Students describe data sets by shape (symmetrical or skewed, clusters, gaps, outliers), centre and spread, and compare two sets on both centre and spread, with numbers and in context (AC9M7ST02, nodes 2 and 3).
Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.
Predict and Run 8 min · Investigate 12 min · Modify 13 min · Practise and Make 12 min
Do the Run and Make boards first. Students need Mean, median, mode and range, and Stem-and-leaf plots.
The one idea: a data set has a shape, a centre and a spread; comparing two needs both centre and spread. The common mistake is comparing single values (the highest score); it is planted in Mia's reasoning and again in Practise.
The board draws the second set above the first, each with its own median line and range arrow; only the first set can be changed.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student compares one value from each set (Mia's mistake). | Does one student's score describe the whole class? | Compare a centre (median) and a spread (range) for each. |
| A student gives numbers without meaning. | What does a bigger range mean for these students? | Say it in context: 'less consistent', 'more varied'. |
| A student confuses the direction of skew. | Where are the few values that trail off? | The tail points to the few values; that is the direction of the skew. |
One possible solution for each task. Other correct programs are fine.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Stretch: Find two data sets with the same median and range but clearly different shapes.
Support: Use the sentence frame and the board's measures for every comparison.
For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.
You are a patient maths coach for a Year 7 student in Australia. Help me understand the ideas in ONE lesson only, from the lesson "Comparing data sets". The ideas: - Describing distribution shape, centre, spread and outliers: I can Students describe the distribution of data in terms of its shape (symmetrical, skewed), centre, spread and the presence of outliers. - Comparing distributions: I can Students compare two distributions using displays and summary statistics, making statements about differences in shape, centre and spread. What understanding looks like: - Describes the shape of a distribution using appropriate vocabulary. - Identifies the appropriate measure of centre for the distribution's shape. - Identifies outliers and comments on their effect. - Makes at least two comparative statements about two distributions (using statistics and display features). - States conclusions in context, not just in mathematical terms. - Does not compare individual values as if they represent the distributions. Mistakes students often make here: - A student compares one value from each set (Mia's mistake). - A student gives numbers without meaning. - A student confuses the direction of skew. How to coach me (rules from the Waypoints Kit coach): - Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question. - Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit). - If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go. - If I seem to be missing the idea that comes before this one (Creating stem-and-leaf plots), check it quickly, then come back. - Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back. - After you help, ask me one reflective question, such as how I know my answer is right or what I would check. - Praise my effort and method, not my ability. - You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so. - Use simple words. - Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Comparing data sets".
Group 1 reaction times (s): median 0.32, range 0.10. Group 2: median 0.28, range 0.35. Compare the groups in one sentence.
Group 2 was faster on a typical try (median 0.28 s against 0.32 s), but much less consistent (range 0.35 s against 0.10 s).
Next: the Chance unit (sample spaces and probability). A statistical investigation (AC9M7ST03) is a class task: pose a question, collect data, display and compare it with these tools (see the unit primer).
Where it leads: sampling and variation (Year 8), the five-number summary and box plots (Years 9 and 10).