Kaprekar's 6174: a process that always ends in the same place

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What to assume they know

Palindromes, and why reverse-and-add usually lands on one: rearranging the digits of a number and treating the result as a new number
Building the largest and the smallest number from a given set of digits
Column subtraction of four-digit numbers, with borrowing
Supercells: a number's status comes from its neighbours: comparing four- and five-digit numbers

What they should be able to do

Carry out one round of the procedure on a given four-digit number
Repeat the procedure and record how many rounds a start takes
Explain why the starting number must not have all four digits the same
Show that 6174 reproduces itself under the procedure
Explain what it means for a procedure to have a resting place
Distinguish "6174 is where it stops" from "every start gets there", and say which the book asserts
Run the same procedure on three-digit numbers and identify where it settles
State the effect of keeping or dropping a leading zero on the round count
Recount who D.R. Kaprekar was and when he found this

Where it usually goes wrong

"6174 is special because of what it is made of." It is special because of what the procedure does to it. Any other number moves; 6174 stays. Show the fixed-point subtraction rather than hunting for properties of the digits.
"You have to try every four-digit number to believe it." You cannot, and the book does not ask you to. What the class can do is check that 6174 stays put and that everybody's chain lands there — which is evidence, not proof, and the chapter is content with that distinction. §3.10 is where it becomes the point.
"Any four-digit number works." Not one with four identical digits. The book states the condition in the same sentence as the example, and it is easy to skip.
"Bigger starting numbers take more rounds." They do not. The chain from 6382 is done in three; other, smaller starts take more. Round count is not related to size.
"The largest and smallest are just the digits sorted." They are — but sorting the smallest one can put a 0 at the front, and whether that is allowed changes the arithmetic. See Notes; this is the one place in the chapter where two honest readings give two different answers.
"The three-digit version also gives 6174." It does not; it settles somewhere else, and finding out where is the book's own closing question.

Questions to check understanding

Perform one round on a given four-digit number
"How many rounds does n need before it settles on the Kaprekar constant?" — the chapter asks this twice, for 5683 and for the student's year of birth
Show that 6174 is unchanged by the procedure
Explain why a number with four identical digits cannot be used
Run the procedure on three-digit numbers and report where it settles
Given a partly filled chain, complete the missing A, B or C
Reasoning items on the difference between checking many cases and proving all of them — the same competence assessed again in The Collatz conjecture: a question a child can ask and nobody can settle

Examples worth working on the board

The Kaprekar passage (§3.6, p.62). Kaprekar taught the subject at a state school in Devlali, in Maharashtra; the book says he found many number patterns nobody had noticed before, and dates this discovery to 1949. A photographic portrait of him is printed beside the paragraph.
The flow chart (§3.6, p.63). Four boxes with arrows: take a four-digit number; build the largest number A from its digits; build the smallest number B; subtract to get C. A side arrow labelled with C's digits loops back to the second box. Beside it a wavy box asks what happens if you keep going. The chart is drawn art and its box text does extract, but the arrows and the loop do not.
The printed chain from 6382 (§3.6, p.63). Four columns, the last one blank:
- A = 8632, B = 2368, C = 6264
- A = 6642, B = 2466, C = 4176
- A = 7641, B = 1467, C = 6174
- A =, B =, C = ← left empty for the student The fourth column is the exercise: filling it produces 6174 again, and that is the moment.
The self-check. Take 6174's own digits — 6, 1, 7 and 4. The largest they make is 7641 and the smallest is 1467, and 7641 − 1467 = 6174. That single subtraction is section 8 and it needs no other case.
The all-same-digit case. Start from a number whose four digits are identical. The largest and the smallest arrangement are the same number, so the subtraction gives 0 and the procedure has nowhere to go. This is why the book requires at least two different digits.
The three-digit version (§3.6, p.63). The book asks the class to run the same steps on three-digit numbers and say what starts repeating. The self-check works the same way: 954 − 459 comes back to 495.
Counting rounds (§3.7, p.65, question 4; and the chapter-end block, p.72, question 2). How many rounds 5683 needs, and how many your own year of birth needs. See Notes — the answer to the first depends on a convention the chapter never states.

Figures to have open

The four-box flow chart from §3.6, p.63, including the loop arrow that feeds C's digits back in. The loop is the whole idea and it is drawn, not written.
The printed chain from 6382 with its blank fourth column (§3.6, p.63). It must start blank.
The portrait of D.R. Kaprekar (§3.6, p.62). It is a photograph in the textbook; the explanation needs a portrait, and this one is printed alongside the passage.
A converging diagram: several start numbers, one destination. Standard schematic, not in the textbook.
No table or dataset is required.

Where this sits in the book

NCERT Class 6 Mathematics (Ganita Prakash), Chapter 3 "Number Play": §3.6 The Magic Number of Kaprekar, pp.62–63
The biographical passage, the portrait, and the date 1949, p.62
The flow chart, the worked chain from 6382, the Explore block, the naming of the Kaprekar constant, and the three-digit question, p.63
§3.7, p.65, question 4, which asks for the round count of 5683
The chapter-end Figure it Out block, p.72, question 2, which asks for the round count of the student's year of birth
Forward link: §3.10, pp.68–69 (The Collatz conjecture: a question a child can ask and nobody can settle), where a procedure that looks just as reliable turns out not to be proved