Comparing two fractions by giving them a common fractional unit

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What to assume they know

Equivalent fractions: many names, one number, and lowest terms: equivalent fractions, and why multiplying above and below by the same number leaves a fraction unchanged
A fraction as an equal share, and why one-ninth is less than one-fifth: more sharers means a smaller share
Common multiples of two numbers, from Common multiples: why the first "idli-vada" is 15
Ordering whole numbers, and reading the greater-than and less-than signs

What they should be able to do

Compare two fractions that already share a bottom number, and say why it is easy
Compare two fractions with the same top number, and explain the result by sharing
Convert a pair of fractions to a shared fractional unit and use it to rank them
Name at least two shared units that will work for a given pair, and say why the product of the two bottom numbers always does
State the comparison method as an ordered procedure
Put three or four fractions into ascending or descending order
Explain why comparing top numbers alone, or bottom numbers alone, is not a valid test

Where it usually goes wrong

"Bigger bottom number means bigger fraction." Already broken in §7.1 for fractional units, and it returns the moment two full fractions appear. The chikki pair on p.169 is the counter-example the book chooses.
"Bigger top number means bigger fraction." True only when the bottom numbers match. Twelve fifths beats eight fifths; nine quarters does not beat five halves. Both cases are in the p.174 exercise, and putting them side by side is the cleanest correction.
"Compare the tops, then compare the bottoms, then decide." There is no such rule. If a student is reaching for one, they have not yet accepted that a fraction is a single number.
"You must use the product of the two bottom numbers." The book itself points out on p.171 that a smaller shared unit had already turned up. Any common multiple works. The product is the guarantee, not the requirement.
"Converting changes the fractions." It changes their names, not their places. Keep both fractions marked on one number line while they are rewritten, so the marks visibly stay put.
"Comparison and equivalence are separate topics." They are the same topic used twice.
"A shorter list of equivalent fractions means a wrong answer." The pair on p.174 needs sixty-three, not one hundred and eighty-nine. Ending early is economy, not error.

Questions to check understanding

Compare two fractions and justify the answer
Rewrite a given pair of fractions so that they share a bottom number
Put three or four fractions in ascending or descending order
Decide which of two sharing situations gives each person more
Name two different shared step sizes that would settle a given comparison
Explain why a stated comparison rule is wrong, using a counter-example
The solutions appendix bound with this chapter answers the §7.6 and §7.7 exercises on its corresponding pages

Examples worth working on the board

The first chikki pair (§7.6, p.169). Checked against the printed page. Two named characters are asked which group of children gets more: one slab between two children, or five slabs among eight. One character reduces the question to a pair of fractions; the other rewrites the first fraction so both use eighths and reads the verdict off. Inputs: the two group compositions.
The second chikki pair (§7.6, p.169). Inputs: one slab between two children against four slabs among seven. Printed erratum: the line naming the pair to compare prints one seventh where the situation requires one half. Checked against p.169. The next printed line rewrites one half as four eighths, and p.170 concludes in favour of four sevenths over one half, so the intended pair is unambiguous.
One printed sharing rule, and its twin left open (§7.6, p.170). Checked against the printed page. Only one of the two is printed as a rule, in a green panel: with the amount of food fixed, more children means a smaller plate. The other green panel on that page is not a rule at all — it is the conclusion of the argument running down from p.169, ranking four sevenths against four eighths and then against one half. The converse — with the number of children fixed, more food means a bigger plate — is put to the reader as a question in the body text, to be discussed rather than read off. Both facts are what every later computation has to agree with, and both are the fastest way to rank a pair that shares one of its two numbers.
The same-numerator comparison (§7.6, p.169). Four slabs among seven children against four slabs among eight. The book settles it from the sharing situation alone, with no arithmetic, in the green panel that closes p.169; the printed rule at the top of p.170 is that argument generalised.
Three quick pairs (§7.6, p.170). Inputs: one fifth against two fifths, three sevenths against four sevenths, one half against five eighths. They are printed as part of the open question about increasing the amount of food, and the reader is asked to show that their own reasoning explains all three. Note that the third pair does not actually share a bottom number as printed and needs one conversion first; that is worth a beat rather than a correction.
Two group questions (§7.6, p.170). Inputs: three glasses among four children against seven glasses among ten; and four glasses among seven children against five glasses among seven. The book then asks which pair was easier and why, which is the question that motivates the whole method.
The hunt for a shared unit (§7.6, pp.170–171). Checked against the printed page. Two characters list equivalent fractions for three quarters and for seven tenths, going step by step. One asks when to stop; the other proposes stopping at the product of the two bottom numbers. A margin remark then notices that a smaller meeting point had already appeared earlier in the two lists. Inputs: the two fractions and both lists.
The matching exercise (§7.6, p.172). Checked against the printed page. Eight pairs lettered a to h, to be rewritten with matching bottom numbers: seven halves with three fifths; eight thirds with five sixths; three quarters with three fifths; six sevenths with eight fifths; nine quarters with five halves; one tenth with two ninths; eight thirds with eleven quarters; thirteen sixths with one ninth. Inputs only. Note that pair (b) is the first where one bottom number already divides the other, so the product is not the smallest choice.
The §7.7 worked pair (§7.7, p.173). Four fifths against seven ninths, both rewritten over forty-five, with a speech bubble naming forty-five as a common multiple of the two bottom numbers. Inputs: the pair and the shared denominator.
The second §7.7 worked pair (§7.7, p.174). Seven ninths against seventeen twenty-firsts, both rewritten over sixty-three. Inputs: the pair and the shared denominator. This is the pair that shows the product is not always the natural choice — nine times twenty-one is much larger than sixty-three.
The stated method (§7.7, p.174). A named summary panel gives the procedure in two numbered steps: rewrite so the step size matches, then rank by the counts. Give it its own section; it is the only place in the chapter where the method is written as a procedure.
The §7.7 exercise (§7.7, p.174). Inputs only. Five pairs to compare with justification — eight thirds with five halves; four ninths with three sevenths; seven tenths with nine fourteenths; twelve fifths with eight fifths; nine quarters with five halves. Then two ascending-order sets and two descending-order sets, of three or four fractions each.

Figures to have open

Two sharing groups drawn side by side, with the food above and the children below, reusable throughout sections 1 to 5. Redraw; the printed slabs and stick figures on pp.169–170 are the book's own artwork.
Two parallel lists of equivalent fractions that can grow one entry at a time, with a highlight that fires when the bottom numbers match. This carries sections 6, 7 and 8 and is the central figure of the topic. Standard schematic.
A number line on which two fractions stay put while their labels are rewritten. Standard schematic; used against the "converting changes the fraction" misconception.
A strip diagram divided once into each bottom number and once into the shared one, so that the shared unit is visible as a physical step rather than a computed number.
No photograph, table or data figure from the textbook is required.

Where this sits in the book

NCERT Ganita Prakash, Class 6, Chapter 7 "Fractions", §7.6 "Equivalent Fractions", pp.169–172 — the two chikki comparisons (p.169); the printed sharing rule, the open question about the converse, the quick pairs and the two group questions (p.170); the hunt for a shared unit and the two meeting points (p.171); the matching exercise (p.172)
§7.7 "Comparing Fractions", pp.173–174 — the two worked comparisons, the stated method and the exercise
§7.1, p.152, for the fractional-unit reasoning the comparisons rest on
Chapter 5 "Prime Time", §5.1, for common multiples
Solutions appendix bound with this chapter file, §7.6 and §7.7 pages