Sea level and freezing point: zero as a chosen reference, not an absence

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What to assume they know

Numbering the floors below the ground: why zero needs another side: Floor 0 as a chosen reference rather than an absence
Laying the integers out in order, and why −8 is less than −2: ordering integers, including two negatives
Subtraction as the movement that gets you from start to target: a difference as the change between two positions
Reading a value off a marked vertical scale, and the metre and the degree as units

What they should be able to do

State what heights on a geographical cross section are measured from
Read approximate heights, positive and negative, off a marked height axis
Arrange marked points in increasing or decreasing order of height
Explain what it means for a place to have a negative height
Read a thermometer scale that continues below its zero mark
State what 0 °C stands for, and say why it is not the absence of temperature
Compare two temperatures below 0 °C correctly
Match a set of temperature readings to plausible times of day, and justify the matching
Identify, in a new setting, what has been chosen as the reference and what would change if a different one were chosen

Where it usually goes wrong

"0 °C means there is no heat." It is the point at which water freezes and nothing more. Temperatures well below it exist, and a student who thinks 0 is the bottom cannot read the lower half of the thermometer.
"Sea level is 0 because the sea is empty." The sea is not the absence of land; it is where the land happens to be at the height everyone agreed to call 0.
"– 4 °C is warmer than – 2 °C, because 4 is more." The same error as – 8 against – 2, in a setting where it has consequences. Put both on the thermometer.
"A negative height means a place under water." It means a place below the chosen reference surface. Some of those places are under water and some are dry land that sits below sea level.
"You can read the exact heights off the cross section." You cannot, and the book does not ask you to. This exercise is about approximate reading, and saying so protects the student from thinking they got it wrong.
"Every scale has its zero at the bottom." These two do not, and neither did the lift. The chapter has now shown the same structure three times in three settings.

Questions to check understanding

Read a stated point's height off a cross section, to the nearest labelled rule
Order a set of marked points by height
State the height of a place described as lying below sea level, with its sign
Compare two temperatures below 0 °C
Say what 0 °C represents
Compute the fall in temperature between two stated readings
Match temperature readings to times of day and justify the matching
The solutions block bound with this chapter file answers the p.261 and p.262 exercises on its footer pages 10–11

Examples worth working on the board

The height axis (p.261). Checked against the printed page. The printed chart carries a vertical axis labelled in metres at 1500, 1000, 500, 0, – 500, – 1000 and – 1500, with the 0 line labelled as sea level and finer dotted rules between the labelled ones. The profile begins on the sea-level line at the left edge of the frame and then crosses that line six times, once between each labelled point and the next.
The seven marked points (p.261). A, B, C, D, E, F and G sit on the profile, three of them below the sea-level line — B, D and F — and four above it — A, C, E and G. The task is to read each height off the axis. The values are approximate by design — this is the chapter's one exercise in reading a scale rather than computing on it.
The two extremes (p.261). The book asks which marked point is highest and which is lowest, and then leaves the drawing entirely to ask the same two questions about the real Earth, requiring the second answer to come out negative.
The boxed note to the teacher (p.261). It explains a cross section as a vertical slice through the ground seen from the side. That sentence is the one thing a student needs before the chart makes sense, and it is addressed to the teacher rather than the reader.
The two thermometers (p.262). Checked against the printed page. Both are drawn with a scale running from – 20 up to 100 in tens, the zero mark plainly not at the bottom. The running text states what the two are reading: 40 °C and 15 °C.
The Leh table (p.262). Four readings — 14 °C, 8 °C, – 2 °C and – 4 °C — to be matched with four times: 02:00 a.m., 11:00 p.m., 02:00 p.m. and 11:00 a.m. The table prints them deliberately out of correspondence.
The second note to the teacher (p.263). It asks for a laboratory thermometer in class, for hot and cold water to be measured, and for the marks below zero to be pointed out — and it is where the book states what 0 °C is.
The places in India that go below 0 °C (p.262). The book asks the class to find them and to say what those places have in common. Do not answer it when explaining it; it is a research prompt and the pattern the class is meant to notice is the point.

Figures to have open

A geographical cross section with a labelled height axis running from – 1500 m to 1500 m in 500 m steps, a sea-level line at 0, and seven marked points on the profile. Redraw; what must survive is that three points lie below the line and four above it, and that the axis is symmetric about 0.
A thermometer whose scale continues below its zero mark, drawn large enough that the negative marks are legible. This is the figure the whole second half depends on.
A three-way comparison panel for section 11, holding the lift shaft, the sea-level axis and the thermometer at the same scale so the shared structure is visible in one frame.
No photograph is required, though a photograph of a real laboratory thermometer would serve section 8 well.

Where this sits in the book

NCERT Ganita Prakash, Class 6, Chapter 10 "The Other Side of Zero", §10.3 "Integers in Other Places", p.260 — the named sub-heading on geographical cross sections, sea level as 0 m, and the convention for heights above and below it
§10.3, p.261 — the cross-section chart, the seven marked points, the two ordering questions, the two real-Earth questions, and the boxed note to the teacher
§10.3, p.262 — the named sub-heading on temperature, the Celsius unit, the two thermometers, the question about places in India, and the Leh table
§10.3, p.263 — the second boxed note to the teacher, and what 0 °C is stated to be
Chapter Summary, p.270, for the book's own restatement of both interpretations
Solutions block bound with this chapter file, footer pages 10–11