Perimeter as the distance all the way round

What to assume they know

A point fixes a location; a segment is the shortest route between two points: a line segment, and the length of one
Shapes come in sequences too, with rules of their own: shape sequences, where regular polygons were first met as a family
Measuring a length in centimetres and metres with a scale or measuring tape
Multiplying and dividing whole numbers, and adding lengths in the same unit

What they should be able to do

State what perimeter measures and why it is a length, not a region
Compute the perimeter of a polygon from its side lengths
Recognise, in a word problem, when the quantity wanted is a perimeter — lace, tape, fencing, rope, a lap of a track
Given a perimeter and all but one side, recover the missing side
Compare two closed paths that are run different numbers of times, and decide which total distance is longer
Locate a position part-way round a closed track, given the distance run
Explain why a step across a grid diagonal is longer than a step along it
Record the perimeter of a dot-grid figure in the book's two-unit shorthand, and say why one number will not do

Where it usually goes wrong

"Perimeter is how much space is inside." The commonest error in the whole chapter, and the reason the book opens with running, buying lace and fencing — every one of those is a length you pay for by the metre.
"The longer track means the longer run." Toshi's loop is shorter than Akshi's and Toshi still covers more ground, because she goes round more times. Distance run is laps × perimeter.
"Three rounds of rope needs three times the length of the field." It needs three times the perimeter. Question 6 on p.132 exists to catch exactly this.
"Nine steps means nine units." The heart of section 10. A step is only a unit if all steps are equal, and on a dot grid they are not.
"So the diagonal is about the same, call it 9." Toshi does not say "roughly more"; she says it cannot be 9. Play the disagreement out and let the measurement settle it, rather than announcing the answer.
"6s + 3d should be simplified to 9 units." It must not be. The book keeps the two letters apart precisely because the two steps are different lengths; collapsing them throws away the whole point.
"Only shapes with a formula have a perimeter." The newspaper cut-outs in Estimate and Verify have no formula at all and still have a definite boundary length.

Questions to check understanding

Find the perimeter of a polygon from its side lengths
Find a missing side given the perimeter and the other sides
Convert a "how much lace / fencing / tape / rope" question into a perimeter
Total distance from laps and track dimensions, and which of two runners went further
Position a runner part-way round a closed track after a stated distance
Rebend a fixed length of wire or string into a different equal-sided figure
Express the perimeter of a dot-grid figure in straight and diagonal units
Cost problems: perimeter × rate per metre
The answer key appended to the cached PDF covers the p.132 set across its footer pages 1 and 2, the p.133 questions and the p.134 Deep Dive on footer page 2, and the p.135 s-and-d exercise on footer page 3

Examples worth working on the board

The definition (p.129). Perimeter is what you cover by travelling the boundary once. For a polygon the book immediately turns that into arithmetic: add the side lengths. Section 2 should make the why explicit — the boundary of a polygon is straight pieces laid end to end, so walking it and adding it are the same act.
Akshi's tablecloth (p.131). A rectangular tablecloth 3 m by 2 m; lace is wanted all round it. Printed answer: 10 m.
Usha's park (p.131). A square park whose side is 75 m, three rounds. Printed working: one round is 300 m, three rounds 900 m.
The p.132 set. (1a) a rectangle of perimeter 14 cm with breadth 2 cm, find the length; (1b) a square of perimeter 20 cm, find the side; (1c) a rectangle of perimeter 12 m with length 3 m, find the breadth; (2) a 5 cm by 3 cm rectangle of wire straightened and bent into a square; (3) a triangle of perimeter 55 cm with two sides 20 cm and 14 cm; (4) fencing a 150 m by 120 m park at ₹40 per metre; (5) a 36 cm string bent into a square, an equal-sided triangle, and an equal-sided six-sided figure; (6) a 230 m by 160 m field fenced with three rounds of rope, drawn as a three-rail fence.
Matha Pachchi! (p.133). Two nested rectangular tracks drawn one inside the other. Outer track: 70 m by 40 m — the book prints that one round of it is 220 m. Inner track: 60 m by 30 m. Akshi runs the outer track for 5 rounds, Toshi the inner for 7. Marker dots are drawn round both rectangles at 10 m intervals — and the questions on pp.133–134 use those dots to ask where each runner stands after 250 m, 500 m and 1000 m. The two starting points are labelled separately and a flag is drawn on the shared side.
Deep Dive (p.134). Two concentric square tracks, inner side 100 m and outer side 150 m, with a single finish line drawn through the middle of one side of both. The race is 350 m. The reader marks the two starting points, A on the inner track and B on the outer.
Estimate and Verify (p.134). Cut random shapes from newspaper, estimate the length round each, then check with a scale or measuring tape. This is the chapter's own bridge between the idea and the instrument.
The nine-units argument (pp.134–135). On a square dot grid the book draws a right-angled triangle in two colours: red along the grid, blue across it. Read off the printed page, the red top edge spans 3 grid steps, the red left edge spans 3 grid steps, and the blue hypotenuse cuts diagonally across 3 grid squares. Akshi's speech bubble claims a perimeter of 9 units; Toshi's replies that it must be more. The reader is asked to lay one red segment against one blue one and see whether they match. The book then names the red edges straight and the blue ones diagonal, and records this triangle as 6s + 3d units.
Four figures in s and d (p.135). Four closed figures drawn on the same dot grid, in purple, pink, green and dark red, the last shaped like the letter N. The reader writes each perimeter in straight and diagonal units. I reconstructed all four from the printed page and worked them out independently: purple 8s + 2d, pink 4s + 6d, green 12s + 6d, dark-red 18s + 6d. The same four values are given in the answer key appended to the cached PDF. These exact four figures come back on p.140 to be measured for area instead — see Estimating the area of a shape with no formula.

Figures to have open

The two nested rectangular running tracks with their 10 m marker dots, the two labelled starting points and the flag. This is the topic's central figure and must match the printed one on p.133, because the marking questions depend on the dots being where the book puts them. Redraw rather than reproduce.
The two concentric square tracks with one shared finish line (p.134). Standard schematic.
The dot-grid right triangle in two colours (pp.134–135), with the straight and diagonal edges distinguishable, plus an inset that lays one red segment against one blue segment so the difference is visible rather than asserted.
The four dot-grid figures of p.135. Redraw on the same lattice; the explanation needs them again in Estimating the area of a shape with no formula, and the two videos must show the same four figures.
No photograph or textbook data table is needed.

Where this sits in the book

NCERT Ganita Prakash, Class 6, Chapter 6 "Perimeter and Area", §6.1 "Perimeter", pp.129–136 — the definition (p.129), the two worked examples (p.131), the Figure it Out set (p.132), Matha Pachchi! (pp.133–134), Deep Dive and Estimate and Verify (p.134), the nine-units disagreement (pp.134–135) and the straight-and-diagonal notation with its four figures (p.135)
Chapter Summary, p.150, for the book's own closing statement about the perimeter of a polygon
Companion topics The rectangle and square formulas are shortcuts for the same addition (the rectangle and square shortcuts) and Triangles and regular polygons: when equal sides let you multiply (equal sides and regular polygons)
Solutions appendix bound into the cached PDF after the book's last printed page, footer pages 1–3, for the §6.1 exercises