Students take samples of a simulated school, describe each sample's shape, centre and spread, compare two samples, and report an estimate with its method and size (AC9M8ST02, node 2).
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 10 min · Modify 12 min · Practise and Make 10 min
Do the Run board yourself first. Students need mean, median, range and dot plots (Year 7) and sampling methods (last lesson).
The one idea: a report describes the sample (shape, centre, spread) and then estimates the population, naming the method and size. The common mistake is reporting a sample's mean as the population's exact value (Leo's mistake).
The board plots the sample's values (rounded to 0.2 h) and gives the mean, median and range; the dashed line is the school's mean, for checking afterwards. Primary data: collected by the student; secondary: by others (ABS, studies).
Wider: find a secondary source (ABS or a health survey) on teenagers' sleep and compare it with the school sample.
Writing 'about' and saying how the sample was chosen. Ask: is this every student, or a sample? How was it picked?
| What you will see | A question to ask | The fix |
|---|---|---|
| A student reports only the mean. | How spread out are the values? What shape? | Shape, centre and spread, every time. |
| A student writes the sample's mean as exact for the school. | Did you measure every student? | Write 'about', and give the method and size. |
| A student can't describe the shape. | Where do most dots sit? Is one side longer? | Symmetric, or skewed towards the long tail; mention clusters, gaps and outliers. |
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.
Stretch: Take five samples of 40 and write each mean. How much do they vary? (Next lesson investigates this.)
Support: A report frame: 'In a [method] sample of [n], the values were mostly [..]. The median was [..] and the range [..]. So the school's students probably [..].'
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 8 student in Australia. Help me understand ONE idea only, from the lesson "Describing a sample". The idea: Analysing and reporting on sample distributions: I can Students collect or obtain a sample, analyse the distribution, and report findings from primary or secondary sources. What understanding looks like: - Collects or obtains a sample using a valid method. - Analyses and describes the distribution appropriately. - Comments on how the sampling method may have affected the distribution. Mistakes students often make here: - A student reports only the mean. - A student writes the sample's mean as exact for the school. - A student can't describe the shape. 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 (Comparing sampling methods), 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 "Describing a sample".
A random sample of 25 students spends a median of 40 minutes on homework a night (range 0 to 120). Write one sentence about the school.
Students at the school probably spend about 40 minutes on homework a night, though some spend much more, based on a random sample of 25.
This completes AC9M8ST02.
Where it leads: how samples vary (next), and full investigations with samples.