Unit 3 Topic 1 (bivariate data, first half) · Mission 1 territory, returning in week 5 · pairs with the regression guide
The concept in one sentence: a scatterplot shows whether two things move together, you describe it with three words every time (form, direction, strength), r puts one number on it, and correlation never, ever proves cause.
The thing that makes it click: r's sign is just the slope's sign, and r's SIZE is how tightly the dots hug the line. Two separate dials, not one.
1 · Prerequisite check (30 seconds)
Plot two points from coordinates, and ask "if footy training causes better kicking, which one is doing the explaining?"
If plotting wobbles: the reading-scales section on foundations.html. If explanatory/response confuses him, use "the explainer and the responder" in plain words before introducing the x/y convention.
2 · The teaching path
Concrete: data from his world: training sessions vs points scored, hours of sleep vs game rating. Sketch 8 to 10 dots together, HIS guesses for the numbers
The three-word chant: form (straight or curved), direction (up or down), strength (tight or scattered). Every plot gets all three words, no exceptions, from day one. It's a complete exam answer disguised as a habit
Then r: show plots with r = 0.9, 0.5, −0.9, 0. He matches number to picture. Sign = direction, size = strength. The r-scale bar on scatterplots.html does this visually
Causation last and loudest: the hot chips story (chip sales and sunburn both rise on hot days). Let HIM find the lurking variable, then generalise: "r can't see WHY, it can only see TOGETHER"
form · direction · strength then r: sign = direction, size = strength
Three words, every plot, no exceptions.
r can't see why. It can only see together.
3 · Misconception catalogue
Looks like
Why brains do it
The fix script
"−0.9 is weak because it's negative"
Minus codes as "bad/less" emotionally
"Sign is the slope, size is the strength. Cover the minus with your thumb: how big is the number?" Then rank a list of r values fast, repeatedly
Explanatory on y (axis swap)
Puts "the interesting one" on y
"The explainer goes on x, the responder goes on y." Check with the sentence: "___ explains ___"
Believes a high r proves cause
Together FEELS like because
Hot chips. Then make him invent his own lurking-variable story for a new pair (ice creams and snake bites). Inventing one inoculates better than hearing one
Quotes r for an obviously curved plot
r feels like it describes everything
"r only measures STRAIGHT togetherness. Curved data can score near zero while being perfectly related. Plot first, number second"
Ignores an outlier in the description
Not part of the pattern, so not mentioned
"The outlier is part of the answer. Name it, and say r would change without it." One stray point drags r around because r is not resistant
Thinks a steeper cloud means a stronger r
Steep looks dramatic
"r measures TIGHTNESS, not tilt. A shallow tight line beats a steep loose one." Two quick sketches settle it for good
Converts R² = 0.64 to r = 0.8 without checking direction
Squaring quietly ate the minus, and un-squaring can't bring it back
"Going from R² back to r LOSES THE SIGN. The scatterplot's direction chooses it: downhill cloud means r = −0.8." Every cohort loses marks here, pre-empt it
4 · Questioning ladder
Rung
Ask
Listen for
Recall
"Rank these: 0.7, −0.95, 0.1, −0.4"
−0.95 first, 0.1 last, no thumb needed
Do
Show any plot: "describe it"
All three words + the r ballpark, in one breath
Explain back
"Why can't r = 0.88 prove one causes the other?"
A lurking-variable story, ideally his own
Transfer
"Phone use and sleep quality, r = −0.85. Your mate says phones ruin sleep. Respond like the exam wants"
Describes the association correctly AND declines the causal leap, with a third-variable candidate
5 · How QCAA examines it
SF form: "describe the association" = the three words in context, plus identifying explanatory and response variables. Free marks once the chant is automatic. One landing note: the exam's strength adjectives are strong / moderate / weak, so the chant's "tight or scattered" must land on one of those three words in the written answer
Interpret r in context: a sentence, not a number: "strong negative linear association between ___ and ___"
The causation question appears constantly, usually as a claim to evaluate. Full marks = correct description + explicit "correlation does not imply causation" + a plausible lurking variable
His Casio CAN compute r (STAT mode → A+BX regression → r), and the syllabus explicitly expects r calculated from raw data USING TECHNOLOGY. Past papers have supplied r, but that's a habit, not a promise: spend ten minutes on STAT mode once this week, then it's his 30-second self-checker for life
R² (the coefficient of determination) is examinable and easy marks once framed: the sentence is "R² = 0.81 means 81% of the variation in [response] is explained by the variation in [explanatory]". Conversions both ways: R² = r², and r = ±√R² where the SIGN comes from the scatterplot's direction
6 · Stuck scripts
Slope up or down? Tight or scattered? Straight or curved?
Which one is doing the explaining?
What ELSE could make both of these rise together?
7 · ADHD delivery notes
This is the friendliest topic in Unit 3, ideal for the week Unit 3 returns: early wins rebuild the "I can do data" identity before regression arrives
The three-word chant is load-bearing: it converts an open "describe" question (executive-function heavy) into a checklist (light)
Sketching plots by hand beats staring at printed ones, keep the pen in his hand
Causation stories are the fun bit, let them get silly. Silly sticks