Students estimate a hidden population value from samples, then plan an ethical sample investigation and state an inference with its uncertainty (AC9M8ST04, nodes 1 and 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 10 min · Investigate 10 min · Modify 12 min · Practise and Make 13 min (the investigation itself is a class task)
Do the Run board yourself first. Students need sampling methods, describing samples and sampling variation (the last three lessons), and the Year 7 investigation cycle.
The one idea: an inference estimates the population that was sampled, with its uncertainty stated (size and method). The common mistake is inferring beyond the population (Zara's one school to all Australian teenagers).
The board hides the school's value until Show the population, so students commit to an estimate first. Ethics: consent, anonymity, no harm, and neutral questions; school approval for real surveys.
The full investigation (collecting real data) is a class task: the Make step plans it. Use a class sample of a short anonymous form on a non-sensitive topic.
Saying how sure you are without overclaiming. Ask: who exactly does this sample speak for, and how close might it be?
| What you will see | A question to ask | The fix |
|---|---|---|
| A student writes an exact value for the population. | Did you measure everyone? | Use 'about' or 'probably', and give the sample. |
| A student generalises to a bigger group. | Who could have been chosen for this sample? | Only that population: the school, the year, the club. |
| A student forgets ethics in the plan. | How will people agree to take part, and stay anonymous? | Add consent, anonymity and a neutral question to the plan. |
Write a question about a population: "How long do Year 8s at our school spend on homework?"
Plan a fair sample: 40 Year 8s chosen at random from the roll, with their permission.
Collect the data anonymously, in the same way for everyone.
Display the data and describe its shape, centre and spread.
Make an inference about the population, and say how sure you can be.
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.
Stretch: Run your investigation twice with two different random samples. How different are the results, and what does that say about your uncertainty?
Support: A five-stage plan template: question, sample, collect (ethically), display and describe, infer with uncertainty.
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 the ideas in ONE lesson only, from the lesson "Investigating with samples". The ideas: - Planning an ethical investigation with sampling: I can Students plan a statistical investigation including ethical and fair sampling methods, anticipate sources of uncertainty, and identify how findings will be used to make inferences. - Conducting, inferring and reporting with uncertainty: I can Students conduct the investigation, make inferences about the population from the sample, and report findings while explicitly acknowledging the uncertainty introduced by sampling. What understanding looks like: - Specifies the population, sample, and sampling method. - Identifies at least one ethical consideration and addresses it in the plan. - States what inference will be drawn from the investigation. - Makes a valid inference about the population from the sample. - Explicitly acknowledges uncertainty in the report. - Connects the degree of uncertainty to the sample size and method. Mistakes students often make here: - A student writes an exact value for the population. - A student generalises to a bigger group. - A student forgets ethics in the plan. 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. - 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 "Investigating with samples".
A random sample of 50 students at your school shows a median of 2 hours of screen time on school nights. Write an inference with its uncertainty.
Students at our school probably have about 2 hours of screen time on school nights, from a random sample of 50; another sample might give a slightly different value.
This completes AC9M8ST04 and Year 8 Statistics.
Where it leads: Year 9 and 10 statistics (comparing samples, scatterplots, evaluating claims in the media).