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 measure area with non-standard units and to explain how gaps and overlaps change the result. The museum offers a text that defines an area as a cubit by a cubit; the record has nothing on gaps and overlaps. Covering real surfaces with tiles, and the gaps and overlaps that appear, are the class's own work. 1
Curriculum expectations, with their official codes
- E2.8 use appropriate non-standard units to measure area, and explain the effect that gaps and overlaps have on accuracy
2 Before you start
A thought to carry into the lesson.
3 The lesson
What does a surface need before you can count its area?
Cover a sheet of paper with square tiles of the same size. Leave no gaps and no overlaps. Then leave a gap and count again. What changes?
Go deeper
Al-Khwarizmi gave measuring a chapter of his Book of al-Jabr and al-Muqabala. The chapter opens by saying that "one by one" means an area, that is, a cubit by a cubit 2. In the preface he lists the measurement of land among the needs he wrote the book for 3. So the record on mensuration shows what is measured (an area), in what unit (a cubit by a cubit), and a need it served (land).
Think about it
Al-Khwarizmi counts an area as a cubit by a cubit and lists the measurement of land among his book's needs. Why might someone who owns land want its area told as a number of squares of one size, and not as "about this big"?
Into the museum
- Mensuration: what is measured, and in what unit, in al-Khwarizmi's chapter.
- Al-Khwarizmi: the author of the book in which the chapter appears.
Try this
Read the record on mensuration. Cover a sheet of paper with square tiles and count them. Then try tiles with half the side and compare the counts.
4 Check yourself
Nothing here is marked or sent anywhere. It is for you.
In your own words: what does Mensuration (ilm al-misaha) have to do with this lesson?
Compare with the card
A cubit by a cubit. Mensuration is the science of measuring areas and volumes. Al-Khwarizmi gave it a chapter of his book, which opens by saying that "one by one" means an area, that is, a cubit by a cubit. A square of side two is four times the cubit-by-cubit area, and a square of side half a cubit is a quarter of it. What would you cover a surface with to count its area?
I can now