Straight and right angles as the landmarks of a full turn

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What to assume they know

An angle is an amount of turn, not a pair of drawn arms: an angle is an amount of turn about a vertex
Comparing two angles without measuring either of them: two angles are equal when superimposition makes both arms coincide
Line and ray: what changes when you refuse to stop: a straight line, and rays leaving a point on it
The idea of half of something, from earlier work on fractions

What they should be able to do

Recognise a half turn as the angle whose arms lie in one straight line
Name that angle and mark it in a figure
Show that any ray from the vertex of a straight angle splits it into two angles
Fold a straight angle into two equal parts and justify why the two parts are equal
Define a right angle as precisely half a straight angle, and hence as a quarter of a full turn
State how many right angles a straight angle contains
Identify perpendicular lines and produce a pair by folding
Produce straight and right angles by joining points on a square dot grid
Sort angles into acute, right and obtuse using only the two landmarks
Count acute angles in a growing figure and describe the pattern

Where it usually goes wrong

"A right angle is an angle that looks square." Corrected in §2.8, p.29 — the definition is precisely half a straight angle, and the chapter says outright that nothing less than exact counts. The 'L' shape is a recognition aid, not the definition.
"A straight angle is not really an angle, because it is just a line." It is the angle of a half turn; the arms are still two rays from one vertex, and the curve at O in Fig. 2.11 is drawn precisely to make that visible.
"Any ray through the vertex splits a straight angle into two right angles." False, and section 4 is built on the gap: any ray splits it into two angles, but only one particular ray splits it into two equal ones.
"Folding is a rough method; measuring would be exact." The reverse is the chapter's position at §2.8, pp.28–29 — the fold brings one arm onto the other, which is superimposition, so the equality is proved rather than estimated. No protractor has been introduced at this point in the chapter.
"Perpendicular means vertical." It is a relation between two lines, not an orientation. Corrected by the slanting-crease exercise at §2.8, p.31, where the right angles are produced on a deliberately tilted fold.
"Acute and obtuse are just labels to memorise." The two words carry their ordinary meanings — the chapter asks the student directly why the sharp one and the blunt one were chosen (§2.8, p.32).

Questions to check understanding

Count the right angles visible in a described room or object
Join a marked grid point to others to produce a straight angle, then a right angle, and list all the ways of doing it
Fold to produce a right angle on a slanting crease, and write down the procedure so that someone else can follow it
Justify why two angles produced by a fold are exactly equal
Pick out which angles in a supplied figure are acute, which are right, which are obtuse and which are straight
Explain the choice of the words acute and obtuse
Extend a figure sequence and predict the next count, stating the pattern

Examples worth working on the board

Vidya's two extreme cases (§2.8, p.27). Two painted illustrations, not photographs: the cover turned all the way over so the book can be held in one hand, and the cover laid open flat on the table. Those are the full turn and the half turn.
Fig. 2.11 (§2.8, p.27). Points A, O and B on one line with arrowheads at both ends, and the angle curve drawn at O. Note that the same picture is simultaneously a line and an angle; that double reading is the section's hinge.
The splitting figure (§2.8, p.28). Straight angle ∠AOB with a ray OC drawn upward from O, producing ∠AOC and ∠COB. A second panel shows the same figure twice, side by side, with a curved arrow suggesting one being folded onto the other.
The fold (§2.8, p.28). A rectangular sheet with A, O and B marked along one edge, folded so that OB lands on OA, then opened. Painted illustrations in the book, not photographs; redraw as three clean steps. The crease through O is the bisector, and the fold is what proves the two angles equal.
Straight angles on a dot grid (§2.8, p.30). A 7 × 6 array of dots. A is marked, B is marked, and the task is to find every straight line through A joining grid points on both sides. Two starting cases are printed — one with B level with A, one with B down and to the right — and the general move is to extend the segment BA past A to another grid point.
Right angles on the same grid (§2.8, p.30). The printed hint is the argument: extend BA past A to C so that ∠CAB is a straight angle, then look for the line through A that halves it. On a square grid the halving line is the one at the perpendicular slope, which is why the grid was chosen.
The triangle count (§2.8, p.32). Three figures. The first is a plain triangle. The second has its three side-midpoints joined, producing one inverted middle triangle. The third repeats the same midpoint construction inside that central inverted triangle, so the newest small triangle is upright and sits within the downward-pointing one, with its horizontal side below the midline — it is not in a corner triangle. The acute-angle counts are 3, 12 and 21, and the next figure in the sequence has 30. The derivation: each stage joins the midpoints of the previous stage's central triangle and so adds three new points, each sitting inside a straight segment with two new rays leaving it, which is three new acute angles per point, so nine per stage.

Figures to have open

Fig. 2.11 — A, O, B collinear with arrowheads and the curve at O. Standard schematic, but the curve must be there.
The ray-OC splitting figure and its folded counterpart (§2.8, p.28).
The paper-folding sequence (§2.8, p.28). Printed as painted illustrations; redraw as three steps — marked edge, fold, crease.
The square dot grid, 7 columns × 6 rows, with A and B placed as printed (§2.8, p.30). Needed at that size; the exercise depends on which grid points are reachable.
The three-group classification panel (§2.8, p.31) — three boxes of unlabelled angles, right angles in the middle box. Needed as three boxes; collapsing it to a list destroys the exercise.
The growing-triangle sequence (§2.8, p.32) — three figures, and a fourth the explanation constructs. This one is worth drawing carefully, since the counting argument is done on it.
No table or dataset is required.

Where this sits in the book

NCERT Class 6 Mathematics (Ganita Prakash), Chapter 2 "Lines and Angles": §2.8 Special Types of Angles, pp.27–32
Named sub-headings inside §2.8 used here: Let's Explore, p.28, and Classifying Angles, p.31 — printed without numbers, so cited by page
Figure it Out items used: §2.8, Q1 on p.29, Q2 and Q3 on p.30, Q4 on p.31, Q1–Q4 on pp.31–32
Summary, p.54, for the settled measures once degrees arrive
Forward pointer: §2.9, p.33, which puts numbers on both landmarks