An angle is an amount of turn, not a pair of drawn arms

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What to assume they know

Line and ray: what changes when you refuse to stop: what a ray is, its starting point, and why the starting point is written first
A point fixes a location; a segment is the shortest route between two points: naming points with capital letters
The everyday sense of turning something about a fixed hinge

What they should be able to do

State what two rays must share before they form an angle
Identify the vertex and the arms of an angle in a drawn figure and in an object
Name an angle with three letters and explain why the vertex goes in the middle
Say when a single-letter name for an angle is legitimate and when it is not
Describe an angle's size as an amount of turn about the vertex
Order a set of hinged pictures by how far the hinge has been opened
Pick out the vertex and both arms of an angle in a compass, a pair of scissors, spectacles or a box lid
Explain why lengthening or shortening the arms leaves the angle unchanged
Count how many angles a given set of points can name

Where it usually goes wrong

"Longer arms mean a bigger angle." The chapter attacks this twice — with the snipping cartoon at §2.7, p.27, and with the printed note to teachers at §2.6, p.25 warning that students commonly believe it. Corrected by the turn definition: the arms record where the turn stopped; how far along them you draw is irrelevant.
"An angle is the region between the two arms." Corrected by section 8 — the size is the amount of turn about the vertex, so an angle can be talked about even when nothing is shaded and even when the arms are only imagined (the slope of a ramp, the swing of a door).
"∠ABC and ∠CBA are different angles." Both name the angle at B between the same two arms; only the middle letter carries information.
"You can always name an angle by its vertex alone." True only when exactly two rays leave that vertex. Section 5 is built on the case where three do.
"Real angles are drawn on paper; objects merely resemble them." Corrected by section 10: the compass and the scissors are two arms about a vertex, and opening them is the rotation itself.
"An angle needs both arms drawn to exist." Corrected later in the chapter by the ramp and the rotated insect (§2.9, p.46), where one arm is a reference direction that is never drawn. Plant the idea here.

Questions to check understanding

Mark the vertex and both arms of an angle visible in a photograph or drawing of an everyday object
Draw and label an angle whose arms are given by name
Explain why a stated one-letter name for an angle is not acceptable in a given figure
Name every angle marked in a supplied figure
Given three or four points in general position, count the lines and the angles they determine, and list them
Order a set of drawn angles from smallest to largest without measuring
One-line justification items: why does shortening the arms not change the angle?

Examples worth working on the board

Fig. 2.8 (§2.5, p.17). Vertex B with one ray running up to D and another running down to E, each labelled as an arm. The single figure carries four names at once: ∠B, ∠DBE, ∠EBD, and the two arms BD and BE. Build the labels onto it one at a time.
Fig. 2.9 (§2.5, p.18). A ray in its initial position, the same ray in its final position, and a curved arrow between them. This is the figure the whole module rests on; it is best shown as a sweep, not shown as a static pair.
Vidya's six cases (§2.5, pp.17–18). Six drawings of the same book being opened further and further, printed side by side as Case 1 to Case 6. Each later case shows more turn than the one before, so the six are already in order. Use them to establish ranking before any number exists.
∠APB and ∠P (§2.5, p.20). A figure with vertex P and three rays leaving it, through A, through B and through C. Because three rays leave P, the single letter P does not pick out one angle, so ∠APB cannot be shortened. Contrast it with Fig. 2.8, where only two rays leave B and ∠B is unambiguous.
Counting angles from points (§2.5, pp.20–21). Mark three points, no two coincident and not all on one line: you get 3 lines, and 3 nameable angles — one at each point. Mark four points with no three on one line: you get 6 lines, and 12 nameable angles. The rule: at each point, three other points give three rays, and choosing 2 of those 3 rays gives 3 angles at that point, so 4 × 3 = 12.
The snip (§2.7, p.27). A three-panel cartoon: a child holds a hinged V-shape; a second child cuts both arms shorter with scissors and declares the angle reduced; the first child answers that it is unchanged. The joke is the argument.

Figures to have open

Fig. 2.8, the two-arm angle at B. Standard schematic, but the word arm must sit along each ray as the book places it.
Fig. 2.9 — the rotation figure with initial position, final position and the amount of turn. This is the single indispensable figure of the topic.
Vidya's six book-opening cases. Redraw as six frames of one hinge opening; the identity of the character does not matter, the monotone increase does.
The three-ray figure at P used for ∠APB (§2.5, p.20). Needed as drawn.
The snipping cartoon (§2.7, p.27). Redraw as a three-panel strip; the printed art is the textbook's own.
Hinged objects for section 10 — compass, scissors, spectacles, wallet, stapler, open box lid, step-ladder, bridge truss. All appear in the chapter at §2.5, pp.18–20; all may be redrawn.

Where this sits in the book

NCERT Class 6 Mathematics (Ganita Prakash), Chapter 2 "Lines and Angles": §2.5 Angle, pp.17–21
Teacher's Note on rotation, §2.5, p.19; Teacher's Note on arm length, §2.6, p.25
The snipping cartoon, §2.7, p.27
Figure it Out items used: §2.5, Q1 on p.19, Q2–Q5 on p.20, Q6 on p.21
Summary, p.54, for the settled statements of vertex, arms and size