Infographics and activity strips: what a visual shows and what it hides

What to assume they know

• Reading a number line with negative and positive values, and what zero means on a scale built from a difference
• Subtracting to form a difference, and the idea of a quantity measured per person
• Reading a legend and a scale bar, and matching a colour to a value
• Time in half-hour steps across a twenty-four-hour day, and adding durations
• Mean = total ÷ count, for the average-day task — The mean as the point where the distances balance
• Enough of the map of India to name states and to see which are coastal, inland, north-western and north-eastern

What they should be able to do

• State what quantity an infographic's colours encode, and read a state's value from the scale
• Explain why a scale built from a difference has a meaningful zero, and what the two ends of it claim
• Say what a maximum value on such a scale does and does not assert about the underlying quantities
• Rank the extremes of a mapped dataset in both directions, and name the states near the middle
• Estimate a deliberately hidden value from the colour of its region and its neighbours, and state the range the estimate can support
• List the questions the map cannot answer and identify the small print that admits it
• Read an activity strip: convert a block of coloured cells into a duration and a clock-time span
• Infer what each colour of a strip stands for from where in the day it sits, how long it lasts and how often it recurs
• Decide which of several strips is a school day, and defend the decision from the strip alone
• Explain what a strip cannot record, and design one for yourself
• Combine several days' strips into an average day, and say what that averaging destroys

Where it usually goes wrong

• "+100 means that state eats no wheat." The chapter says so explicitly, and it is the most likely misreading of the whole figure. +100 is about the gap being widest, and a scale built from a difference cannot say anything about either quantity on its own.
• "The states with the same colour have the same value." They have values in the same band. Karnataka's colour supports a range in the high seventies to nineties, which is why the item says guess.
• "A darker shade means more people." It means a larger difference per person. Population is nowhere in this figure.
• "The red line is data." It is drawn on top of the data to point out a pattern in it. Removing it loses nothing measurable and loses most of the figure's punch.
• "A map can be measured." Not this one, and it says so in the corner. Infographic maps are drawn to be read, not to be scaled off.
• "The strip's colours are labelled, so decoding them is trivial." The chapter deliberately does not label them. The decoding is the exercise, and the argument runs from position, duration and repetition — nothing else is available.
• "Two strips with the same amount of orange describe the same day." Order matters. Three hours in one block bracketed by travel is an outing; six half-hours scattered through the evening is a phone.
• "An average day is a real day." It is a computation. Averaging a school day with a Sunday produces a strip in which Manoj is at school for four hours, which happened on no day at all.
• "An infographic is a graph with pictures on it." A graph puts a value at a position on an axis you can read off. These two encodings put values into colours and lengths, which is why they are fast and why they cannot be read back exactly.

Questions to check understanding

• Read a state's value off a colour-coded map and say what the value measures
• Explain what the maximum of a difference scale asserts, and what it does not
• Rank the extremes of a mapped dataset both ways and name the states nearest to zero
• Estimate a hidden value from its region's colour and give the range the estimate supports
• List two questions the figure cannot answer, and identify the disclaimer that admits one of them
• Convert a block of strip cells into a duration, and a duration into a number of cells
• Identify what each colour of an unlabelled strip stands for, giving the reason for each
• Decide from a strip alone whether the day included school, and how long it lasted
• Draw your own strip for a stated day, and compute the average time spent on one activity across several strips

Examples worth working on the board

Values marked printed appear on the page. Values marked not in the book are added readings off the printed pages and the printed page, or reasoning added here on them. The chapter prints no answers to any of these questions and Part II has no answer appendix.

• The infographic (Part II p.124, printed; the whole figure is artwork and almost none of its lettering extracts). It is titled for wheat against rice. A graded colour bar runs from orange at one end to purple at the other, labelled −100 for mostly wheat, −50 for preferring wheat, 0 for preferring both, +50 for preferring rice and +100 for mostly rice. A red line is drawn diagonally across the country from the north-east down to the south-west. A large figure of +13.48 sits to the lower right, labelled as the national preference, with the words that rice wins. The words about the map not being to scale sit at the lower left. A source line under the figure credits the 68th round of the National Sample Survey, June 2014, with the data itself from 2011–12, and names iipmaps.com as the tool used to draw it.
• What the number on each state means (Part II p.124, printed). The difference between per-person rice consumption and per-person wheat consumption, mapped onto the range from −100 to +100. The page is explicit that +100 does not mean a state eats no wheat: it means that state leans furthest towards rice, with the largest gap between the two.
• Every printed state value (not in the book, read off three close-ups). Towards wheat: Rajasthan −93, Haryana −81, Punjab −78, Madhya Pradesh −60, Delhi −45, Gujarat −37, Uttar Pradesh −30, Himachal −19, Uttarakhand −18, Maharashtra −15. Towards rice: Bihar +3, Undivided Jammu Kashmir +41, Jharkhand +45, Goa +57, Andaman and Nicobar +65, Bengal +68, Kerala +79, Chhattisgarh +80, Lakshadweep +80, Puducherry +80, Tamil Nadu +85, Odisha +86, Sikkim +86, Assam +91, Undivided Andhra +92, Arunachal +93, Meghalaya +95, Tripura +96, Mizoram +97, Nagaland +99, Manipur +100. Karnataka carries a name and no number — that is the hidden value the item asks about.
• The four questions (Part II p.124, printed, unanswered). Guess Karnataka's value; name the top five rice states and the top five wheat states; list some states where the two are more or less balanced. Added answers: rice — Manipur, Nagaland, Mizoram, Tripura, Meghalaya; wheat — Rajasthan, Haryana, Punjab, Madhya Pradesh, Delhi; balanced — Bihar at +3 is the nearest to zero, then Maharashtra, Uttarakhand and Himachal, all within twenty of it.
• Guessing Karnataka (not in the book, and the item's real content). Its fill is the same mid-purple as Undivided Andhra at +92, Tamil Nadu at +85 and Kerala at +79, and it is bordered by those three and by Goa at +57 — and also by Maharashtra at −15, printed immediately above it, which is the one neighbour arguing the other way and must be named rather than quietly dropped. Since the whole beat is about what the neighbours license, show Maharashtra and then say why it loses: Karnataka's fill matches the mid-purple band its southern and eastern neighbours sit in, not Maharashtra's pale cream, so the colour outranks the adjacency. A value in the high seventies or eighties is defensible and anything below about +50 is not. The point to make is that the colour supports a range, not a number — which is the cost of the encoding, stated by the encoding itself.
• What the map cannot answer (not in the book). How much rice a person in Manipur actually eats; whether either quantity is rising; whether the +100 states eat more rice than the +85 states or merely have a wider gap; and any distance or area question at all, which is what the disclaimer in the corner is for. Each of those is a question a student will try to ask of the figure, and each has the same answer: the encoding threw that away.
• The activity strips (Part II p.125, printed; three vertical strips down the right of the page, hour numbers 1 to 24 beside each, two cells per hour, forty-eight cells in all). The prose says Manoj records what he does by colouring a strip in half-hour steps from midnight to midnight, that these are three different days of the week, and lists the activities: sleeping; eating; meeting friends, hobbies, media and family time; attending classes, studying and homework; showering, dressing, yoga or exercise; and travelling.
• The block structure of each strip (not in the book, read off the printed page; each reading below accounts for all forty-eight cells, which is the check that no block was missed). Times are given to the nearest half hour and carry the alignment caveat in §Notes.
  • Strip one: a 7-hour sleep block from midnight; then about 2 hours purple; 1 hour yellow; a half-hour green; 2½ hours orange; a half-hour green; a half-hour grey; 3 hours orange; a half-hour grey; a half-hour of light blue in mid-afternoon; 1 hour yellow; a half-hour green; 1½ hours orange; and 3 hours of sleep to midnight. No long yellow block anywhere in the middle of the day.
  • Strip two: an 8-hour sleep block; 1 hour purple; a half-hour green; a half-hour grey; 3 hours yellow; a half-hour green; a half-hour orange; 3 hours yellow; a half-hour grey; 1½ hours orange; a half-hour green; a half-hour yellow; 1 hour orange; 3 hours of sleep. The yellow-plus-break span runs exactly 7 hours.
  • Strip three: an 8-hour sleep block; 1 hour purple; a half-hour green; a half-hour grey; 3 hours yellow; 1 hour orange; a half-hour grey; a half-hour green; 1 hour light blue; 3 hours orange; a half-hour grey; a half-hour green; a half-hour yellow; 1½ hours orange; 2 hours of sleep.
• The colour reading (not in the book, with its evidence). Light blue must be sleeping — it is the long block every strip begins and ends with. Purple sits immediately after waking in all three, so it is washing and dressing. Green appears three or four times a day in half-hour bursts, so it is eating. Grey appears only in half-hour cells that bracket the long yellow and orange blocks, so it is travelling. Yellow fills the long mid-day stretches on two strips, so it is classes and study. Orange fills the day on the strip with no classes and the evenings on the other two, so it is friends, hobbies, media and family. Each of those six is an argument from position, duration and repetition — which is exactly the reasoning the chapter's first question is asking for.
• Which day is which (not in the book). Strip two has a full seven-hour school span, which is a full school day. Strip three has a three-hour yellow block and then an afternoon free, which is a half day. Strip one has no school block at all. Name the strips rather than giving an order, because the natural reading of "in that order" inverts the assignment: strip two is Friday (the full seven-hour school span), strip three is Saturday (the three-hour block, afternoon free) and strip one is Sunday (no school block). That fits both the chapter's own statement elsewhere that Manoj's weekday school runs seven hours (Part II p.131, item 13) and the common pattern of a half-day Saturday.
• Where the long film is (not in the book). On strip one, a 3-hour orange block is bracketed by a half-hour of grey before it and a half-hour of grey after it — going out, three hours, coming back. That travel-block-travel signature is the only place in the three strips where it occurs, and it falls in the early afternoon of the day with no classes.
• The lunch break (not in the book). On both school strips a half-hour green cell interrupts the long yellow block about three hours in, which puts the school's lunch break around the middle of the day. On strip two it is followed by a further half hour of orange, so the break there is a full hour of which half is spent eating.
• What a strip cannot record (not in the book, and the pair to section 7). Anything shorter than half an hour; anything done at the same time as something else — homework in front of a screen is one cell, not two; the difference between two hours of one activity and four half-hours of it separated by minutes; and how any of it felt. A cell forces one label onto a half hour, which is the price of being readable from across a room.
• The three prompts after the strips (Part II pp.125–126, printed): draw your own weekday strip and compare it with Manoj's; draw a strip for a day of the holidays, under a Try This flag; and make a strip for an adult at home and compare, under a Math Talk flag.
• Item 12 (Part II p.131, printed as an individual project). Make your own strips for different days of the week; say whether you eat and sleep at regular times and how long you are outdoors; compute the average time spent per activity and draw that average day as a strip; then track an adult and compare. Not in the book: this is where the two halves of the chapter meet — the average of several days, activity by activity, is a mean computed on data the student collected, and drawing it as a strip makes the averaging visible. It will usually produce a strip nobody actually lived, which is the honest lesson: the average day smooths out the day that had no school and the day that had seven hours of it.
• The two speech bubbles (Part II p.125, printed), which respond to the map on the facing page: one reader wonders what the rice-preferring and wheat-preferring states have in common, the other whether preferences were the same a century ago. They belong to Telling a story with data, and letting it raise the next question, whose thesis is that data raises the next question; this topic should show them and hand them on.

Figures to have open

• The rice-and-wheat map, redrawn. This one is worth care: the argument of sections 2 to 7 needs the graded colour bar, the state values, the red line, the national figure and the corner disclaimer all present. Redraw as a simplified outline with the same values rather than reproducing the printed art, and keep the disclaimer.
• A colour-bar-to-value ruler placed beside the map so a student can do the matching that section 6 asks for.
• The three activity strips, redrawn from the block structure above, with hour labels and half-hour divisions visible. These are the topic's second half and it does not work without them.
• A single magnified cell labelled with its half hour and with two activities crammed into it. Not in the chapter, and it carries section 11.
• An average-day strip computed from the three, drawn beside them.
• No photograph is needed. The two cartoon readers on Part II p.125 can be reduced to two captions.

Where this sits in the book

• NCERT Ganita Prakash Class 8, Part II, printed Chapter 5, "Tales by Dots and Lines", §5.2 "Visualising and Interpreting Data", Part II pp.123–126. Two unnumbered bold subheadings cover this stretch: "Infographics" (opening at the foot of Part II p.123, with the figure and its four questions on Part II p.124) and "What can a Strip Say?" (Part II p.125, with the three follow-up prompts running onto Part II p.126). The two speech bubbles sit at the top of Part II p.125.
• The paragraph opening the infographic subsection points back to Class 6, where infographics were first met; that is a backward reference outside this unit.
• Exercise item owned by this topic: Part II p.131 item 12, the individual strip project.
• Sibling topics: line graphs and their mechanics are Line graphs, and what change over time looks like; judging candidate inferences against a figure is Interrogating a real dataset: traffic, and rainfall, and its habits apply directly to both figures here; the speech bubbles and the group sleep project are Telling a story with data, and letting it raise the next question; the mean that item 12 asks for is The mean as the point where the distances balance.
• Backward pointer inside this unit: the pie chart of animal sleep times in Part II printed Chapter 3 is another encoding of the same kind, and is covered by Building a pie chart: turning counts into angles.