Line Graphs and Data Interpretation
Warm-up
Show two displays of the same week of classroom temperatures: a bar graph and a line graph. Ask: "Which display makes it easier to see the TREND — and which day-to-day CHANGE was biggest?" Discussion lands on the line graph's superpower: its slopes carry the story between the points.
Name the divide: bars compare CATEGORIES; lines track CHANGE over a continuous quantity (usually time). Choosing the wrong one isn't a style error — it's a meaning error.
Explore
Line-graph construction lab: plot the school's recycling data (weeks 1–8: 12, 15, 14, 20, 22, 21, 26, 30 kg) with honest axes — time on the horizontal, kilograms vertical, scale chosen to fit, points plotted then joined.
Interrogation round: Where was the steepest climb? (Week 3→4: slope tells.) Any dips? (Week 5→6.) Predict week 9 — and defend using the trend, not hope. Then the interpolation trap: "What does the line between week 2 and 3 MEAN?" — the line segment suggests values between measurements; for weekly totals those in-between points are fiction. Joining points is a readability choice that also makes implicit claims.
Formalize
Formalize the reading levels for line graphs: read points (values), read slopes (changes — steeper = faster change; downhill = decrease), read trends (the long arc across the whole graph):
The interpolation honesty rule: connected lines invite between-point readings; that's meaningful for continuous measurements (temperature through a day) and fictional for period totals (weekly recycling). Sophisticated readers know which kind of data they're holding.
Practice
Practice: build one line graph from a table; answer value/change/trend questions on a provided graph; one "which display?" sort (six datasets to match with bar, line, or pictograph plus a defence sentence); one misleading-graph autopsy (truncated axis on a line graph exaggerating a trend).
Exit ticket: from the class graph — "between which two weeks did recycling grow fastest, and how can you tell WITHOUT reading numbers?" (Steepest segment.)
Exit ticket
Practice: build one line graph from a table; answer value/change/trend questions on a provided graph; one "which display?" sort (six datasets to match with bar, line, or pictograph plus a defence sentence); one misleading-graph autopsy (truncated axis on a line graph exaggerating a trend).
Exit ticket: from the class graph — "between which two weeks did recycling grow fastest, and how can you tell WITHOUT reading numbers?" (Steepest segment.)
The graph: a bean plant's height, measured daily for 10 days, climbing from 2 cm to 19 cm with a flat weekend.
Level 1 — value: "How tall on day 6?" Trace up from 6, across to the axis: 11 cm.
Level 2 — change: "Between which days did it grow most?" Hunt the steepest segment: day 4→5 (3 cm in one day). The flat segment (days 7–8) means zero growth — visible instantly as horizontal.
Level 3 — trend: overall upward, roughly 1.9 cm/day on average (), with growth slowing near the end.
Wrap: three question types, three reading skills, one graph — and only level 1 needed numbers off the axis. The shape carried levels 2 and 3.
Dataset A: favourite pizza toppings of the class. Dataset B: temperature every hour during a school day. Dataset C: money raised by five different classes.
Step 1: A → BAR graph (or pictograph): categories with no order; a line joining pepperoni to mushroom would claim a topping in between — nonsense.
Step 2: B → LINE graph: time is continuous, temperature exists BETWEEN measurements, and the trend (morning climb, afternoon dip) is the story. Interpolation here is meaningful.
Step 3: C → BAR graph: five classes are categories. Ordering bars by size is allowed and helpful; joining them is not.
Step 4: The defence template students should own: "I chose ___ because the data is [categories/continuous change], and the question I want the reader to answer is [comparison/trend]." Display choice is the first act of data storytelling.
The graph: two lines on one grid — Class A's and Class B's weekly book totals across 6 weeks. A starts higher; B climbs steadily; the lines CROSS at week 4.
Step 1: Read the crossing: at week 4 the classes tied. Before it, A led; after, B led. A crossing point is the graph shouting "the ranking changed here."
Step 2: Compare slopes, not positions: B's line is consistently steeper — B improved faster the whole time, even during the weeks it was LOSING. Position is who's ahead; slope is who's gaining.
Step 3: The prediction question: "who wins week 8?" If both trends hold, B — extend the slopes lightly, state the assumption loudly.
Step 4: The life skill hiding in the exercise: race charts, savings-vs-savings, follower counts — two-line graphs are how the world displays rivalries, and slope-versus-position is exactly the reading that separates informed takes from vibes.