A whole number times a fraction, read as repeated distance

What to assume they know

A fraction as a number of equal parts of a whole, and where it sits on a number line
Whole-number multiplication read as repeated addition
Adding fractions with the same denominator
Mixed fractions, and rewriting one as a single fraction (Class 6, reinforced in Part I, §8.1, p.176)
Speed as distance per hour, informally: Answering "could this possibly fit?" by estimating in stages for the habit of reasoning about a quantity in stages

What they should be able to do

Explain why a fractional speed does not change how a distance is computed
Compute a whole number times a fraction by repeated addition, and say what makes that reading available
Compute a fraction times a whole number by dividing the whole number into equal parts and then collecting some of them
Identify the multiplier and the multiplicand in a written product, and say which one gets cut and which one does the cutting
Use the multiplier's denominator to fix how many equal parts to make, and its numerator to fix how many of them to keep
Rewrite a mixed fraction as a single fraction before multiplying, and say why that step is done first
Recognise, from 1/5 × 3 = 3/5, that a product can be smaller than the number being multiplied

Where it usually goes wrong

"You cannot multiply by a fraction, because you cannot add something a fractional number of times." This is a fair objection to repeated addition, and the chapter answers it by changing the procedure rather than the meaning: for a fractional multiplier you cut the multiplicand and collect pieces. The situation — how far in this much time — is what stays fixed and decides what the answer must be.
"Multiplying makes a number bigger." 1/5 × 3 = 3/5 breaks it on p.174, before the chapter ever raises the question.
"The number under the multiplier's bar is something you multiply by." It is something you divide by: 5 in 2/5 says cut into five, and 2 says keep two. The p.176 arrow diagram shows the two steps in that order.
"3 × 1/4 and 1/4 × 3 are different problems." In this section they really are different procedures — repeat three quarters, versus cut 3 into four — and that is worth showing. They are not different numbers, which the chapter settles separately on p.186.
"One and a quarter means one times a quarter." The chapter rewrites 1¼ as 5/4 before doing anything else, on p.176. Show the rewriting as its own step.
"A fractional speed is a special case needing a special formula." The chapter's whole opening move is that it is not.

Questions to check understanding

Compute a whole number times a fraction and convert the result to a mixed fraction (the printed exercise on p.177 is exactly this, four times)
Compute a fraction times a whole number and say which number was cut and into how many parts
Given a word problem, decide whether it is asking for repetition or for sharing, and write the product accordingly
Multi-step rate items: given a per-day or per-hour amount, find the amount for a fractional or multi-day stretch (the milk, canal, oil and Moon items on pp.176–177 are all this shape)
Rewrite a mixed fraction as a single fraction as a first step, and be marked on that step
Explain, in words, why a fractional speed does not change the method

Examples worth working on the board

Aaron's five hours (Part I, §8.1, p.173). Inputs: 3 km in 1 hour, 5 hours. The chapter writes the answer out as five 3s added, then as 15 km. Use the addition line — it is the only place in the topic where the repeated-addition reading is shown in full.
The tortoise's three hours (Part I, §8.1, pp.173–174). Inputs: 1/4 km in 1 hour, 3 hours. The chapter writes three quarters added, giving 3/4 km. Note: the printed sentence that this changes nothing about how the distance is worked out is the hinge of the whole section.
The number line on p.173. Checked against the printed page. A line from 0 with tick marks a quarter apart; a short arrow spanning the first tick is labelled as the distance in one hour, and a long arrow beneath spans three of them, labelled as the distance in three hours. The 1/4 km label sits under the first interval.
One-fifth of an hour (Part I, §8.1, p.174). Inputs: 3 km in 1 hour, 1/5 hour. The chapter divides 3 km into 5 equal parts and reads off 3/5 km, then records 1/5 × 3 = 3/5. Checked against p.174: the number line runs from 0 to a labelled 3 km with four interior ticks, and the first of the five intervals is bracketed as the distance in a fifth of an hour.
Two-fifths of an hour (Part I, §8.1, p.175). Inputs: the 3/5 km just found, and the observation that 2/5 is twice 1/5. The chapter multiplies 3/5 by 2 to get 6/5 km, and records 2/5 × 3 = 6/5. Checked against p.175: the same 0-to-3 km line, now with a second bracket covering two of the five intervals.
The labelled callout (Part I, §8.1, p.175, repeated p.176). Checked against the printed page. Two speech-bubble labels point at 2/5 × 3: Multiplier at the fraction, Multiplicand at the 3. The p.176 version adds two curved arrows showing 3 ÷ 5 = 3/5 first, then 2 × 3/5 = 6/5.
Example 1 (Part I, §8.1, p.176). Inputs: 5 grandchildren, 2/3 acre each. The chapter writes five thirds-pairs added and gives 10/3. This is the repeated-addition procedure applied to a fractional multiplicand.
Example 2 (Part I, §8.1, p.176). Inputs: ₹8 for one hour, 1¼ hours. The chapter first rewrites 1¼ as 5/4, then computes 5/4 × 8 by taking 8 ÷ 4 = 2 and then 5 × 2, reaching ₹10. Note that the chapter divides the multiplicand by 4 before multiplying by 5 — the same two-step order as the number-line work, not the "multiply then simplify" order.
Figure it Out, p.176 and p.177. Inputs only, no answers: Tenzin drinks half a glass of milk a day (asked for one week, and then for all of January); a team builds 1 km of canal in 8 days (asked for one day, and for a five-day week); Manju and two neighbours share 5 litres of oil three ways (asked for one week and for four weeks); the Moon sets 5/6 hour later each day, starting 10 pm Monday (asked for Thursday); and four products to convert to mixed fractions — 7 × 3/5, 4 × 1/3, 9/7 × 6, 13/11 × 6.

Figures to have open

A number line that can carry unit ticks, sub-ticks at quarters and at fifths, and two bracket-arrows above and below it. Standard schematic, but it must be able to reproduce both printed arrangements: 0 with quarter ticks (p.173) and 0 to 3 km with five equal intervals (pp.174–175).
A horizontal bar that can be cut into equal pieces and have pieces lifted out, for sections 5 and 6.
The multiplier/multiplicand callout, redrawn — the two labels must point at the correct halves of the written product.
The two-arrow flow of the p.176 diagram: divide, then multiply.
No photograph or data table from the textbook is needed. The chapter's opening illustration of a boy with a dog and a tortoise is decoration and carries no mathematics.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 8 "Working with Fractions", §8.1 "Multiplication of Fractions", pp.173–177 — Aaron and the tortoise with the two number lines (pp.173–175), the Discussion block naming multiplier and multiplicand and setting out the two steps (pp.175–176), Examples 1 and 2 (p.176), and the Figure it Out set that closes on p.177
Same part, §8.1, p.186, for the order-independence this topic deliberately leaves open
Same part, SUMMARY, p.198, for the chapter's own compressed statements
Solutions appendix bound after p.202 in the cached PDF (not part of the printed book), consulted only to check that the exercise inputs above are stated correctly