al-Uqlidisi — A. S. Saidan's DSB biography, decimal-fraction discussion
- 3. Öklîdisî — TDV encyclopaedia, pp. 25–26