Turning an argument into a question you can settle with data

What to assume they know

• Counting a set of objects reliably, and comparing two counts
• Reading a simple list where each entry pairs a name with a word
• Mathematics is the search for patterns *and* for why they hold — the habit of asking not only what the pattern is but why it holds; this chapter asks the same of a claim about people
• No prior work on tables, tallies or graphs is assumed

What they should be able to do

• State what this book means by data, and give an example that is not numbers
• Distinguish a question that requires collecting new data from one answered by a fact already known, and justify the sorting
• Given a disagreement about a group's preferences, restate it as a question naming the group to be asked and the thing to be recorded
• Explain why a personal favourite is not evidence about a class
• Collect a small set of first-hand data from classmates and record it as a list
• Explain, from the book's own example, why an unordered list of responses is data but is not yet an answer
• Identify the group being described when a claim is made, and say what would change if a different group were asked

Where it usually goes wrong

• "I already know the answer, so collecting is a formality." This is exactly Navya's position on p.74, and the printed list refutes it: cricket comes joint second. The chapter is built so that the confident guess loses.
• "Data means numbers." The book's own definition names facts, observations and descriptions alongside numbers, and its first example is a list of colours (p.74). A column of game names is data.
• "Any question can be answered by asking people." India's capital city can be put to thirty-one classmates and is still not settled by their replies — it is settled by a recorded fact, and surveying it measures only what people happen to believe.
• "More responses is always better." The chapter's questions are about a named class. Asking a hundred strangers answers a different question. Fix the group first.
• **"The list is the answer."** The book stages this directly: Navya announces she can now find the winner, and other children say they cannot see it. Data and a readable answer are two different things — that gap is the next topic.
• "My favourite counts extra because I feel strongly." Every entry in the list is one entry.

Questions to check understanding

Class 6 has no board paper, so these are the question shapes the book itself uses and that school and competency-based assessments repeat:

• Given a described situation, decide whether data must be collected or a known fact consulted, and justify it (the book's own Pari item, p.75)
• Given an unsorted list of responses, name the category that occurs most often
• Rewrite a vague claim ("everyone likes hockey") as a question that names the group and the thing to be recorded
• Explain why one person's preference is not evidence about a class
• Design a short collection: what will you ask, whom, and how will you record it
• Identify which of several conclusions a given data set actually supports

Examples worth working on the board

• The disagreement. Navya's favourite is cricket and she believes cricket is the class's most popular game; Naresh plays cricket sometimes but likes hockey most, and says he is not sure how they could find out (p.74). Four speech bubbles, drawn.
• The class list (p.75). Thirty-one classmates in three printed columns, each name paired with one game. Games named: kabaddi, hockey, cricket, satoliya (also printed as pittu), football, badminton. The list is printed in an unsorted order — that is the point of it.
• The counts. Hockey 8, kabaddi 6, cricket 6, satoliya 5, football 4, badminton 2. Total 31. These are added counts of the printed list; the answer key accompanying the chapter gives hockey with frequency 8, which agrees. Note: cricket and kabaddi tie at 6, so Navya's belief is not even second on its own — it is joint second. That tie is worth showing.
• Pari's four questions (pp.75–76): her classmates' most popular TV show; the date of India's independence; how much water is being wasted in her locality; the capital of India. She must tick the ones needing collection.
• The tree count (p.78): a two-column table, tree name against number seen, to be filled from a walk between home and school.
• The letter count (p.78): tally five named letters — c, e and i, plus r and x — across a pasted news cutting. The book states that nearly every reader ends up ranking them x, then c, then r, then i, then e, and asks why that should be. Use this as the example of data whose pattern is stable across collectors — it is the chapter's one hint that data can reveal something about English itself, not just about one newspaper.

Figures to have open

• The printed class list of thirty-one name-and-game pairs (p.75). Redraw rather than reproduce: the values are the data and are needed exactly, but the page's layout and artwork are the book's. A standard three-column list is fine.
• Navya and Naresh in conversation (p.74). The four speech bubbles carry the argument; standard schematic, no need to copy the book's characters.
• Pari's four questions with tick/cross boxes (pp.75–76). Standard schematic.
• The empty tree-count table (p.78). Standard schematic; two columns.
• No pictograph, bar graph or tally table is needed here — all three arrive in later topics and showing them now spoils the sequence.

Where this sits in the book

• NCERT Class 6 Mathematics (Ganita Prakash), Chapter 4 "Data Handling and Presentation", §4.1 "Collecting and Organising Data", pp.74–79 — this topic uses the chapter opening and §4.1 up to the sweets table.
• Chapter-opening definition of data, p.74.
• The class list and its "Figure it Out", p.75; Pari's four questions, pp.75–76.
• The self-collection tasks: your own class's favourite game is item 3 of the "Figure it Out" on p.75; the trees and the newspaper letters are items 4 and 5 of the "Figure it Out" that starts on p.77 and runs onto p.78, and both are printed on p.78.
• Teacher's Note closing §4.1, p.79 — it asks for guess-then-collect activities, which is the shape of this whole topic.
• Forward pointers: Tally marks and frequency: organising data so it can be read (organising the list), Pictographs, and why the scale has to be stated (picturing it).