A line of symmetry is a fold that makes the halves coincide

What to assume they know

Recognising and naming ordinary plane shapes: triangle, square, rectangle, circle
A point fixes a location; a segment is the shortest route between two points: the habit of labelling points with capital letters
Line and ray: what changes when you refuse to stop: a line as a straight path that does not stop
The physical experience of folding a sheet of paper along a straight crease (Class 5 paper work is assumed by the chapter)

What they should be able to do

State the fold test for a line of symmetry in one sentence, without using the word looks
Given a figure and a drawn line, decide whether that line is a line of symmetry and justify the decision by what happens at the fold
Explain why a line through the middle of a figure need not be a line of symmetry, using the four-piece jigsaw as the counter-case
Identify figures that have no line of symmetry at all
Find a line of symmetry in a figure whose fold line is slanted rather than upright or flat
Use the two printed names for the same object — line of symmetry and axis of symmetry — interchangeably

Where it usually goes wrong

"A line down the middle is a line of symmetry." This is exactly what the jigsaw figure on p.219 is printed to destroy. Its dotted line halves the square by area and still fails, because the tabs and sockets do not land on each other.
"Symmetric means it looks balanced or pretty." The chapter starts from beauty on p.217 and then narrows to a mechanical test by p.219.
"Lines of symmetry are vertical." Corrected in section 8 with the square standing on a corner and with the diagonal fold lines of Q11 (p.229).
"Every figure has at least one line of symmetry." The clouds (p.218) and several of the Q2 outlines (p.219) have none. Zero is a legitimate answer.
"A line of symmetry has to be drawn on the figure to exist." The dotted lines in the book are aids. A figure has whatever fold lines it has, drawn or not; the exercises on p.227 ask students to supply them.
"Nearly overlapping is overlapping." The word exactly in the definition is not decoration. A fold that leaves a sliver over has failed.

Questions to check understanding

Given a figure with a line drawn on it, state with reason whether the line is a line of symmetry
Trace a printed figure and draw in all its lines of symmetry, or write none
Identify, from a set of figures, the ones that have no line of symmetry
Complete a half-figure across a given line so that the line becomes a line of symmetry (the pattern of §9.1, p.228, Q11)
Explain in one line why a stated line fails the test for a given figure
Find the lines of symmetry of a traditional design — a kolam, a rangoli, a paper cut-out (the pattern of §9.1, p.228, Q8)

Examples worth working on the board

The two figures of §9.1, p.219. Figure (a): a blue triangle carrying a magenta disc at its apex and a yellow disc at each of its two base corners, with a dotted line running down through the apex. Figure (b): a red four-piece jigsaw square — four interlocking pieces with tabs and sockets — with a dotted line down the middle. (a) passes the fold test; (b) does not. The pair is the argument of this topic and both is best shown as folds, not shown as stills.
The chapter's opening set, p.217. Flower, butterfly, rangoli, pinwheel. Counted on the printed page: the flower is drawn with six petals around a round centre; the pinwheel is a blue design built on a central hexagon with one repeated shape attached to each of its six sides, each attachment slanted the same way so the whole appears to turn. The chapter's own hint on p.218 tells the student to look at the hexagon first and then name the repeated shape. What the chapter actually asks about these pictures, at Q1 on p.219, is whether any line of symmetry can be seen in them at all — not how many. It prints no answer either way, so any count the explanation reaches it must derive from the picture rather than assert.
The clouds, p.218. A photograph placed deliberately as the negative case: nothing in it comes back anywhere.
The rangoli fact the chapter states, p.218. The book says the design's red petals return to their own positions under a 90° turn about the centre, and that its other parts do the same. The first half holds: the four red petals are alike and set a quarter turn apart, so a quarter turn does carry them onto one another. The second half does not survive the printed artwork — the small motifs above and below the design are not the same as the ones at its left and right (see Notes), so a quarter turn moves those onto motifs of a different shape. Printing slip to work around, of the same kind as the one recorded for the p.231 square panels: keep this beat on the four red petals and do not show a quarter turn of the whole rangoli, because the explanation would then say unchanged while the figure showed the outer motifs moving. Note also that this is a fact about turning, which module m02 takes up; it is not a fold.
Taj Mahal and gopuram, p.218. Two photographs the chapter puts up without answering. Useful as the "symmetry in built structures" beat; do not claim a count of lines for either, since a photograph is a view, not a plane figure.
Figure it Out, §9.1, p.219, Q2. Five plain outline figures to be tested: a concave arrow-like polygon, a kite-shaped quadrilateral, a quadrilateral with one upright side and a slanted top, an L-shape of right angles, and a thin triangle. Work each; the chapter prints no answers.
A slanted fold line, §9.1, p.226, Q6a. A square drawn resting on one corner. Its four lines of symmetry are its two mid-side lines, which run diagonally across the page, plus its two diagonals, which in this position appear as one upright line and one flat one. (A square standing on a corner cannot have two upright lines of symmetry — turning it 45° turns its axes too.) Beside it, an eight-pointed star. Both are there to break the habit of looking only for vertical folds.
The rotate-the-book hint, §9.1, p.229. Printed under Q11 for parts (c) and (f), whose blue line runs corner to corner. Use it as the chapter's own signal that orientation on the page is not part of the mathematics.

Figures to have open

The p.219 pair, (a) triangle and (b) jigsaw, redrawn. Indispensable, and the fold must show. The book's own art may be redrawn rather than reproduced.
The four opening pictures. A six-petalled flower, a butterfly and the hexagon-based pinwheel are standard schematics; the printed photographs are not required. The rangoli is the exception: redraw it from p.217 rather than substituting a generic four-fold floor design, because the count section 9 reaches depends on how its outer motifs are actually printed.
A cloud photograph or a freehand cloud outline. Standard, not from the book.
A square drawn on one corner, with all four of its fold lines. Standard schematic.
The five outline figures of Q2, p.219. Must be redrawn from the printed page — their exact shapes are the exercise.

Where this sits in the book

NCERT Class 6 Mathematics (Ganita Prakash), Chapter 9 "Symmetry": the unnumbered chapter opening, pp.217–218
§9.1 Line of Symmetry, p.219 — the two figures, the definition, and the first Figure it Out
§9.1, pp.226–229 — Figure it Out items Q6, Q7, Q8, Q9, Q11, used here for slanted fold lines and for figures with no line of symmetry
Summary, p.241 — the settled statement, and the second name axis of symmetry