Critiquing Statistical Claims: a week of ready-to-teach maths
Five days of lessons for Year 6 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus claim cards and critic’s question cards, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Cut out the claim cards and the critic’s question cards, one set of each for each pair.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Ask the class to bring in a claim with a number in it from an advertisement, a packet or a website by Day 5.
No maths background needed
This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: a statistical claim can be true in its numbers and still mislead, through who was asked, how the data is drawn, or what is concluded from it. A critic asks the same few questions every time: who was asked and how many, how the data is shown, and whether the words and the conclusion match the numbers.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
Words to watch
A claim is what someone wants you to believe; the evidence is the data offered for it. A sample is the part of a group that was asked or measured; it is representative when it is like the whole group. A leading question pushes people toward one answer. A cut axis is a vertical axis that does not start at 0. Spin is wording that makes the numbers sound bigger or smaller than they are.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Spot the statistics | Find the claim, the evidence and the source in media items, tell an argument from an opinion, and ask a critic’s first question | Questions to ask |
| 2 | Graphs that mislead | Measure how much a cut axis exaggerates, redraw a graph from 0, and name four display tricks | The truncated axis; Spot the problem |
| 3 | Who was asked? | Compare small and large samples from one class, find who a sample leaves out, and fix leading questions | How big is the sample? |
| 4 | Words and conclusions | Find the facts behind spun headlines, write fair ones, and judge whether conclusions follow from the data | Same data, different headline; Does the conclusion follow? |
| 5 | Be the critic | Critique an advertisement and an online poll with the critic’s questions, and write a fair version | Spot the problem; the self-check quiz |
How the week builds
Day 1 finds statistical arguments in newspapers, packets, websites and posts; Day 2 checks how the data is drawn; Day 3 checks who was asked and how; Day 4 checks the words and the conclusion; and Day 5 puts the four checks together on a whole advertisement and an online poll. It builds on comparing data sets by mode, range and shape (AC9M6ST01). It leads to planning a fair investigation of their own (AC9M6ST03) and, in Year 8, to sampling methods (AC9M8ST01).
Materials for the week (one trip)
- All week: grid paper, rulers and coloured pencils.
- For Day 1: the claim cards, one set for each pair. For Day 5: the critic’s question cards.
- Claims the children bring from home: advertisements, packets, newspapers or printed web pages.
- A few real newspapers or catalogues, if you have them, for children who bring nothing.
Words for the word wall
claim, evidence, source, statistic, sample, representative, biased, leading question, survey, poll, axis, scale, exaggerate, spin, conclusion, critique
Dear families
This week in maths, Year 6 learns to read statistical claims carefully: who was asked, how the numbers are drawn, and whether the words match the data.
Try this at home
- Find a claim with a number in it on a packet, in a catalogue or on a website. Who is making it?
- Look at a graph together. Does its vertical axis start at 0?
- Ask: how many people were asked, and how were they chosen?
- Turn a dramatic headline into a plain one that says exactly what the numbers show.
Our claim collection
Fill one row a day. Write a claim you found, where it came from, and one question you would ask about it.
| Day | The claim | Where | Our question |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Printed from the free seegongsik Critiquing Statistical Claims teaching pack · seegongsik.com/au/y6/statistics/AC9M6ST02/pack
Spot the statistics
A statistically informed argument uses data to persuade: it makes a claim, offers numbers as evidence, and comes from someone who may gain if you believe it. These arguments fill traditional media (newspapers, TV, posters, packets) and digital media (websites, apps, posts). A number alone is not an argument, and an opinion with no data is not a statistical one. Children pull apart media items, sort claim cards and ask a critic’s first question.
We are learning to
- find the claim, the evidence and the source in a media item,
- tell a statistical argument from an opinion with no data,
- ask a critic’s first question of a claim.
Success criteria
- I can underline the claim and circle the numbers offered as evidence.
- I can say who made a claim and what they might gain if I believe it.
You need
The worksheet, one per child, and the claim cards (cut-outs), one set for each pair.
Lesson flow (about 50 minutes)
| 10 min | Questions to ask Show the board (see the box). Children vote A, B or C before you press. Ask: “Why is ‘How many were asked, and who?’ such a good first question?” |
| 15 min | Sort the claims Pairs sort the claim cards under the three heading cards. Ask: “The app notification card gives a number. Why is it not an argument?” |
| 25 min | Pull it apart Children do Parts A, B and C. Ask: “The pet-food company wrote item 2. What might it gain if you believe it?” |
Two half-sessions instead? Split after the card sort; start Session B with Part A.
Watch for these ideas
- Thinking any sentence with a number in it is a statistical argument.
- Trusting a claim because it is printed or on a screen.
- Taking “experts agree” or “everyone knows” as evidence when no data is given.
Answers
- Part A (claim; evidence; made by; first question): (1) the skate park is a winner; 2,140 visits in its first month; the council, which built it; How many visits did the pool have? (2) dogs are happier on this food; 8 in 10 owners noticed a happier dog; the company that sells it; How many owners, chosen how? (3) the school needs a safer crossing; 64 walkers a day in 2020, 41 now; the school; Is the crossing why fewer walk?
- Part B: (1) A, (2) O, (3) O, (4) A, (5) A, (6) O.
- Part C, for example: 12 of 28 chose the zoo, more than any other place, so we should go there. A critic asks: 12 is less than half; 16 children chose somewhere else.
Spot the statistics
A. Pull it apart
Underline the claim in each item. Circle the numbers offered as evidence. Then fill the table.
| Item | Who is making the claim? | What might they gain? | The first question you would ask |
|---|---|---|---|
| 1 | |||
| 2 | |||
| 3 |
B. Argument or opinion?
Write A (an argument that uses data) or O (an opinion with no data).
| 1. In our survey of 120 Year 6 students, 74 chose strawberry, so strawberry should be the flavour at the fete. | |
| 2. Strawberry is the best ice-cream flavour. | |
| 3. Experts agree this is the best phone you can buy. | |
| 4. Our bus was late on 3 of every 5 school days this term, so the timetable should change. | |
| 5. The tuckshop sold 210 apples and 95 bananas this term, so it should order more apples. | |
| 6. Everyone knows homework is pointless. |
C. Make an argument
Class 6R voted for an excursion: Zoo 12, Museum 7, Beach 9. Write a statistical argument for one place. Then write the question a critic would ask about your argument.
Argument: ________________________________________________________________
A critic asks: ____________________________________________________________
Graphs that mislead
In a column graph the eye compares bar lengths, so each length should be in proportion to its number. When the vertical axis starts above 0 (a cut axis), every bar loses the same bottom piece, and small differences look large. Other tricks: no scale at all, uneven gaps along an axis, and a picture enlarged in two directions, so its area grows faster than its number. Children measure the exaggeration in a canteen graph, redraw it from 0, and name four tricks.
We are learning to
- explain how a vertical axis that does not start at 0 exaggerates differences,
- redraw a misleading column graph honestly,
- name the trick in a misleading display.
Success criteria
- I can say how many times taller a bar looks, and how many times bigger its number really is.
- I can redraw a column graph with its axis starting at 0.
You need
The worksheet, one per child, a ruler, and a calculator for each pair.
Lesson flow (about 50 minutes)
| 10 min | Cut the axis Show the board (see the box). Children say how many times taller bar C looks than bar A, then you press. Ask: “The numbers did not change. What did?” |
| 25 min | Measure the trick Children count squares and compare in Part A, then redraw the graph from 0 in Part B. Ask: “Who might want the Wednesday bar to look so tall?” |
| 15 min | Name the trick Children name the tricks in Part C, then the class votes on the first two claims on the board. Ask: “Is a cut axis ever fair? When?” |
Two half-sessions instead? Split after Part A; start Session B with the redraw in Part B.
Watch for these ideas
- Reading the bar lengths instead of the numbers on the axis.
- Thinking every axis must start at 0: a clearly labelled line graph of the day’s temperatures can start at 10.
- Comparing two pictures by height when they also grew wider.
Answers
- Part A: Mon 2, Tue 5, Wed 8 squares; Wed looks 4 times as tall as Mon; Mon 52, Tue 55, Wed 58 pies; 58 ÷ 52 is about 1.1 times, only 6 more pies.
- Part B: bars at 52, 55, 58 on an axis from 0 look almost the same height, which is the truth.
- Part C: (1) picture grows both ways, (2) uneven gaps, (3) cut axis, (4) no scale.
Graphs that mislead
A. Pies sold at the canteen
1. Count the squares in each bar. Mon ____ Tue ____ Wed ____
2. How many times taller does Wed’s bar look than Mon’s? ______
3. Read the pies sold. Mon ____ Tue ____ Wed ____
4. Use a calculator: how many times more pies did Wed really sell than Mon? ______
B. Redraw it from 0
Draw the three bars on this axis.
What does your graph show that the first one hides? ______________________________
C. Name the trick
Use each of these once: cut axis · no scale · uneven gaps · picture grows both ways
Who was asked?
A claim about a group rests on a sample, the part of the group that was asked. Small samples swing by chance; a sample from one corner of the group, such as one club or the canteen queue, is not representative; people who choose to answer an online poll are not typical; and a leading question pushes people toward an answer. Children see how far small samples swing, find who a sample leaves out, and rewrite leading questions.
We are learning to
- explain why a small sample can mislead,
- say who a sample leaves out and suggest a fairer one,
- rewrite a leading question so that it is fair.
Success criteria
- I can compare a small sample’s result with the result for the whole class.
- I can turn a leading question into a fair one.
You need
The worksheet, one per child, and a calculator for each pair. If you like, take the lunch vote in your own class first.
Lesson flow (about 50 minutes)
| 10 min | How big? Show the board (see the box). Children say whether each sample can be trusted before you read its label. Ask: “Would 200 people from one football club be a fair sample of a whole town?” |
| 25 min | Table by table Children work out each table’s result in Part A and compare it with the whole class. Ask: “Table 5 found only 20%. Did that table count wrongly?” |
| 15 min | Fair samples, fair questions Children do Parts B and C. Ask: “Who is never in the canteen queue?” |
Two half-sessions instead? Split after Part A; start Session B with Part B.
Watch for these ideas
- Thinking a big sample is always fair: a big sample from one club is still one-sided.
- Taking a small sample that happened to match the class as proof that small samples are fine.
- Believing an online poll with thousands of votes speaks for everyone.
Answers
- Part A: tables 1 to 6, 100%, 40%, 60%, 80%, 20%, 60%; tables 1 to 3, 10 of 15, about 67%; tables 4 to 6, 8 of 15, about 53%; whole class 18 of 30, 60%. The bigger samples came closer.
- Part B: (1) leaves out children who do not buy lunch there; ask children from every class. (2) leaves out everyone who does not play soccer; ask a bigger group from every class. (3) leaves out people who never visit the site; anyone can vote, perhaps more than once; ask chosen children, once each.
- Part C, for example: (1) Should the library open at lunch: yes, no or not sure? (2) What do you think of the new playground? (3) Should recess be longer, shorter or stay the same?
Who was asked?
A. Should lunch be longer?
Class 6R answered at their six tables. Y means yes and N means no.
| Sample | Yes | Out of | Percentage yes |
|---|---|---|---|
| Table 1 | 5 | ||
| Table 2 | 5 | ||
| Table 3 | 5 | ||
| Table 4 | 5 | ||
| Table 5 | 5 | ||
| Table 6 | 5 | ||
| Tables 1 to 3 | 15 | ||
| Tables 4 to 6 | 15 | ||
| The whole class | 30 |
Which samples came closest to the whole class? What do you notice about the tables? ______________________
B. Who is left out?
1. To find out whether students like the canteen, the canteen manager asks the children waiting in the canteen queue. Who is left out? A fairer way? ______________________________
2. To decide whether to build a new soccer field, the principal asks the 12 players in the school soccer team. Who is left out? A fairer way? ______________________________
3. A gaming website asks, “Should kids get more screen time?” 3,000 people vote in its online poll. Who is left out? A fairer way? ______________________________
C. Make the question fair
1. “Don’t you agree that the library should open at lunch?” Fair version: ______________________________
2. “How much do you love our new playground?” Fair version: ______________________________
3. “Most students want a longer recess. Do you?” Fair version: ______________________________
Words and conclusions
The same numbers can be reported fairly or spun. Spin words (soar, collapse, almost everyone) make numbers sound bigger or smaller than they are, and a percentage of a small number can sound huge: up 100% only means doubled, perhaps 4 books becoming 8. A conclusion can also go further than its data: from one class to a country, from a few days to forever, or from two things happening together to one causing the other.
We are learning to
- find the facts behind a spun headline,
- write a headline that says what the numbers show,
- decide whether a conclusion follows from its data.
Success criteria
- I can explain what up 100% means, and why it can sound bigger than it is.
- I can explain why two things happening together does not prove one causes the other.
You need
The worksheet, one per child, and a calculator for each pair.
Lesson flow (about 50 minutes)
| 10 min | Two headlines Show the board (see the box). For each spun headline, children suggest a fair one before you press. Ask: “60 of 100 is more than half. Is ‘almost everyone’ fair?” |
| 25 min | Facts behind the words Children do Part A, then Part C. Ask: “‘Library borrowing up 100%!’ sounds enormous. What really happened?” |
| 15 min | Does it follow? Show “Does the conclusion follow?” (see the box), then children judge the conclusions in Part B. Ask: “More umbrellas are sold and more children are late on the same days. What else happens on those days?” |
Two half-sessions instead? Split after Part A; start Session B with the board’s conclusions, then Part B.
Watch for these ideas
- Taking a headline’s words as the data without checking the numbers.
- Thinking up 100% means 100 more: from 4, it is only 4 more.
- Treating two things that rise together as cause and effect.
Answers
- Part A: 4 to 8, 4 more books; 12 to 15, 3 more hats; 45 to 42, 3 fewer bikes; 36 of 60 is 60%, not almost everyone. Fair headline, for example: Saturday borrowing doubles, from 4 books to 8.
- Part B: (1) unfair: one class cannot speak for every child in Australia; (2) unfair: rain causes both; two things happening together does not mean one causes the other; (3) fair: a large survey across many schools, and the conclusion stays with those schools; (4) fair: it says exactly what was counted, for exactly those weeks; (5) unfair: three days is too short to say anything about the whole year.
- Part C, for example: spun, “Recycling surges!”; fair, “Recycling up 3 kg a week, from 30 to 33 kg”.
Words and conclusions
A. The facts behind the headline
| Headline | The facts | What really changed? | A fair headline |
|---|---|---|---|
| Library borrowing up 100%! | Books borrowed on Saturday: 4 last week, 8 this week. | ||
| Huge jump in lost hats! | Hats in lost property: 12 last term, 15 this term. | ||
| Bike riding collapses! | Bikes in the rack each day: 45 last month, 42 this month. | ||
| Almost everyone wants a school pool | 36 of the 60 students asked said yes. |
B. Does the conclusion follow?
Write F (fair) or U (unfair), and why.
| Data and conclusion | F or U | Why? |
|---|---|---|
| 1. 20 of the 26 children in our class have a pet. So most Australian children have a pet. | ||
| 2. On days when more umbrellas are sold, more children are late to school. So umbrellas make children late. | ||
| 3. A survey of 400 Year 6 children from 20 schools found 260 read every week. So about 65% of Year 6 children in those schools read every week. | ||
| 4. Over four weeks the school counted 380 bikes and 120 scooters in the racks. So bikes were parked more often than scooters in those four weeks. | ||
| 5. Canteen pie sales rose three days in a row. So they will keep rising all year. |
C. Spin it, then fix it
Fact: the recycling the school collects each week went from 30 kg to 33 kg.
A spun headline: ______________________________ A fair headline: ______________________________
Be the critic
A critique checks a claim’s method (who was asked, how many, how they were chosen, what exactly they were asked), its display (where the axis starts, whether there is a scale), its words and its conclusion, then says what would make it fairer. Children critique a muesli-bar advertisement and an online poll with the critic’s question cards, write a fair version, and play the unit’s quiz.
We are learning to
- critique a claim’s method, display, words and conclusion,
- explain what would make a claim fairer,
- write a fair version of a misleading claim.
Success criteria
- I can find four problems in the advertisement and name the critic’s question each one answers.
- I can describe a fair way to find out what children think of the muesli bar.
You need
The worksheet, one per child, the critic’s question cards (cut-outs) for each pair, and the claims children brought in.
Lesson flow (about 50 minutes)
| 10 min | Spot the problem Show the board (see the box). Children vote A, B or C on all three claims. Ask: “Which of these tricks have you seen in the claims you brought in?” |
| 25 min | Critique the advertisement Pairs lay a question card beside each problem they find in the advertisement, then write Part A. Ask: “The makers chose the question. How might the question change the answers?” |
| 15 min | Fair version and quiz Children do Parts B and C, then play the unit page’s quiz as a class game. Ask: “Which problem would you fix first, and how?” |
Two half-sessions instead? Split after Part A; start Session B with the poll in Part B.
Watch for these ideas
- Listing problems without saying why each one matters.
- Calling the advertisement a lie: its numbers may be true and still mislead.
- Suggesting a fairer survey that is still one-sided, such as asking only one class.
Answers
- Part A, with the card each answers: only 10 asked (How many were asked?); at the makers’ open day, after a free bar (How were they chosen?); a leading question (What exactly was the question?); “chose” with no other bar, “can’t get enough” (Do the words match the numbers?); axis from 38: Mar looks 3.5 times Jan, sales grew about 1.1 times (Where does the axis start?); 9 of 10 at one open day becomes all kids (Does the conclusion go further than the data?); the makers gain (Who gains if I believe it?).
- Part B: 900 of 1,200 is 75%, but anyone can vote, adults too, perhaps more than once, and only visitors to a gaming website saw it. Fairer: ask students chosen from many schools, once each.
- Part C, for example: 9 of the 10 children we asked at our open day, after a free bar, said yes; monthly sales rose from 40 thousand to 45 thousand bars.
Be the critic
A. Critique the advertisement
Find as many problems as you can. For each, write the critic’s question card it answers.
| Problem | Question card |
|---|---|
| 1. | |
| 2. | |
| 3. | |
| 4. | |
| 5. | |
| 6. |
B. Critique the poll
Two problems: ______________________________ ______________________________
A fairer way to find out: _____________________________________________________
C. Make it fair
Rewrite the advertisement’s claim so that it says only what the survey and the sales really show.
________________________________________________________________________________
________________________________________________________________________________
Claim cards
Print one set for each pair and cut along the dashed lines. Lay out the three heading cards, then sort the claims under them.
Teacher note: an argument with data, 1, 4, 6, 8; an opinion with no data, 2, 3, 7; a number with no argument, 5. Card 8 uses data, but its conclusion goes further than its survey can show: a good one to come back to on Day 4.
Critic’s question cards
Print one set for each pair and cut along the dashed lines. Lay a card beside each problem you find in a claim. Some problems answer two cards.
Teacher note: the cards follow a claim from start to finish: method (4), display (2), words (1), conclusion (1), source (1). Pairs use them on Day 5 with the advertisement; keep them for any claim the class brings in.
What we know: Critiquing Statistical Claims
Work on your own. Show your thinking if you can.
- The council website says: “Our new bike path is a hit: 1,450 trips in its first month.” Underline the claim and circle the evidence. Why might the council want you to believe it? ______________________
- Tickets sold for the school play. How many times taller does the Sat bar look than the Thu bar? How many times more tickets were really sold? ______________________
- A poster shows two bins. The second bin is twice as tall and twice as wide, to show twice as much recycling. Why does the poster mislead? ______________________________
- The canteen asks 5 students in its queue whether the canteen is good. 4 say yes. The canteen reports: “80% of students love our canteen!” Give two problems. ______________________________
- Rewrite this question so that it is fair: “Wouldn’t a longer recess be great?” ______________________________
- Headline: “Lost property doubles!” The lost items went from 3 to 6 this week. Write a fair headline. ______________________________
- “The three tallest children in our class eat cereal for breakfast, so cereal makes you tall.” Does the conclusion follow? Why? ______________________________
- An online poll on a football club’s website finds that most voters want a bigger stadium. Who might be missing from this poll? ______________________________
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- Claim: the bike path is a hit. Evidence: 1,450 trips in its first month. The council built the path, so it gains if it looks a success.
- The Sat bar looks 4 times as tall (8 squares against 2), but 36 ÷ 30 is 1.2 times.
- It covers four times the space, so it looks like four times as much recycling.
- Only 5 students were asked, all from the queue, who already buy there; and “love” is stronger than “good”.
- For example: Should recess be longer, shorter or stay the same?
- For example: 3 more lost items this week, 6 instead of 3.
- No: three children is a tiny sample, and two things happening together does not show that one causes the other.
- People who do not visit the club’s website, such as people who do not follow the club; and some may vote more than once.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Finding claims (Q1, Q8) | treats any sentence with a number in it as an argument | finds the claim, the evidence and who made it | asks what the source gains and who is missing |
| Displays (Q2, Q3) | compares bar lengths or picture sizes by eye | shows how a cut axis or a doubled picture exaggerates | redraws a misleading display fairly and explains the choice |
| Methods (Q4, Q5) | trusts a result whoever was asked | spots a small or one-sided sample and a leading question | designs a fair sample and a neutral question |
| Words and conclusions (Q6, Q7) | takes a headline’s words as the data | rewrites a spun headline and rejects a conclusion that goes too far | explains why two things happening together need not mean one causes the other |
Eight questions, four ideas. A child at standard finds a claim and its source, and critiques how its data was gathered, drawn and reported.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Claims | Graphs | Samples | Conclusions | Critique |
|---|---|---|---|---|---|
The five columns are the five days: finding claims, graphs that mislead, samples and questions, words and conclusions, and the whole critique.