How many numbers have a given number of digits, and why digit sums behave

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What to assume they know

Placing a large number on the number line by feel: numbers up to five digits, and where the digit count changes on a number line
Writing whole numbers in the Indian grouping, with a comma after the thousands digit
Adding a short string of one-digit numbers in your head
Knowing there are ten digits, 0 to 9, and that a number does not start with 0

What they should be able to do

State how many whole numbers have exactly one, two, three, four and five digits
Explain the count by choices per position rather than by listing
Say where the 5-digit numbers begin and where they end
Compute the digit sum of a given number
Produce several numbers with a stated digit sum
Find the smallest number with a given digit sum, and justify why it is smallest
Find the largest 5-digit number with a given digit sum, and justify it
Explain why there is no largest number at all with a given digit sum
Describe how digit sums move as you count from 40 to 70, and explain the drop
Explain why 3-digit numbers with consecutive digits always give digit sums that are threes, and say where the list stops
Count how many times a chosen digit gets written across a range of numbers

Where it usually goes wrong

"There are ten 1-digit numbers." The book counts from 1, so there are nine. Whether 0 belongs is a convention.
"To count the 3-digit numbers you have to list them." You have to count the choices. Listing 900 things is not an option and the whole point of the exercise is that you never needed to.
"A big number has a big digit sum." 90,000 has digit sum 9; 99 has digit sum 18. The digit sum is not a measure of size, because it has thrown size away.
"There is a largest number with digit sum 14." There is a largest 5-digit one. Allowing any length, you can always insert more zeros and get a bigger number with the same digit sum. This distinction is exactly what part (c) and part (d) of question 1 are testing, and they are easy to conflate.
"Digit sums go up steadily as you count." They rise by one within a decade and then fall by eight when the units digit rolls over. Watching 49 → 50 is the cheapest way to see that the fall is a carry.
"How many 7s from 1 to 100 means how many numbers contain a 7." Those are different questions and give different answers, because 77 is one number that was written with two 7s.
"The consecutive-digit pattern goes on forever." It stops at 789. There are only seven such numbers, and the book's follow-up question asks precisely this.

Questions to check understanding

"How many 4-digit numbers are there?" with the reasoning demanded
Compute the digit sum of a given number
Write three numbers with a stated digit sum
Find the smallest number with a stated digit sum
Find the largest number of a stated length with a stated digit sum
Explain why numbers with a given digit sum have no largest member
"How many times does the digit d occur from 1 to 100 / 1 to 1000?"
Spot-the-pattern items on digit sums of consecutive-digit numbers
Items that turn on the difference between counting numbers and counting digits

Examples worth working on the board

The digit-count table (§3.4, p.60). Five columns headed for 1-, 2-, 3-, 4- and 5-digit numbers. The first column is filled in for you — from 1 to 9, so nine of them — and the other four are blank.
The choices argument. For a k-digit number the front position may hold any of 1 to 9 and each of the remaining k − 1 positions may hold any of 0 to 9. That is the reason the counts multiply by ten each time. The book does not spell this out; it asks the class to find the counts.
Komal's three numbers (§3.4, p.60). 68, 176 and 545. Their digit sums are the same. The book prints this on a small whiteboard drawn beside the paragraph, showing the three additions worked out; the sums are inside the artwork and do not extract.
Digit sum 14 (§3.4, p.60, question 1). Four parts: write other numbers with digit sum 14; find the smallest; find the largest 5-digit one; then ask how big a number with that digit sum can get. The fourth part is the interesting one and has no finite answer — pad with zeros and you can always go bigger.
Digit sums from 40 to 70 (§3.4, p.60, question 2). Thirty-one numbers. What the class is meant to notice is the shape: inside a decade the sum climbs by one each time; at 49 → 50 it falls by eight, and again at 59 → 60 and 69 → 70.
Consecutive-digit numbers (§3.4, p.60, question 3). The book's own example is 345. The complete list of 3-digit numbers whose digits run consecutively upward is 123, 234, 345, 456, 567, 678, 789 — seven of them, and no more, because 890 would need 10 to follow 9 and 012 is not a 3-digit number. Their digit sums are 6, 9, 12, 15, 18, 21 and 24. The reason they are all threes: digits n, n+1, n+2 add to three lots of n+1.
Digit Detectives (§3.4, p.61). Dinesh has written out 1 to 100 and wonders how many 7s that took. Two questions follow: the count of 7s among 1–100, and among 1–1000. Beside the text the book draws a whiteboard scattered with numbers — 237, 57, 877, 7041, 1799, 676 — under a magnifying glass held over a 7. Those numbers are inside the artwork and were read from printed page 61.
The counting method for Digit Detectives. Count positions, not numbers: in 1–100 the units place carries a 7 ten times and the tens place carries a 7 ten times. In 1–1000, take three positions across a thousand numbers.

Figures to have open

The five-column digit-count table (§3.4, p.60) with only the first column filled. Must start incomplete.
Komal's whiteboard with the three digit-sum additions (§3.4, p.60). It is drawn art and carries the numbers; redraw it, but keep all three additions.
The Digit Detectives whiteboard (§3.4, p.61) with its scattered numbers and the magnifying glass over a 7. Redraw; the magnifier is what makes "count the written 7s" concrete.
A row of empty boxes that can be filled with digit choices, for sections 3 and 4. Standard schematic.
A 10 × 10 grid of the numbers 1 to 100 with every 7 highlighted, for section 12. Not in the textbook, and worth building — it makes 20 visible at a glance and shows 77 contributing twice.

Where this sits in the book

NCERT Class 6 Mathematics (Ganita Prakash), Chapter 3 "Number Play": §3.4 Playing with Digits, pp.60–61
The digit-count table and the opening sentence about starting from 1, p.60
The bold sub-heading Digit sums of numbers and Komal's example, p.60
The Figure it Out block, questions 1–3, p.60
The bold sub-heading Digit Detectives and Dinesh's two questions, p.61
Backward link: §3.2, p.59, for the comma after the thousands digit
Forward link: §3.5, pp.61–62 (Palindromes, and why reverse-and-add usually lands on one), which starts on the same page and reuses the habit of looking at digits rather than at size