The arithmetic mean as fair-share

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What to assume they know

Division with a remainder, and division giving a decimal answer
Turning a vague comparison into a question with a data answer — a statistical question is one that data has to settle, because the values vary
Reading a small table with a blank cell in it
Class 6 Ganita Prakash: adding a short list of whole numbers reliably
When an approximate answer is the better answer — comfort with an answer stated as "about"

What they should be able to do

State why the total of a group is not a fair basis for comparing two groups of different sizes
Compute the arithmetic mean of a small data set from its total and its count
Explain the mean as an equal share: the value every member would hold if the total were levelled out
Say what the mean of a rate-like quantity means — flowers per day, runs per match, guavas per person
Decide what the denominator should be when a value is missing (a match not played) rather than zero
Recognise the mean in everyday statements about rainfall, mileage, yield and waste, and name the group each one summarises
Connect the mean to the Indian mathematical tradition that named it after sama, "equal"

Where it usually goes wrong

"The bigger total wins." The guava example on p.100 is engineered to kill this: two groups, one total, different shares. Show it before any formula.
"The average is always one of the numbers you started with." The chapter supplies the counter-example itself: Vaishnavi's five days are 2, 7, 9, 4, 3 and the printed average is 5, which is not one of those five values (Part II, §5.2, p.100). The bounce set is the coincidence — 6, 2, 9, 5, 4, 6, 3, 5 also averages 5, and there a 5 does appear, twice (Part II, §5.2, "Figure it Out" 1, p.101). Put the two side by side, and reinforce it with the enrolment figures, which average to a number no year actually had.
"Dividing by the number of values is just the recipe." It is the sharing. If the explanation cannot say what is being shared among whom for a given data set, it has not understood that data set.
"A blank cell counts as a zero." The dash in Yashasvi's Match 4 means he did not bat; a 0 would mean he batted and scored nothing. Counting it as a 0 changes the denominator and leaves the total alone; leaving it out changes neither. The chapter separates the two explicitly later, at Part II, §5.2, p.111 — flag it here and hand it forward.
"An average always describes each member well." It does here, because these examples are tame. It fails badly in the very next sub-section — hold this misconception open rather than closing it, and hand it to Outliers, and why the median survives them.
"Average and total are two words for the same idea." They answer different questions: how much altogether, versus how much each. The chapter's opening disagreement is exactly two students using the two words as if they were one.

Questions to check understanding

Compute the mean of a short list of whole numbers or decimals
Compare two groups of unequal size and say why the totals do not settle it
Work backwards: given the mean and the count, find the total; given the mean and the total, find the count
Given a set with one value missing and a stated mean, find the missing value
Decide whether a missing entry should reduce the denominator or count as zero, and justify it
"The mean of these five numbers is 12. What happens to it if a sixth value of 30 is added?" — the standard lead-in to outliers
Interpret an average of a rate in words: what would have to be true for every day/litre/hectare for the average to be the actual value

Examples worth working on the board

First cricket series (Part II, §5.2, p.98). Four matches each. Shubman 0, 17, 21, 90. Yashasvi 67, 55, 18, 35. The chapter prints three rival readings on pp.98–99: same-ish because each was ahead in two matches; Shubman because he made the single highest score; Yashasvi because his total is larger. A fourth reading is offered — Yashasvi is steadier because his highest and lowest sit closer together.
Second cricket series (Part II, §5.2, p.99). Checked against p.99. Shubman 23, 07, 10, 52, 18 across five matches. Yashasvi 26, 53, 02, —, 15, where the dash in Match 4 means he did not play, so his count is four. The chapter's own totals are 110 and 96. Printing slip on this page: the worked line divides 110 by 5 and prints the result as 21. It is 22. The conclusion the page draws is unaffected (24 is larger than 22 as it is larger than 21), but an explanation that reads the printed digit aloud will teach a wrong division. Say 22.
The guava groups (Part II, §5.2, p.100). Checked against p.100. Shreyas and four friends collect 3, 8, 10, 5, 4 — five pickers. Parag and five friends collect 5, 4, 6, 3, 4, 8 — six pickers. Both groups total 30. This is the cleanest example in the chapter, because the totals are identical and the shares are not; use it as the proof that a total cannot decide the question.
The levelling picture (Part II, §5.2, p.100). Checked against the printed page. Four panels of stacked guava icons: each group's ragged columns on the left, an arrow, and the same fruit redistributed into columns of equal height on the right, with the sum written under both. Rebuild this as a movement — bars slumping into a flat row is the single most useful image in the topic.
Vaishnavi's hibiscus (Part II, §5.2, pp.100–101). Five days: 2, 7, 9, 4, 3. The chapter's gloss on the answer is the important part — it is the count you would see each day if the same number bloomed daily. Keep that conditional.
The Sanskrit names (Part II, §5.2, p.101). Five terms, five scholars, with the dates the book prints. Brahmagupta used samarajju in 628 CE, glossing it as a mean measure of a line. In 850 CE Mahāvīrācārya used samīkaraṇa — levelling, or equalising. Śrīpati, writing in 1039 CE, used sāmya, which carries equality and impartiality. samamiti, a mean measure, is used by Bhāskarācārya in 1150 CE and by Gaṇeṣa four centuries after him, in 1545 CE. Every one of the five is built on sama, meaning equal, which the chapter points out itself. Put the five on one timeline.
Figure it Out (Part II, §5.2, p.101). Four sets of numbers, all give-able raw. Bat-and-ball bounces over 8 attempts: 6, 2, 9, 5, 4, 6, 3, 5. Sprint times in seconds over a week — Nikhil 17, 18, 17, 16, 19, 17, 18; Sunil 20, 18, 18, 17, 16, 16, 17. School enrolment over six years: 1555, 1670, 1750, 2013, 2040, 2126. Note for whoever writes the explanation: the two runners' sets are built to come out level, so "who ran quicker on average" has a deliberately flat answer. Do not let the script pick a winner before doing the arithmetic.
Averages Around Us (Part II, §5.2, pp.104–105). Six statements printed as artwork; checked against p.105. In paraphrase: July rainfall in Jharkhand averaging 37.2 mm a day; a scooter returning about 45 km per litre; wheat yields of 4.7 tonnes per hectare in Punjab against 2.9 in Bihar; phones checked 58 times a day; 0.45 kg of waste generated per person per day; 3126 Indian feature films released annually on average between 2017 and 2024. For each, the explanation's job is to name the group being averaged over — days, litres, hectares, people, years.

Figures to have open

The two score tables. Standard schematic; the second must show the empty cell as a dash and not as a zero.
The levelling picture: two before-and-after pairs of stacked-unit columns. This is the book's own artwork on p.100 and it carries the argument, so redraw it — ragged bars on the left, an arrow, flat bars on the right, sums written underneath both.
A timeline strip for the five Sanskrit terms, 600 CE to 1600 CE.
Six statement cards for "Averages Around Us". Standard schematic; the book's own are drawn as coloured panels, so redraw rather than lift.
No figure needs to be taken from the textbook.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part II, printed Chapter 5, "Connecting the Dots...", §5.2 "Representative Values", pp.98–101 and pp.104–105. Within §5.2 the named sub-headings used are "Average as Fair-Share" (p.100), the first "Figure it Out" (p.101) and "Averages Around Us" (pp.104–105); none of these carries a number, because the book prints only one level of section numbering.
The SUMMARY restatement of the mean is at Part II, p.134.
Source file gegp205.pdf / gegp205.txt, printed pp.97–135; PDF page 1 is printed page 97.