Reading and drawing an angle with a protractor

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What to assume they know

The degree: why a full turn was cut into 360 equal parts: the degree as one of 360 equal parts of a turn; the handmade protractor and the marks produced by folding
Straight and right angles as the landmarks of a full turn: straight angle 180°, right angle 90°
An angle is an amount of turn, not a pair of drawn arms: vertex, arms, and three-letter naming
Subtraction of two-digit and three-digit numbers

What they should be able to do

Describe how a protractor's scale is built — a straight angle divided into 180 unit parts, with long marks every 10° and medium marks at each 5°
Read an angle by counting unit parts when the vertex sits at the centre
Read the same angle from the numbered scale instead of by counting
Read the numbers where two arms cross the scale and subtract to get the angle
Place a protractor so that no subtraction is needed, and say why that works
Explain the purpose of the two opposing rows of numbers
Diagnose a wrong protractor placement and describe the correction
Draw an angle of a stated measure using a protractor and a ruler
Find an angle larger than 180° by measuring its companion and subtracting from 360°
Estimate an angle by eye and score the estimate against a measurement

Where it usually goes wrong

"The protractor gives the angle; you just look at it." It gives two readings. Corrected in §2.9, pp.36–37, where the chapter explicitly reads two numbers and subtracts before showing the shortcut.
"Use the outer scale." Neither scale is correct in itself. The rule is to use the row whose zero lies on your chosen arm, which is exactly why two rows are printed.
"Line the arm up with the edge of the protractor." The base edge and the zero line are not the same thing on most instruments, and several of the six faulty panels on p.44 turn on that confusion.
"If the angle is bigger than the protractor, it cannot be measured." Corrected at §2.9, p.41 — measure the rest of the turn and subtract from 360°.
"A smaller reading means a smaller angle." Not if the vertex has drifted off the centre. Section 8 is built on the fact that a wrong placement returns a perfectly confident number.
"Estimating is what you do when you have no protractor." The chapter treats it as a skill to be practised and scored, and its Teacher's Note at §2.10, p.49 asks for the game to be repeated on different days.
"The three angles of a triangle add to 180° — that is a rule we know." At this point in the book it is a conjecture drawn from measurement, and §2.9, p.43 says the explanation comes later. The explanation should not smuggle in the proof.

Questions to check understanding

Find the degree measures of several named angles in one protractor figure
Read an angle whose arms cross the scale away from zero, showing the subtraction
Identify the incorrect use of a protractor in a given picture and state the correct reading
Draw angles to stated measures — the chapter's own list is 110°, 40°, 75°, 112° and 134°
Reproduce a given angle without being told its measure, and write down the steps
Find the measure of an angle larger than a straight angle
Measure the three angles of a triangle and state what the total suggests
Compute a clock angle at a stated hour and justify it

Examples worth working on the board

The unlabelled protractor and ∠KAL (§2.9, p.35). A protractor with marks but no numbers, vertex A at the centre, and rays to K, L, W and T. The book works ∠KAL by counting unit parts and gets 30°; ∠WAL and ∠TAK are left to the student.
The labelled protractor and the six rays at O (§2.9, pp.36–37). A half-circle protractor with its centre at O, and rays to P, Q, R, S, T and U. Reading from the ray OP end of the scale, the arms sit at 0, 35, 95, 125, 160 and 180. Every angle in the figure is then a difference of two of those numbers. Working outward from each arm in turn, and all consistent with the printed figure: measured from OP the four other rays give 35°, 95°, 125° and 160°; measured from OQ they give 60°, 90°, 125° and 145°; measured from OR, 30°, 65° and 85°; measured from OS, 35° and 55°; and OT to OU is 20°.
∠TOS on the other scale (§2.9, pp.36–37). On the scale that runs the other way, OT reads 20 and OS reads 55, and 55 − 20 = 35°, matching ∠SOT above. This is the cleanest demonstration that the choice of scale does not change the answer, only the two numbers you subtract.
∠AOB with an arm on zero (§2.9, p.37). The same protractor placed so that OB runs along the base through the zero mark, and OA rises from O. One reading is zero, so the other reading is the measure. The book asks for the value and does not print it.
Mind the Mistake, Mend the Mistake! (§2.9, p.44). Six panels, each showing a protractor placed on an angle and a stated reading: ∠U = 35°, ∠V = 80°, ∠W = 70°, ∠X = 150°, ∠Y = 120°, ∠Z = 85°. In each the placement is wrong — vertex off the centre, the arm not laid along zero, the protractor tilted or turned over. The exercise is to name the fault and say what the reading should have been. Do not present the six printed numbers as measurements; they are the errors.
Drawing ∠TIN = 30° (§2.10, pp.46–48, Fig. 2.22). Four steps: draw the base ray IN; put the protractor's centre on I with IN along the zero line; count up to 30 and mark T; join I to T with a ruler. Note that the drawing procedure is the reading procedure run backwards, which is the point of putting the two sections together.
Reading a reflex angle (§2.9, p.41, Q4). An angle whose marked opening is bigger than the protractor. Measure the unmarked opening instead and subtract from 360°. The answers supplement bundled with the chapter PDF works it as 360° − 100° = 260°.
Angles at one vertex on a straight line (§2.9, p.42, Q6). X sits on the straight line AE with two further rays XB and XC. Taking the readings off the printed figure gives ∠AXB = 65°, ∠BXC = 30°, ∠CXE = 85°, and hence ∠BXE = 115°. The check: 65 + 30 + 85 = 180, and 65 + 115 = 180.
The clock (§2.9, p.45). Twelve equal intervals fill 360°, so one interval is 30°. At one o'clock the hands stand 30° apart, and up to six o'clock each further hour adds another 30° — 60° at two, 90° at three, 120° at four, 180° at six. The printed question asks only for two, four and six, and the rule has to stop there: past a half turn, n × 30° measures the turn the hour hand has made and so names the reflex angle, while the two hands stand 360° − n × 30° apart. At nine that is 360° − 270° = 90°, at seven 150° and at eight 120°.
The game scoring (§2.10, pp.48–49). A team scores the size of its error: guessing 39° against a true 49° scores 10; drawing 25° when 34° was called scores 9. Lowest total wins — the scoring is a distance, so it rewards accuracy in both directions.
Fig. 2.21, the angle-sum conjecture (§2.9, p.43, Q9). Three differently shaped triangles, each labelled A, B, C. Measure all three angles of each and add. The chapter asks for a conjecture and states that the reason is left for a later year.

Figures to have open

The unlabelled protractor (§2.9, p.35) with the K, L, W, T rays. Needed as drawn; the whole of sections 1 to 3 depends on the marks being visible and the numbers absent.
The labelled protractor with the six rays at O (§2.9, p.36). Needed as drawn, with both number rows legible. This is the topic's central figure.
The zero-aligned placement figure for ∠AOB (§2.9, p.37).
The six-panel misuse figure (§2.9, p.44). Needed as six; the printed labels ∠U, ∠V, ∠W, ∠X, ∠Y, ∠Z and their wrong values must be kept.
The four drawing steps for ∠TIN (§2.10, pp.47–48). Step 1 is a plain base ray and Steps 2 and 3 are the only two protractor figures, all three on p.47; Fig. 2.22 itself is Step 4 on p.48, the finished angle with a ruler laid along the second arm.
The reflex-angle item (§2.9, p.41, Q4) and the straight-line figure at X (§2.9, p.42, Q6).
The three clock faces (§2.9, p.45) and Fig. 2.21's three triangles (§2.9, p.43).
All of the above are line art or photographs of instruments and may be redrawn; none is a dataset.

Where this sits in the book

NCERT Class 6 Mathematics (Ganita Prakash), Chapter 2 "Lines and Angles": §2.9 Measuring Angles, pp.35–37 and pp.41–46; §2.10 Drawing Angles, pp.46–50
Named sub-headings inside §2.9 used here: Unlabelled protractor, p.35; Labelled protractor, p.36; the protractor-misuse panel, p.44; Where are the angles?, p.45 — all printed without numbers, so cited by page
Named blocks inside §2.10: Let's Play a Game #1, p.48; Let's Play a Game #2, pp.48–49; Teacher's Note, p.49
Figure it Out items used: §2.9, Q1 on p.35, Q1 on p.40, Q3–Q5 on pp.41–42, Q6 and Q7 on p.42, Q9 on p.43, Q1 on p.45; §2.10, Q1 on p.49, Q2 and Q3 on p.50
Summary, p.54, for the settled statement that degree measures are read with a protractor