Paper folding: the growth that outruns intuition

What to assume they know

Multiplying and dividing decimals by 2, and by powers of 2
Reading a quantity across changing units — centimetres, metres, kilometres — and converting between them
The Indian place-value groupings up to lakhs and crores (What makes a number a perfect square and the Class 7 chapter on large numbers)
Reading a two-column table where one column indexes the other
Nothing about exponents; this topic runs entirely on repeated doubling and hands the notation to Exponential notation: repeated multiplication written once

What they should be able to do

Continue a doubling table from a given starting value and fill missing entries
Convert a doubled quantity into a sensible unit at each stage and say why the unit has to change
Compute the difference and the quotient between two entries of a doubling table, and say which of the two is stable
State that ten doublings multiply a quantity by 1024, and check it at more than one starting point
State that three doublings multiply by 8, and verify it from the printed table
Distinguish a fixed increase from a fixed multiplier, and classify a described situation as one or the other
Read the symbol for "approximately equal to" and say what a rounded table entry does and does not claim
Explain why a physical limit on folding does not affect the arithmetic being done

Where it usually goes wrong

"Each fold adds the same amount." This is the error the whole section exists to break. Show the four differences together — a centimetre, a ten-metre gain, a ten-kilometre gain, an eleven-thousand-kilometre gain — and ask what rule could produce all four. Nothing additive can.
"Somebody dropped some zeros." The chapter itself voices this objection through a character. Answer it with the table, not with an assertion.
"You could really fold paper 46 times." You could not; the chapter opens by inviting the student to find the physical limit, and only then says to imagine the limit away. The arithmetic is about doubling, and it is correct whether or not any paper survives.
"The paper reaches the Moon, so it must be very long." It is the thickness that grows. Each fold halves the area and doubles the stack.
"≈ means the same as =." A rounded entry is a claim about size, not an exact value. The chapter introduces the sign the first time it needs it (Part I p.20) and then uses rounded and unrounded forms of the same quantity within two pages.
"1024 is a coincidence." It is 2 multiplied by itself ten times, and it appears again in the very next section as 2¹⁰. Ten doublings must multiply by it; there is nothing to discover.
"Growth this fast means the early folds were already big." They were invisible. The first six folds together do not reach a millimetre. Fast growth says nothing about where the process started.

Questions to check understanding

Complete a doubling table from a given starting thickness across a stated range of folds
Given the thickness at fold k, state it at fold k + 3 without working through the intermediate folds
Compute the factor by which a doubling quantity grows over a stated number of steps, and justify it
Decide, for a described situation, whether the change is by a fixed amount or by a fixed multiplier
Convert a table entry between cm, m and km and choose the appropriate unit
Explain in words why differences between successive entries of this table are not constant while quotients are — the reasoning-style question the board now favours
Estimate which fold first exceeds a stated landmark height, given the table

Examples worth working on the board

Every number below is printed on the page cited. The blanks are the chapter's own; leave them blank.

The opening exchange (Part I p.19). Estu reports having heard that no sheet can be folded more than seven times; Roxie asks whether thinner stock — newspaper, tissue — would change that. The student is told to try it. Then the chapter drops the physical question and asks for a guess at the thickness after 30 folds.
The three speech bubbles (Part I p.19, artwork). One child claims 46 folds would reach the Moon; a second calls this absurd and says several zeros must have been dropped after the 46; a third tells them to settle it themselves. The argument is the hook, and the chapter never resolves it in words — the table does.
Starting thickness: 0.001 cm.
The printed doubling table (Part I p.20), folds 1 to 17, all filled in: 0.002, 0.004, 0.008, 0.016, 0.032, 0.064, 0.128, 0.256, 0.512, 1.024, 2.048, 4.096, 8.192, 16.384, 32.768, 65.536 cm, then ≈ 131 cm at fold 17. The chapter notes 10 folds clears 1 cm and 17 folds is a little over four feet.
The first table to fill (Part I p.20). Folds 18, 19, 20 are given as ≈ 262 cm, ≈ 524 cm and ≈ 10.4 m; folds 21 to 26 are blank. Under it, the chapter states that fold 26 is about 670 m, and sets that beside the Burj Khalifa in Dubai at 830 m.
The second table to fill (Part I p.20). Fold 27 is given as ≈ 1.3 km; folds 28, 29, 30 are blank. Under it: fold 30 is about 10.7 km, which the chapter matches to the height planes typically fly at, and sets against the Mariana Trench at 11 km deep.
The third table to fill (Part I p.20). Folds 31 to 45, fifteen cells, all blank. This is the run.
The pay-off (Part I p.21): after 46 folds the thickness passes 7,00,000 km.
Three paired boxes (Part I p.21). Fold 4 → 0.016 cm beside fold 5 → 0.032 cm; fold 9 → 0.512 cm beside fold 10 → 1.024 cm; and separately fold 4 → 0.016 cm beside fold 6 → 0.064 cm. The first two show one doubling at different heights on the table; the third shows two doublings.
The stated claim about three folds (Part I p.21): any three folds multiply the thickness by 8, which the chapter writes as 2 × 2 × 2 and asks the student to check.
The four-row growth table (Part I p.21) — the centre of this topic. Its three columns are the fold interval, the change in thickness, and the factor. Row by row, as printed:
Across folds 0 up to 10 — subtraction gives 1.024 cm minus 0.001 cm, so 1.023 cm; division gives 1.024 over 0.001, so 1024.
Across folds 10 up to 20 — subtraction gives 10.485 m minus 1.024 cm, so about 10.474 m; division gives 10.485 m over 1.024 cm, so 1024 again.
Across folds 20 up to 30 — subtraction gives 10.737 km minus 10.485 m, so about 10.726 km; division gives 10.737 km over 10.485 m, so 1024 once more.
Across folds 30 up to 40 — subtraction gives 10995 km minus 10.737 km, so about 10984.2 km; division gives 10995 km over 10.737 km, and again 1024.
Note as a check: the fold-20 and fold-30 values used here (10.485 m, 10.737 km) are stated to more figures than the rounded ≈ 10.4 m and ≈ 10.7 km given a page earlier. Same quantity, two roundings; say so rather than let a student think the table disagrees with itself.

Figures to have open

One vertical scale carrying every landmark in the chapter — a person, the Burj Khalifa at 830 m, cruising altitude at about 10.7 km, the Mariana Trench at 11 km, and the Earth–Moon gap. The chapter scatters these across the page as separate remarks; putting them on one axis is what makes fold 46 land. An added figure, and the most important one here.
The doubling table itself, redrawn, with the blank cells left blank. Anyone who fills the chapter's blanks has destroyed the exercise.
A stack diagram for one fold: the sheet halving in area while the stack doubles in height. Standard schematic; the chapter draws no such figure.
The four-interval comparison panel — differences on the left, quotients on the right. This is the chapter's own Part I p.21 table restructured so the contrast is visible at a glance.
No photograph is needed. The Burj Khalifa illustration on Part I p.20 and the two children watching from the foot of the page are decorative.

Where this sits in the book

NCERT Ganita Prakash Class 8, Part I, printed Chapter 2, "Power Play", §2.1 "Experiencing the Power Play ...", Part I pp.19–21, including the unnumbered subheading "An Impossible Venture!" (Part I p.19).
The four-row growth table and the naming of multiplicative / exponential growth sit at Part I p.21, immediately before §2.2 begins on the same page.
A "Math Talk" flag sits beside the guess-the-thickness prompt at Part I p.20.
Forward pointers inside the same chapter: the notation for these products is taken up at Part I pp.21–22 (Exponential notation: repeated multiplication written once); the same 46 folds are set against a ladder to the Moon at Part I pp.35–36 (Additive growth versus multiplicative growth); the chapter's SUMMARY restates the growth contrast at Part I p.46.
Part I p.19 carries a QR code in the chapter banner. Its target was not opened and nothing here depends on it.