A letter-number stands for any number, not one number

What to assume they know

Writing a situation as an expression before computing it — writing a situation as an arithmetic expression before evaluating it (Part I, Chapter 2)
Reading an arithmetic expression as a sum of its terms, and evaluating one
The idea that a relationship between two quantities can be stated in words ("3 more than", "twice as many as")
Perimeter of a square and of simple regular figures, and the word regular as it was used in Class 6
Multiplication tables and the idea of a multiple

What they should be able to do

State what a letter-number is and why the chapter calls it that
Turn a described relationship between two quantities into an algebraic expression, choosing the letter yourself
Evaluate an algebraic expression by replacing its letter-number with a given number
Reverse a stated relationship (given one quantity, express the other) and say why the two expressions are not the same expression
Write an expression that uses two different letter-numbers, and say what each one counts
Distinguish an expression that names a number from a formula that names a general relation
Explain why one algebraic expression replaces a whole table of worked cases

Where it usually goes wrong

"The letter is a secret number I have to find." Nothing in this section asks for the value of a. The letter is not hiding a number; it is holding a place so the relationship can be written down. The chapter never solves for a letter — it substitutes into one.
"a always means the same thing." The chapter reuses letters freely: a is an age here and reappears elsewhere in the chapter as the first input of a number machine and as the top-left entry of a calendar square. The letter means what the sentence introducing it says it means, and nothing more.
"a stands for absolutely any number at all." What a letter-number refuses to do is name one particular number; what it may stand for is still fixed by the situation. An age or a count of matchsticks cannot sensibly be negative or fractional. Say this once, plainly, rather than letting "any number" harden into a false rule.
"s = a + 3 and a = s – 3 are two different facts." They are one relationship written from two ends.
"An expression with letters cannot be a number." It becomes one the moment its letter-numbers are replaced — that is the whole of Section 5.
"Two quantities need one letter each only if they are unrelated." The coconut-and-jaggery expression needs two letters because the two counts move independently. If a problem tied the jaggery to the coconuts, one letter would do. The count of letters tracks how many things can vary, not how many nouns the sentence has.

Questions to check understanding

Given a relationship in words, write the algebraic expression and say what your letter counts
Given an expression and a value for its letter-number, find the number it takes
Choose, from a list of candidate expressions, the one that fits a described situation — the flour-mill item on p.84 is exactly this shape and is the form competency-based papers use most
Given a stated relationship, write the reverse relationship
Write a formula for the perimeter of a named regular figure
Invent a situation that a given expression could describe (the chapter asks this twice, on pp.85 and 103)
Complete a table in which some rows are numbers and the last row is letters

Examples worth working on the board

The age relation (Example 1, Part I, §4.1, p.81). Shabnam is three years older than Aftab. Inputs the page supplies: when Aftab is 10, Shabnam is 13; Aftab is later 18. The letters the book chooses are a for Aftab's age and s for Shabnam's, and the relation is written s = a + 3. The page states outright that any other letter would have done.
Fig. 4.1 (Part I, §4.1, p.81). A hand-lettered two-column table headed with Aftab's age and the expression for Shabnam's age. The left column runs 4, 10, 23,?, a; the right column runs 4 + 3, 10 + 3, 23 + 3,? + 3, a + 3. Checked against p.81 — the table is drawn artwork and extracts as loose fragments. The last two rows are the whole point of the figure and must not be dropped when it is redrawn.
Substituting (Part I, §4.1, pp.81–82). Put 23 in place of a; the expression a + 3 takes the value 26.
The reverse relation (Part I, §4.1, p.82). Aftab's age from Shabnam's is a = s – 3. The page then asks for Aftab's age when Shabnam is 20 and leaves it to the student.
Matchstick Ls (Example 2, Part I, §4.1, p.82, Fig. 4.2). Each L is two matchsticks. The figure prints three arrangements — one L, two Ls, three Ls — drawn as matchsticks with dark heads; checked against p.82. Counts the page gives: 5 Ls need 5 × 2, 7 Ls need 7 × 2, 45 Ls need 45 × 2. With n for the number of Ls the expression is 2 × n.
Coconuts and jaggery (Example 3, Part I, §4.1, pp.82–83). A coconut costs ₹35; a kilogram of jaggery costs ₹60. The page works one case fully — 10 coconuts and 5 kg give 10 × ₹35 + 5 × ₹60 = ₹350 + ₹300 = ₹650 — then asks for 8 coconuts and 9 kg, and finally for the general expression c × 35 + j × 60. A three-column table on p.83 lays out quantity, relationship and expression; read.
Perimeter of a square (Example 4, Part I, §4.1, p.83). Four times the sidelength, written 4 × q. The page then asks for the perimeter when the sidelength is 7 cm.
The first Figure it Out (Part I, §4.1, pp.84–85). Its inputs, not its answers: formulas for the perimeters of an equilateral triangle, a regular pentagon and a regular hexagon; a 20 m pipe joined to another of length k metres; a currency table whose rows are (3, 5, 6), a row given only as the expression 6 × 100 + 4 × 20 + 3 × 5 = 695, then (8, 4, z) and (x, y, z) for notes of ₹100, ₹20 and ₹5 — checked from p.84, where the table cells wrap and do not extract in order; a flour mill that takes 10 seconds to start and 8 seconds per kilogram, offered with five candidate expressions; four phrases to translate ("5 more than a number" and three like it); two expressions to invent situations for; and a 2 × 3 block of calendar dates whose bottom middle cell is called w.

Figures to have open

The p.81 table redrawn: two columns, five rows, ending with the "?" row and the letter row. This carries the whole argument of the topic and must keep its order. Redraw rather than lift — the printed version is hand-lettered artwork.
A row of matchstick Ls, one, two and three, with the individual sticks visible. Standard schematic; the textbook's Fig. 4.2 shows the same thing.
A square with a labelled sidelength. Standard schematic.
The three-column relationship table for coconuts and jaggery. Redraw; the content is three short cells per row.
No photograph is needed for this topic.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 4 "Expressions using Letter-Numbers", §4.1 The Notion of Letter-Numbers, pp.81–85. Includes Fig. 4.1 (p.81), Examples 1–4 (pp.81–83), Fig. 4.2 (p.82) and the Figure it Out block on pp.84–85.
Backward pointer: Part I, Chapter 2 Arithmetic Expressions, for terms and for reading an expression before evaluating it.
Forward pointer inside the same chapter: Part I, §4.3, pp.86–87, where the multiplication sign in 2 × n and 4 × q is dropped.