Why multiplying by a decimal below 1 shrinks a number

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What to assume they know

Multiply as whole numbers, then count the decimal digits — how to obtain a decimal product at all
Why multiplying can make a number smaller — the same argument already made for fractions: multiplying can make a number smaller
Comparing two decimals and saying which is larger
Knowing that 0.75 and three-quarters are the same quantity, so that "a part of" is a reading available for a decimal too
Reading a table with a situation column and an outcome column

What they should be able to do

State, before multiplying, whether a product will exceed both factors, fall below both, or land between them
Justify each of the three outcomes by the position of the factors relative to 1
Explain why the count of decimal places is irrelevant to this question
Recognise that a factor exactly equal to 1 leaves the other factor untouched, and that this case sits outside the chapter's table
Show by a counterexample that a single factor below 1 does not force a product below 1
Decide which of a list of products fall below 1 without carrying out any multiplication
Give a pair of decimals whose product is a whole number

Where it usually goes wrong

"Multiplication always makes a number bigger." The habit the whole topic exists to break. It is true only when you multiply by a number greater than 1, and the chapter's second example — the digits 25 and 8 again, with the point moved — breaks it in one line.
"If any factor is less than 1, the product is less than 1." False, and it is the dangerous one, because the chapter never states it and never knocks it down — it only prints the numbers and moves on. 18 × 0.12 has a factor below 1 and a product above 2. The true statement is narrower: if both factors are below 1, the product is below both of them and therefore below 1.
"More decimal places means a smaller number." 12.5 has one decimal place and stands above 1; 0.9999 has four and stands below it. The count of places is the wrong thing to look at; the comparison with 1 is the right one.
"Multiplying by 0.75 is smaller because 0.75 is a small number." It shrinks because 0.75 is below 1, not because it looks small. 0.99 also shrinks, by almost nothing.
"There is a fourth case for a factor equal to 1." There is a case, but it is not in the book's table, and it is not a shrink or a stretch — the other factor comes through unchanged. Name it as the boundary rather than presenting it as a printed row.
"A product with a point in it can never be a whole number." 2.25 × 8 = 18 is on Part II p.72 and refutes it, and Part II p.70 asks the question directly.
"This is only about decimals." It is the same argument made for fractions in Why multiplying can make a number smaller. The chapter says outright that decimals are only a way of writing fractions, so the behaviour has to carry across.

Questions to check understanding

Given a multiplication, say whether the product exceeds, falls below, or lands between the two numbers, and justify it
Pick out, from a list, the products that fall below 1 — the shape of Q8 and Q9 on Part II p.73
Fill two boxes so their product is a stated value, in more than one way (the shape of Q7 on Part II p.94)
Arrange a set of products and quotients of the same number in increasing order without computing them (the shape of Q11 on Part II p.95)
Give an example of two decimals whose product is a whole number
Explain why a stated general claim about products is false, by exhibiting one counterexample

Examples worth working on the board

The three opening products (Part II, §4.2, p.72). 2.25 × 8, then 0.25 × 8, then 0.25 × 0.8. The book prints all three with their answers, and the three answers are the whole demonstration: the first clears both factors, the second clears one, the third clears neither. Keep the digits 25 and 8 constant across all three so the only thing changing is where the point sits.
The situation table (Part II, §4.2, p.72). Checked against the printed page. Three rows, three columns headed Situation, Multiplication and Relationship. The worked instances are 3.4 × 6.5 for both factors above 1, 0.75 × 0.4 for both between 0 and 1, and 0.75 × 5 for one of each. The relationship column states the outcome in words and quotes the product in brackets. Note: the table has exactly these three rows — verified on the printed page — so it says nothing about a factor equal to 1 and nothing about 0.
A pair. 1 × 0.4, and 1 × 6.5. Neither is in the book. They are the missing row of the table and they are what makes 1 the pivot rather than an arbitrary landmark.
"Figure it Out" Q9 (Part II, §4.2, p.73). Four products — 7 × 0.6, 0.7 × 0.6, 0.7 × 6 and 0.07 × 0.06 — with the instruction to decide which fall below 1 without multiplying.
"Figure it Out" Q8 (Part II, §4.2, p.73). Given 18 × 12 = 216: 18 × 1.2, 18 × 0.12, 1.8 × 1.2, 0.18 × 0.12, 0.018 × 0.012 and 1.8 × 12, followed by the same which-are-below-1 question. Six products, one digit string, six different sizes.
The pair that separates the true rule from the false one (Part II, §4.2, "Figure it Out" Q8, p.73). 18 × 0.12 against 0.18 × 0.12 — the same factor 0.12, below 1, standing in both. The products are 2.16 and 0.0216, one either side of 1, so a factor below 1 forces nothing on its own. The digits are the book's and Q8's closing question points straight at the comparison, but the book never lifts the two out and states the conclusion; section 10 does, and that is where it gets its teeth.
The two questions on Part II p.70. Whether two decimals can multiply to a natural number, and whether a natural number multiplied by a decimal can. The book poses both and answers neither. Two pages later, under the subheading on Part II p.72, 2.25 × 8 lands exactly on 18 and settles the second one, and the explanation is allowed to notice that; the book does not join them up.

Figures to have open

A number line carrying 0, 1 and a few whole numbers, on which a factor can be dropped and shown above or below 1. This is the topic's central image and it must be reusable in every section from 3 to 10.
A three-row situation table, revealable row by row, matching the book's columns. Redraw it; do not lift the printed table.
A shaded length bar for section 7 — a bar of 5 units with 0.75 of it shaded. Standard schematic.
No photograph, no data set and no textbook artwork is required for this topic.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part II, printed Chapter 4 "Another Peek Beyond the Point", §4.2 "Decimal Multiplication", p.72 — the bold subheading "Is the Product Always Greater …?", the three opening products, the two questions about when a product exceeds or falls below both factors, and the three-row situation table
Same part, same chapter, §4.2, p.70 — the two questions about a product being a natural number
Same part, same chapter, §4.2, "Figure it Out", p.73 — questions 8 and 9
Same part, same chapter, §4.4, "Figure it Out", pp.94–95 — questions 7 and 11, which are the same reasoning applied at the end of the chapter
Backward pointers: Why multiplying can make a number smaller and Multiply as whole numbers, then count the decimal digits
Forward pointer: Dividing when the divisor has a decimal, where the mirror-image question is asked about division