Where our way of writing fractions comes from

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What to assume they know

Brahmagupta's method: you can only add units of the same size: the method for adding and subtracting fractions, and Brahmagupta's name attached to it
A fraction as an equal share, and why one-ninth is less than one-fifth: a fractional unit, and the tri-pada remark on p.153
Equivalent fractions: many names, one number, and lowest terms: equivalent fractions and lowest terms, needed for the puzzle
Reading dates given as CE, and placing centuries in order

What they should be able to do

Give the Sanskrit words the chapter reports for a fraction, and what they mean
Describe how a fraction was written in the Bakshali manuscript, and what is missing from it compared with today's form
Place the named mathematicians and the arrival of the dividing line in chronological order
Explain what a system restricted to fractional units can and cannot express directly
Write a given fraction as a sum of different fractional units
Say what Brahmagupta contributed beyond the method itself
Argue that no two different fractional units can total one whole
Find the only set of three different fractional units totalling one whole, and explain why it is the only one

Where it usually goes wrong

"The history is a decorative aside." It is the chapter's argument about why the notation is shaped the way it is. Section 7 has to make the connection explicit or the whole topic collapses into a list of names.
"Fractions were invented in India." The chapter does not say that — it says fractions were also used in Egypt and Babylon, and that the general form with an unrestricted top number, and its rules of arithmetic, came from India. The distinction is the interesting part and must not be flattened.
"An Egyptian fraction is a different kind of number." It is the same number, written as a sum. Show nineteen twenty-fourths marked once on a number line and then written three ways.
"Any amount can be written as a sum of different fractional units, so it is a trick with no content." The three-piece puzzle has exactly one answer, and the four-piece one has six. Constraint, not freedom, is what makes it a puzzle.
"The dividing line has always been there." It arrived centuries after the stacked form did, and from somewhere else. That is the single most surprising fact in the section and should be staged as such.
"Older notation means worse mathematicians." The chapter's own list runs from 300 CE to 850 CE with the notation barely changing, and general rules stated in the middle of it. Notation improved; the mathematics was already there.

Questions to check understanding

Name the Sanskrit words the chapter gives for a fraction and what they mean
Place the named mathematicians and the arrival of the dividing line in order
Say what the Bakshali form has in common with today's form and what it lacks
Write a given fraction as a sum of different fractional units
Explain, in your own words, why no two different fractional units total one whole
Find three different fractional units totalling one whole
Say who is credited with first setting down the general rules, and when
Competency-based questions in this chapter's history section are rare in written papers, but the puzzle is a standard source of higher-order items; the solutions appendix bound with this chapter does not carry a §7.9 section

Examples worth working on the board

The three Sanskrit words (§7.9, p.182). The chapter reports one word meaning broken and two meaning part or piece.
The Bakshali notation (§7.9, p.182). Checked against the printed page. The book prints one half twice in the same sentence — once in today's form and once as the two digits stacked with no line between them — and says the older form is close to the modern one. The absence of the line is the whole content of the sentence and it does not survive text extraction.
The chronology (§7.9, pp.182–183). Inputs, in the book's own order: the Bakshali manuscript around 300 CE; Aryabhata 499 CE; Brahmagupta 628 CE; Sridharacharya about 750 CE; Mahaviracharya about 850 CE; Al-Hassar in the twelfth century; general use in Europe around the seventeenth century.
The Egyptian and Babylonian design (§7.9, p.183). Checked against the printed page. The chapter states that those civilisations mainly wrote fractions with 1 on top, and that anything else had to be given as a sum of such pieces, a practice now named after Egypt. Inputs: the restriction with the book's own mainly kept, and the name.
The worked expansion (§7.9, p.183). The chapter's own example splits nineteen twenty-fourths into three different fractional units, the largest being one half. Inputs: the fraction and the three denominators.
What was invented in India (§7.9, p.183). The chapter's claim is not only about symbols: it says fractions with an unrestricted top number, together with rules for adding, subtracting, multiplying and dividing them, were first introduced in India, and cites the Sulba treatises as evidence that operations with fractions were known in the Vedic period. Treat this as the chapter's claim and attribute it that way.
Brahmagupta's own statement (§7.9, p.183). Checked against the printed page. The book quotes a verse from Brahmagupta's treatise, cited as verse 12.2 of the Brahmasphuṭasiddhānta, 628 CE. Do not reproduce the quotation. Its content is the same three-step method the previous topic built: multiply each fraction's two numbers by the other denominators to reach a shared denominator, then add or subtract the top numbers.
The transmission (§7.9, p.183). Inputs: the methods travelled to Europe via Arab scholarship over some centuries and were in general use in Europe by about the seventeenth century, then spread worldwide.
The puzzle, two pieces (§7.9, p.184). The chapter first shows the easy case — equal fractional units adding to one whole — then asks for different ones. Its argument that two different pieces cannot work: one half is the largest fractional unit there is, and two halves already make exactly one whole, so any substitution makes the total fall short. Inputs: the argument's two facts.
The puzzle, three pieces (§7.9, pp.184–185). Checked against the printed page. The chapter's reasoning starts from three thirds, argues that one of them must be enlarged and therefore must become one half, then repeats the move on what is left to force a third, and asks the reader to supply the last piece. It states that there is exactly one answer, up to reordering. A coloured disc is printed beneath it, cut into six equal sectors and grouped three, two and one by colour, with the three-term sum written under it. Inputs: the reasoning steps and the disc's grouping.
The puzzle, four pieces (§7.9, p.185). The chapter states that this problem has six answers and invites the reader to find them, suggesting either the same style of reasoning or a method of their own, and then to draw each one as a divided circle. Inputs: the count of six, and the invitation. The six were checked by hand while writing this brief and the book's count is right; the explanation may confirm it but should not present the list as the chapter's, because the chapter prints none of them.

Figures to have open

One horizontal chronological axis carrying 300 CE to about 1700 CE, reused in sections 3, 4 and 9 so that the whole history is one picture and not three. Standard schematic.
A stacked one-half with and without the dividing line, large enough that the difference is unmissable. Redraw; the printed pair on p.182 is set in the book's own type.
A disc divisible into equal sectors that can be recoloured in groups, for sections 11 and 12. The textbook prints one such disc on p.185; redraw rather than reproduce.
A number line carrying one point labelled in two ways, for the Egyptian-fraction misconception.
No photograph, map or data table from the textbook is required. The chapter prints no manuscript image and no portrait of any of the named mathematicians — checked against pp.182 and 183.

Where this sits in the book

NCERT Ganita Prakash, Class 6, Chapter 7 "Fractions", §7.9 "A Pinch of History", pp.182–185 — the Sanskrit words, the Bakshali notation and the chain of mathematicians (p.182); Al-Hassar, the Egyptian and Babylonian systems, the worked expansion, the Indian contribution, the quoted verse and the transmission to Europe (p.183); the puzzle for two and three pieces (pp.184–185); the six-solution statement and the divided circle (p.185)
§7.1, p.153, for the "Knowledge from the past!" panel and tri-pada, which this topic completes
§7.8, p.178, where Brahmagupta is first named and the method attributed
Summary, p.186
The Brahmasphuṭasiddhānta of Brahmagupta, verse 12.2 (628 CE) — cited by the chapter on p.183, quoted there and deliberately not reproduced here