Every curve in these figures is part of a circle

What to assume they know

Measuring and marking a length in centimetres and millimetres with a ruler
A point fixes a location; a segment is the shortest route between two points — a point fixes a location, and the distance between two points is a definite length
The idea that two things can be the same distance apart without being in the same place

What they should be able to do

State what the book counts as a curve, and give an example that is not bent
Describe the set of all points at a fixed distance from one point, and name the shape it forms
Identify the centre and the radius of a drawn circle
Set a compass to a stated radius using a ruler, and explain why the ruler step comes before the drawing step
Given a drawn arc, say what has to be found before it can be redrawn
Work out the radius needed for a half circle from the length it has to span
Explain why two arcs that must match need two carefully placed centres

Where it usually goes wrong

"A curve is the bendy sort of line." The book's own list of curves on p.188 includes a straight line and a closed blob alongside the circle. Curve here means drawable stroke, and that is why a figure of straight lines and arcs can be discussed as one thing.
"An arc is a different kind of object from a circle." It is a piece of one. Every arc has a centre and a radius even though the rest of its circle was never drawn — which is exactly what makes it recoverable.
"The compass draws the circle; the ruler is a separate exercise." The ruler sets the radius before the compass moves, p.189. Skip it and the circle is the right shape at the wrong size.
"The centre is somewhere on the curve." It is off the curve entirely, at the one place that is the same distance from all of it.
"Freehand is good enough if you are careful." The book has students try freehand first and then asks whether the instruments made it easier, p.189. The point of the comparison is that a compass makes a claim a hand cannot: every point of this stroke is exactly this far from that point.
"Both halves of an eye come from one compass position." Two arcs bulging opposite ways need two centres on opposite sides, p.215.

Questions to check understanding

What shape is made by all the points that are a fixed distance from a given point, and what are that shape's centre and radius called?
A half circle has to span a 6 cm line. What must the compass be opened to?
Given AB = 8 cm with the first wave a half circle, find AX and the radius (the chapter asks exactly this on p.191)
Copy a drawn arc: mark the centre you used and state the radius
Which of these drawings can be made with a compass and a ruler alone?
Explain why a straight line counts as a curve in this chapter
Draw a ring: two circles, one inside the other, sharing a centre

Examples worth working on the board

Fig. 8.1, p.187. Five drawings; every curved stroke in them is part of a circle. Checked against p.187: two equal circles side by side touching at one point; a smaller circle sitting inside a larger one about the same centre; three equal circles in a row, each overlapping the next; a mouse-like face — one large circle with two smaller circles for ears, two small circles for eyes with a filled dot inside each, one filled dot for a nose and a short straight segment for a mouth; and two straight strokes crossing in an X, with a small circle at each of the two lower ends. Nothing in the figure is labelled and none of it extracts from the text.
The 4 cm exploration, p.188. Mark P. Mark points 4 cm from P in different directions. The printed figure shows only two of them — Q at 4 cm horizontally and R at 4 cm on a slant, both on dashed lines. The book then asks what all such points would look like.
Fig. 8.2, p.189. Two panels. Left: a compass opened against a ruler graduated 0 to 7, tip and pencil straddling 4 cm. Right: the same compass drawing a circle, with P marked and the words centre and radius set as labels on the drawing.
A Person, p.190 (the first of §8.1's three named Construct items, the other two being Eyes and Wavy Wave). Two components, printed separately below the whole figure: a circle for the head with a short straight segment below it, and a four-sided body outline whose top edge has been replaced by an arc that bulges downwards. The book's own advice is to fix a radius and try the tip in different places until the arc sits right, estimating rather than calculating.
Wavy Wave, p.191. Central line AB with AB = 8 cm and a point X on it. Over AX the book puts a half circle bulging upwards; over XB, an identical one bulging down. The figure prints a question mark for the compass opening and another for AX; both are asked, not given. Inputs: AB = 8 cm; two matching half circles; each sits on its own part of AB. From those, AX = 4 cm and the compass opening is 2 cm.
Eyes, p.192, with the hint on p.215. Each eye is bounded by two arcs meeting at the two ends, with a filled circle inside it. The hint page shows two faint horizontal supporting lines and marks a point A above the eye and a point B below it as the two places the compass tip goes — one centre for the upper arc, a different one for the lower. Checked against p.215.
Later payoffs. Square with a Hole and Square with Curves, p.203, and the roof arc of the House, p.214. All three are the same problem: choose a centre and a radius. The 8 cm sidelength of Square with Curves is printed; the arc radii are not.

Figures to have open

Fig. 8.1 redrawn as five panels. This is the topic's anchor image and must be faithful in structure — touching circles, a ring, three overlapping circles, the face, the crossed strokes — but redrawn rather than reproduced.
A construction of the circle as a set: P, then points appearing all round it at a constant distance until they close up.
A compass-on-ruler schematic. Standard, does not need to come from the book.
The Wavy Wave as an annotated line: A, X, B with 8 cm, 4 cm and the 2 cm compass opening marked.
The two-centre diagram for the eye, showing the upper and lower centres on either side of the shape.
No photograph or dataset is required.

Where this sits in the book

NCERT Ganita Prakash, Class 6, Chapter 8 "Playing with Constructions", §8.1 "Artwork", pp.187–192 — Fig. 8.1 on p.187, the definition of curves and the 4 cm exploration on p.188, Fig. 8.2 with centre and radius on p.189, and the three Construct figures on pp.190–192
Hints A, p.215, for the Eyes construction
Summary, p.216, for the circle, centre and radius statement and for the line on what a compass is for
Forward pointers inside the chapter: §8.4, p.203 (Square with a Hole, Square with Curves) and §8.6, p.214 (the roof arc)