Lesson 12 · True numbers, collected badly
The mirror image of last lesson. In Lesson 11 the numbers were true and the picture lied. Today the picture is honest — it is the proper chart from last lesson, drawn from zero — and the problem is in how the data was collected. Three faults, all findable in the article itself.
| Minutes | What happens |
|---|---|
| 0–6 | Warm-up. Two claims, one obviously silly. What exactly is silly about it? |
| 6–16 | Launch. Read the article twice. First for the story, then for the method. |
| 16–42 | Explore. Find the three faults, then write an honest version. |
| 42–52 | Summarise. The three questions to ask any statistic you are shown. |
| 52–55 | Exit ticket. |
The three faults, in the order the worksheet asks for them
1. Who was asked. The Spinner Stall team ran the survey themselves, standing at their own stall, asking the Preps queuing for it. A Prep who tried it and wandered off was never in that queue. The sample is made of people who had already chosen the thing being judged.
2. How many were asked. Twelve. There were forty Preps at Games Day and 406 students at Riverbend, and the headline is about “Riverbend students”. Twelve is fewer even than the twenty who visited that one stall.
3. What was left out. The team say plainly that they asked about the Treasure Bag as well, and those answers appear nowhere. Reporting the half that suits you is the quietest of the three faults and usually the last one found.
The claim that is fine, and why it matters
Eleven out of twelve really is 92%. The sum is correct, the chart is drawn properly from zero, and the Treasure Bag’s bar is there at its true height. Students who have just done Lesson 11 arrive primed to attack the chart, and the chart is innocent. That is the whole reason these two lessons sit next to each other.
The number that does the work
The article says 92%. The class’s own full count of all twenty Preps at that stall gives 80%. Both are true of the group they describe. The twelve-point gap was manufactured entirely by who was standing in the queue, and students can see it without being told.
Differentiation
Support
- The article with the three relevant sentences already highlighted.
- Fault names supplied; the job is to match each one to its sentence.
- Sentence frames for the critique.
- The honest rewrite done as a cloze rather than from scratch.
Core
- Find all three faults unaided and name each one.
- Identify the claim that is sound.
- Rewrite the opening honestly without changing any number.
Extension
- Write the survey instructions the team should follow next year.
- Work out how many Preps they would need to ask to speak for all forty.
- Find a real advertisement or headline that does one of these three things.
What we are learning
- That a statistic can be arithmetically correct and still not be trustworthy.
- To ask who was asked, how many were asked, and what was left out.
- To say what is wrong with a claim and what would be right.
- To notice the parts of a report that are done properly.
How you will know you have it
- You can name all three faults and point to the sentence that shows each one.
- You can explain how 92% and 80% can both be true.
- You can rewrite the opening honestly without changing a single number.
Set your goal for today
Which of those is the biggest stretch for you? Write it down.
Not sure? The last one. Being honest without being able to change the numbers is harder than it sounds.
How hard is each question?
Every question is labelled so you know what kind of thinking it needs.
SF — simple familiar
Read a number straight out of the article.
CF — complex familiar
Name a fault and explain what it did to the result.
CU — complex unfamiliar
Rewrite the claim honestly, or design a survey that would work.
Warm-up · two claims
Claim 1. “I asked everyone at the swimming carnival whether they like swimming. All of them said yes. So everyone at our school likes swimming.”
Laughter, then: what exactly is wrong with it?
“Not the counting. The counting is perfect. The problem is who was standing there. People who hate swimming were somewhere else that day.”
Claim 2. “I asked four people in my class what their favourite subject is. Two said maths. So half the school’s favourite subject is maths.”
“Same question. What is wrong? … This time it is not who, it is how many. Four people cannot speak for four hundred.”
Why the silly one first
The swimming carnival claim is absurd enough that every student can see it is wrong, which means the whole class gets to practise the hard part — saying precisely what the fault is — on a case where nobody is stuck on whether there is a fault at all. “It’s just wrong” is not an answer; “the people who disagree weren’t there to be asked” is.
Hold the line on the counting
Someone will say the swimming claim is wrong because “they didn’t count properly”. They did. Every number in both claims is correct. That distinction is the one thing this lesson has to establish before the article is handed out.
Launch · the article
Hand out The Riverbend Record. Read it twice, and say what each reading is for.
| First reading | For the story. What is this article telling you? Do not look for anything wrong yet. |
|---|---|
| Second reading | For the method. Where did these numbers come from, and who provided them? |
“Hands up if you believed it the first time through. … Good. It is a well-written article. The chart is honest — look, it starts at zero, and the Treasure Bag’s bar is right there at its real height. After last lesson you were probably ready to catch it out on the chart, and the chart is fine.
Second reading. Three questions, and they are the same three every time: who was asked, how many were asked, what was left out.”
Who wrote it
Worth pausing on the byline before anything else. The article is written by the Spinner Stall team, about the Spinner Stall, using a survey the Spinner Stall team ran at the Spinner Stall. None of that is against the rules and none of it is a fault on its own — but it tells you where to look.
If nobody finds the third fault
Point at this sentence and read it aloud: “We also asked them what they thought of the Treasure Bag while we had them, but we have focused on our own stall for this article.” Then ask where those answers are. It is said openly and still slides past almost everyone, which is exactly why it is worth teaching.
Explore · critique the method
On the worksheet. For each fault: name it, point to the sentence, and say what it did to the result.
Choose your path
Match the three faults, finish the sentences, then fill the gaps in the honest version.
How many Preps did the Spinner Stall team ask?
How many Preps were at Games Day altogether? How many students are there at Riverbend?
Fault 1 — who was asked. Where were the Preps standing when they were asked the question? Why does that make a difference to the answer?
The article says 92% said it was fun. The maths class counted 16 out of 20, which is 80%. Both are true and nobody miscounted. Explain how that is possible.
Fault 2 — how many. The headline is about “Riverbend students”. Is 12 Preps enough to say that? Write a headline that the survey would actually support.
Fault 3 — what was left out. The team say they asked about the Treasure Bag too. Where are those answers, and why does leaving them out change the story?
One thing in this article is done perfectly well. Find it and explain why it is fine.
Rewrite the first two paragraphs so they are honest. You may not change any of the numbers.
Write three instructions the team should follow if they run this survey again next year, so the result could be trusted.
1. 12.
2. 40 Preps at Games Day; 406 students at the school.
3. They were queuing at the Spinner Stall, and the Spinner Stall team was doing the asking. Everyone in that queue had already chosen that stall, so they were likely to say they liked it before a single question was asked. A Prep who tried it and walked away was never in the queue to be counted.
4. They are about two different groups. 92% is 11 out of the 12 queuing Preps. 80% is 16 out of all 20 Preps who went to that stall. The queue was a friendlier group than the full twenty, so its percentage came out higher. Same stall, same day, no mistakes — the difference was made by who got asked.
5. No. 12 is fewer than the 20 who visited that one stall, less than a third of the 40 Preps, and about 3% of the school. Something like “Most of the Preps queuing at the Spinner Stall said it was fun” is supportable; anything about Riverbend students is not.
6. They are not in the article at all. The Treasure Bag answers are the only thing that would let a reader compare the two stalls, and without them the Spinner Stall cannot be judged against anything. The class’s chart shows the comparison the article leaves out.
7. Either answer is right. The percentage: 11 out of 12 really is about 92% — the arithmetic is correct. The chart: it starts at zero, the bars are the true heights, and the Treasure Bag is shown at its real value. Nothing is wrong with the maths or the picture; the problem is entirely in how the data was gathered and what was reported.
8. Open, but it must keep 92, 11 and 12 and lose the words that overreach. Something like: “We asked 12 Prep buddies who were queuing at the Spinner Stall near the end of Games Day, and 11 of them — 92% — said our stall was fun. We did not ask Preps anywhere else, so we cannot say what the rest of the school thinks.” Full marks need the sample described, not just the overclaim removed.
9. Open. Strong answers: ask Preps somewhere away from both stalls, so the queue does not choose the sample; ask all 40 rather than 12; ask about both stalls and report both. Accept anything that fixes one of the three faults and would actually work on a Games Day.
While they work
The 92% against 80% conversation
This is the one to pull the class back for. Twelve Preps queuing for the Spinner Stall gave 92%. All twenty Preps who visited it gave 80%. Nobody lied, nobody miscounted, and the gap is twelve percentage points — created purely by standing in the right place to ask. That is as clean a demonstration of sampling bias as Year 6 will get, and it is on their own data.
Question 7 is the one that sorts them
“One thing in this article is done perfectly well.” Students who have decided the article is The Bad Article will struggle, and that struggle is the point. Accept either the percentage calculation or the chart; both are correct. A critique that cannot tell the sound parts from the faulty ones is not a critique.
Question 8 — no changing the numbers
The constraint is what makes it work. They cannot retreat to “it should have been 80%”; they have to write something like “We asked 12 Preps who were queuing at our stall, and 11 said it was fun”. Honest reporting turns out to be mostly about saying who you asked.
Summarise · three questions, any statistic
“You will be shown numbers for the rest of your life — in ads, on packets, in the news, on your phone. Three questions, and they take about four seconds.
Who was asked? Were they the kind of people who would say yes before you started?
How many were asked? Enough to speak for the group in the headline?
What was left out? What did they find out and not tell you?”
| Fault | What it looks like | What it does to the answer |
|---|---|---|
| Who was asked | The sample is made of people who already chose the thing. | Pushes the result up. 92% instead of 80%. |
| How many | A small group spoken about as if it were everyone. | The result might be right by luck, and you cannot tell. |
| What was left out | Data was collected and not reported. | Removes the comparison that would change your mind. |
Exit ticket
A two-sentence claim from a cereal packet, with one fault in it. Name the fault and say what it does to the claim. One minute, and it tells you who is ready for Part B’s critique item.
Check what stuck
| Where they are | What the ticket looks like | Next move |
|---|---|---|
| Not yet | “They lied”, or attacks the arithmetic, or says everything is wrong. | Back to the warm-up claims. The counting is always correct; the question is who was counted. |
| There | Names one of the three faults and says what it does to the claim. | Ready for Part B. |
| Beyond | Names the fault and suggests what would need to change to make the claim trustworthy. | Give them the survey-design extension. |
Evidence this lesson contributes
| Dimension | What to look for |
|---|---|
| Understanding | Knows a correct calculation can still support an untrustworthy claim. |
| Reasoning | Explains how the sample produced 92% where the full count gave 80%. |
| Problem-solving | Rewrites the claim honestly, or designs a survey that would avoid the fault. |
Keep the honest rewrites
Question 8 is the closest thing in the unit to Part B’s critique item. File them next to the Lesson 11 redraws and you have two pieces of pre-assessment evidence on both halves of AC9M6ST02 before anyone sits the assessment.
What to print
| File | Who gets it |
|---|---|
| l12-01-article.pdf | One per student. The article itself, with room in the margin for annotation. Also worth projecting. |
| l12-02-worksheet-core.pdf | One per student. The three faults, the sound claim, the honest rewrite and the exit ticket. |
| l12-03-worksheet-support.pdf | Article sentences supplied, fault names given to match up, rewrite as a cloze. |
Where this sits in the achievement standard
AC9M6ST02 — identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusions.
Lesson 11 covered data representations. Today covers methods and the conclusions drawn from them. Between the two lessons every word of that descriptor has been taught and assessed.
The link forward to Part B
Part B asks students to critique a short claim about data. It is this task on unfamiliar material, which is what makes it a complex-unfamiliar item rather than a repetition. Students who can do question 8 here will manage it.
And the link sideways to AC9M6ST03
The extension question — write the survey instructions the team should follow next year — is planning an investigation, which is ST03. It is offered rather than required, because the investigation strand is carried by the Games Day itself earlier in the unit.
Australian Curriculum content descriptions and achievement standard extracts © ACARA 2010–present, licensed under CC BY 4.0. ACARA does not endorse this material.