Why whole units are not enough to measure with

What to assume they know

Reading a length off a ruler against whole-centimetre marks (Class 6)
The idea of a fraction as some number of equal parts of one whole
Recognising halves and quarters of a length
Comparing two fractions with the same denominator
When an approximate answer is the better answer — the idea that an answer can be usefully approximate rather than exact (Part I, Chapter 1)

What they should be able to do

Explain why a difference too small to see can still decide whether an object works
Read the same length on rulers marked in whole units, in halves and in tenths, and write down what each ruler entitles you to say
Say why a coarse reading is not a wrong reading, and what a finer ruler adds
Write a measured length as a whole number of units plus a number of tenths
Read such a length aloud in the form the chapter uses
Given a length that falls between two marks, state the two numbers it lies between
Describe, in general, the move the chapter makes when an answer must be sharper: cut the unit into equal parts rather than change the unit

Where it usually goes wrong

"The first two readings were wrong and the third was right." All three are true of the same screw. The screw is between 2 cm and 3 cm; it is also more than 2½ cm and less than 3 cm; it is also 2 and 7 tenths. Each reading rules out more than the last. Getting this backwards turns the whole chapter into a story about correcting errors, which it is not.
"2 and 7 tenths is the exact length." It is exact to a tenth. The very next section takes the same move again and splits each tenth into ten, for the same reason. A student who thinks the tenth-scale ends the story will find §3.3 unmotivated.
"Small differences do not matter." The opening scene exists to kill this. The two screws differ by an amount nobody can see, and one of them fails.
"To measure something small you need a smaller unit." The chapter's move is to cut the unit you already have into equal parts, and to keep the unit's name. A separate small unit — the millimetre — does arrive, but not until §3.5, and it turns out to be one of these parts rather than an independent idea.
"2½ cm and 2 and 5 tenths cm are different lengths." They are the same length read off differently marked rulers. The half-marked ruler is not wrong, it is just cut a different way — a point the chapter returns to head-on at Part I, §3.4, p.59.
"The number of marks is what makes a ruler good." What matters is that the parts are equal. Every split in this chapter is into equal parts, and the word does real work.

Questions to check understanding

Given a drawing of an object above a marked scale, write its length in units and tenths
Given a length, say which two whole numbers it lies between
Given two scales, say which one can tell two nearly equal lengths apart, and justify it
Read a length written in units-and-tenths form aloud, and write down a length read aloud to you
Explain why a reading such as "between 2 cm and 3 cm" is a useful answer even though it names no single number
Measure a real object and state the reading together with the scale it was read on

Examples worth working on the board

The screw that was the wrong size (Part I, §3.1, p.46). Two screws from the same box, indistinguishable by eye, one of which fixes the toy and one of which does not. The page carries two drawings — a parent holding a screw over a toy, and a boy looking at two screws side by side. Checked p.46; both are artwork and extract as nothing.
The three-ruler figure (Part I, §3.1, p.47). Read. Three photographs of the same screw, each above a different ruler, all three rulers running 0 to 3. Top ruler: marks at whole numbers only, and the printed answer names two whole numbers, 2 and 3. Middle ruler: marks at whole numbers and halves, and the printed answer uses 2½ and 3. Bottom ruler: marks at tenths, and the printed answer is a single value, 2 and 7 tenths of a centimetre. The right-hand half of the same figure repeats all three rulers under a second screw and leaves the three answers blank for the student.
The second reading the page supplies (Part I, §3.1, p.47). 3 and 2 tenths of a centimetre, offered so the student sees the written form twice.
How the tenth-scale reading is built (Part I, §3.1, p.47). Travel from 0 to 2, then take seven of the ten parts that fill the next centimetre.
Three objects on tenth-scales (Part I, §3.1, p.48). An eraser, a pencil and a piece of chalk, each drawn above its own tenth-marked ruler, with the measurements left blank. Do not supply values for these — the printed page gives none.
Objects to measure yourself (Part I, §3.1, p.47). A pen and a sharpener, plus anything the student chooses. No values are printed.

Figures to have open

The three-ruler screw figure. This is the topic. Redraw rather than lift: a single screw graphic repeated three times over three rulers whose only difference is where the marks fall. The printed version is photographic and its labels sit outside the artwork.
A pair of near-identical screws with the difference exaggerated in a callout. Standard schematic.
A tenth-marked ruler with the ten parts of one unit individually visible. Standard schematic; needed again in the next topic.
No photograph from the textbook is required.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 3 "A Peek Beyond the Point", §3.1 The Need for Smaller Units, pp.46–48. The three-ruler figure and both worked readings are on p.47; the three objects on tenth-scales and the closing sentence of the section are on p.48.
Forward pointers inside the same chapter: Part I, §3.2, pp.48–52, which builds arithmetic on the tenth; Part I, §3.4, p.59, which asks outright why the unit is split into ten rather than four; Part I, §3.5, p.64, where the millimetre is identified as a tenth of a centimetre.
Backward pointer: Part I, Chapter 1, §1.4, for approximate versus exact values.