Acute, obtuse and reflex: one classification covering every angle

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What to assume they know

Straight and right angles as the landmarks of a full turn: the straight, right, acute and obtuse angles, introduced there by comparison and without numbers
The degree: why a full turn was cut into 360 equal parts: the degree, and 360° in a full turn
Reading and drawing an angle with a protractor: reading and drawing an angle with a protractor
Comparing two numbers, and the strict-inequality language of "more than" and "less than"

What they should be able to do

State the degree measures of a straight angle and a right angle
Define an acute angle by two bounds, and give examples
Define an obtuse angle by two bounds, and give examples
Explain why the classification is incomplete before reflex angles are added
Define a reflex angle by two bounds
Classify a measured angle correctly, including at the boundary values
Recognise that one pair of arms carries two angles summing to 360°, and read the marked curve to tell which is meant
Produce angles of each type on a dot grid and mark the intended angle
Use a straight angle to find an unknown angle by subtraction
Draw a figure to a specification given as a list of angle types or measures
Solve a numerical puzzle whose answer is a range rather than a single value

Where it usually goes wrong

"A right angle is a kind of acute angle, since it is not obtuse." The bounds are strict: acute stops below 90°, obtuse starts above it, and 90° is its own name. Corrected by reading the two definitions on pp.50–51 side by side.
"Every angle is acute, right or obtuse." This is exactly the belief §2.11, p.51 interrupts, by asking whether all possible measures have been covered.
"A reflex angle is a mistake in the drawing." It is the other angle at the same vertex, and it is chosen by the curve. Corrected in §2.11, p.52 by an exercise that asks for both.
"180° is a reflex angle because the arms are spread wide." Reflex begins above 180°; 180° is the straight angle. Corrected by the strict wording of the reflex definition on p.51.
"An angle can be 360°, or 0°." Neither end is included by the chapter's four named groups — acute starts above 0° and reflex stops below 360°. Worth naming as an open edge rather than glossing over, since students notice it.
"Classifying is guessing from the picture." The chapter's own exercise (p.52, Q2) requires measuring first and classifying second, in that order.

Questions to check understanding

Measure each angle in a figure, then say whether it is acute, right, obtuse or reflex
Draw angles to stated measures, including one above 180° — the chapter's own list is 140°, 82°, 195°, 70° and 35°
Estimate an angle, then measure it, then classify it
Construct a figure containing a stated number of acute, right and obtuse angles
Draw a letter shape to given angle measures
Find an unknown angle using a straight angle or a right angle and subtraction
Compute the angle between adjacent spokes of an evenly spoked wheel, and the largest acute angle it can form
Range puzzles: find all whole-degree measures satisfying stated multiples

Examples worth working on the board

The acute examples (§2.11, p.50). Three drawn angles carrying their measures: 40° at vertex P between rays PR and PQ; 50° at vertex T between rays TS and TR; 75° at vertex F between rays FQ and FE. Different orientations, all under 90°.
The obtuse examples (§2.11, p.51). Two drawn angles: 110° at vertex I between rays IX and IS, and 130° at vertex W between rays WT and WS.
The reflex examples (§2.11, p.51). Two drawn angles, each with a large curve sweeping the long way round the vertex — one at A with arms towards P and B, one at M with arms towards T and S. The curves carry no numbers; the sweep is the whole information, and it is drawn, not printed.
∠PTW and ∠WTP (§2.11, p.52, Q2). One vertex T with four rays, to P, R, Q and W, and a reflex curve drawn round T. The exercise asks for four measures and their classifications, and it lists ∠PTW and ∠WTP as two separate items — so the two letter-orders are being used to distinguish the small angle from the reflex one. Whatever the two values, they must total 360°.
The 80° split (§2.11, p.53). Rays ES and ET rise from E on the straight line BR, with 80° marked for ∠TER and 90° marked for ∠SER. Because ∠REB is a straight angle, ∠BET = 180° − 80° = 100°, and ∠SET = 90° − 80° = 10°. Two subtractions from two different landmarks — that contrast is the exercise.
The letters M and Y (§2.11, p.53, Q4 and Q5). An 'M' whose two outer angles are 40° each and whose middle angle is 60°; a 'Y' whose three angles are 150°, 60° and 150°. The Y is worth dwelling on: its three angles meet at one point and 150 + 60 + 150 = 360, so the specification is a full turn split three ways. The M's three numbers carry no such constraint — they are simply a drawing brief.
The Ashoka Chakra (§2.11, p.54, Q6). 24 spokes evenly spaced, so the angle between neighbouring spokes is 360 ÷ 24 = 15°. The largest acute angle available between two spokes is the largest multiple of 15 that stays under 90°, which is 75°.
The puzzle (§2.11, p.54, Q7). An acute angle whose double, triple and quadruple are all still acute, but whose quintuple is obtuse. Quadruple under 90° forces the measure under 22.5°; quintuple over 90° forces it over 18°. So it lies strictly between 18° and 22.5°, and in whole degrees that is 19, 20, 21 or 22.

Figures to have open

The three acute examples with their printed measures (§2.11, p.50) and the two obtuse examples (§2.11, p.51). Standard schematics, but keep the varied orientations — that variety is the point of printing three.
The two reflex examples (§2.11, p.51). These must carry the long sweeping curve; without it the figures read as ordinary acute and obtuse angles. The curve is drawn art and appears nowhere in the extracted text.
The four-ray figure at T with its reflex curve (§2.11, p.52). Needed as drawn.
The dot grids for the acute, obtuse and reflex constructions — two grids for each of the three parts, each 7 columns × 6 rows; part (a) is on p.51, parts (b) and (c) on p.52. Exactly one of the six is worked as a model, the left-hand grid of part (a), which carries a second arm and the marking curve; the other five carry a single drawn segment only. No letter A is printed on any of the six: the vertex is only the endpoint of that drawn segment, so the redraw has to mark A itself or the exercise cannot be read. (Contrast the §2.8 grids on p.30, which do print A and B.)
The 80° figure at E on the line BR (§2.11, p.53).
The six unlabelled angles for estimation (§2.11, p.53, Q2).
The Ashoka Chakra image (§2.11, p.54). The 24 spokes must be countable.
A single scale strip from 0° to 360° carrying all five names. This is an added figure; the chapter states the ranges in prose and never draws them on one axis, and drawing them is the argument of the topic.

Where this sits in the book

NCERT Class 6 Mathematics (Ganita Prakash), Chapter 2 "Lines and Angles": §2.11 Types of Angles and their Measures, pp.50–54
Named blocks inside §2.11 used here: Let's Explore, p.53 — printed without a number, so cited by page
Figure it Out items used: §2.11, Q1 on pp.51–52 and Q2 on p.52; Q1–Q5 on p.53; Q6 and Q7 on p.54
Backward pointer: §2.8, pp.31–32, where acute and obtuse first appear without degree measures
Summary, p.54, which lists all five types with their ranges