Pictorial Graphs and Data Representation
Warm-up
Display a concrete cube graph from a class survey. How would we show this same information without the cubes? Students suggest: draw pictures, use stickers. What rules should we follow? (One picture per person, all the same size, in columns.)
Explore
Full data cycle: (1) pose a survey question, (2) collect data from classmates with tally marks, (3) build a concrete cube graph, (4) transfer to a pictorial graph on grid paper (one drawn symbol per tally). Compare the two graphs: same data, different representations.
Formalize
Three-level questioning on the completed graph: Level 1 (direct): how many students chose autumn? Level 2 (compare): how many more chose summer than winter? Level 3 (interpret): what does this graph tell us about our class? What questions does it NOT answer?
Pictorial Graphs and Data Representation
Graph integrity discussion: what would happen if one student used a very large picture and another used a very small one? The large picture would look like more data. Why does the grid help? All symbols in the same-sized square keep the comparison fair. This is why standards in data representation exist.
Practice
Students conduct a class survey, build a concrete graph, transfer it to a pictorial graph, and answer 5 questions (at least one of each level). Exit ticket: write one thing the graph shows and one question it cannot answer.
Exit ticket
Students conduct a class survey, build a concrete graph, transfer it to a pictorial graph, and answer 5 questions (at least one of each level). Exit ticket: write one thing the graph shows and one question it cannot answer.
Step 1: Collect live data: each student places one cube on the row for their pet type. Suppose: dogs 7, cats 5, fish 3, none 6.
Step 2: Translate the concrete graph to paper: one drawn symbol (a simple circle sticker) per cube, rows labelled with the categories, symbols aligned in neat one-to-one columns so heights can be compared at a glance.
Step 3: Add the two pieces every real graph needs: a TITLE ("Our Pets") and a KEY ("each ⚪ = 1 child"). Without the key, the picture is decoration, not data.
Step 4: Read it at all three levels: How many have fish? (3.) How many more have dogs than cats? (2 — compare the overhang, don't recount both rows.) How many children were surveyed? (7+5+3+6 = 21.)
The through-line to keep saying: the graph must tell the truth by itself — a stranger should learn our pet data from the page alone.
Step 1: Survey favourite recess games and record with TALLIES first — the collecting tool: soccer 𝍸𝍸 (8), tag 𝍸| (6), swings ||| (3). Practice the five-bar gate: four strokes, fifth across.
Step 2: Convert the tallies to a pictograph — the DISPLAY tool: 8 symbols, 6 symbols, 3 symbols in labelled rows.
Step 3: Compare the two representations honestly: which is faster to record DURING the survey? (Tallies — one stroke per vote.) Which is easier to READ afterwards? (The pictograph — heights compare instantly.)
Step 4: State the workflow that professionals actually use: collect with tallies → display with a graph. Different tools for different jobs, and the data flows through both.
Quick integrity check: do the tally total and the symbol count match? 8+6+3 = 17 both ways ✓. If they disagree, the translation dropped or invented a vote.
The scene: a lovely column of stickers, no title, no row labels, no key. The maker can read it perfectly — today.
Step 1: Run the stranger test: cover the student's mouth (playfully) and ask a classmate to read the graph cold. "Something has seven… of something?" The graph fails without its maker attached.
Step 2: Let the maker experience the fix: add row labels (dogs, cats…), a title (Our Pets), and the key (each sticker = 1 child). Re-run the stranger test — now it reads itself.
Step 3: Name the principle: a graph is a MESSAGE to someone who wasn't there. Labels aren't decoration for the teacher; they're the part of the message that survives when you walk away.
Step 4: Institute the pre-flight check for every future graph: Title? Labels? Key? One-to-one symbols? Four boxes ticked before any graph is "done."