Lesson 9 · Which stall did they like more?
One idea, and only one: two sets of data can have the same range and still be nothing alike. Everything today runs off one printed sheet. No spreadsheets.
| Minutes | What happens |
|---|---|
| 0–5 | Warm-up. Mode and range from a short list, out loud. |
| 5–15 | Launch. The two stalls on the board. Both go from 1 to 4. Are they the same? |
| 15–40 | Explore. Shade both charts on the sheet, then the questions. |
| 40–50 | Summarise. One sentence that compares, using the structure. |
| 50–55 | Exit ticket. |
Why the ranges match
Both stalls have a rating of 1 somewhere and a rating of 4 somewhere, so both ranges are 3. That is the trap, and it is worth letting the class walk into it. Range is built from two values and nothing else; it says how far apart the extremes are and nothing at all about where everybody sits.
The shapes are completely different. Sixteen of the Spinner Stall’s twenty Preps gave a 3 or a 4. Nine of the Treasure Bag’s did. The mode moves from 3 to 2.
Keep the group sizes equal today
Twenty Preps at each stall, on purpose. Comparing counts fairly when the groups are different sizes is a real idea, but it is not today’s idea, and putting both in one lesson is what made the old version hard to follow. It appears as a Going Further prompt only.
The sentence is the point
Naming the mode is not comparing. The structure to insist on, every time: name the feature that differs, give both values, say what it means.
Differentiation
Support
- One chart already shaded, so the second is a copy of a model.
- Three questions instead of seven.
- The comparison sentence as a fill-in frame.
- Counting done in the tally table, which is printed, not worked out.
Core
- Shade both charts, then all seven questions.
- Writes the comparison sentence from the structure.
Extension
- Two prompts: invent a set where the mode misleads, and why range is a weak comparison here.
- The second one is the idea Lesson 11 opens with.
What we are learning today
We are learning to compare two sets of data by looking at their shape, not just at one number.
I will know I can do it when…
- I can find the mode and the range of a set of data;
- I can turn a tally into a bar chart;
- I can explain why two sets with the same range can still be very different;
- I can write one sentence that compares two sets, instead of two sentences that describe them.
Set your goal for today
Read the list above. Which one is the biggest stretch for you? Write it down.
Not sure? The last one. Nearly everybody writes two descriptions the first time.
How hard is each question?
Every question is labelled so you know what kind of thinking it needs.
SF — simple familiar
Read a number off the table. Find the mode. Work out a range.
CF — complex familiar
Explain what the charts show, and write a sentence that compares them.
CU — complex unfamiliar
Answer somebody who has drawn the wrong conclusion from the range.
Warm-up · mode and range
1. 3, 5, 3, 8, 3, 6. Mode? 3. Range? 5.
2. 10, 12, 12, 15, 15, 20. Mode? Two of them, 12 and 15. Range? 10.
3. 7, 7, 7, 7. Range? 0. Not “none” — zero.
4. Two sets both have a range of 5. Are they the same? Hold that thought.
Question 4 is the whole lesson
Take a show of hands and do not settle it. Most of the class will say yes, or will not be sure. Write the question on the board and leave it there — you are coming back to it in forty minutes with their own charts as the evidence.
Question 2 is worth ten seconds of its own: a set of data can have two modes. Students arrive certain there is always exactly one.
Two stalls at Riverbend’s Games Day
Riverbend State School ran a Buddy Games Day last year. Twenty Prep buddies played at each of two stalls, and each one was asked how much they liked it.
| How much they liked it | The Spinner Stall | The Treasure Bag |
|---|---|---|
| 1 — did not enjoy it | 1 | 4 |
| 2 — it was okay | 3 | 7 |
| 3 — I liked it | 9 | 6 |
| 4 — I loved it | 7 | 3 |
| Preps altogether | 20 | 20 |
“Twenty Preps at each stall. Both stalls had somebody give a 1, and both had somebody give a 4.
So the range is the same for both. Three.
Does that mean the Preps liked them about the same? … Shade the two charts on your sheet and then tell me.”
Shading, not plotting
The grids on the sheet are already drawn and labelled, so this takes three minutes rather than fifteen. Drawing axes is not what is being assessed today, and the old version lost a whole lesson to it.
Then put both charts on the board
Open Compare Two Sets and press the Ratings button. Both charts appear on the same scale, which is the thing that makes the difference visible. Leave it up while they work on the questions.
Shade the two charts first
When both charts are shaded, put them side by side and look at the shapes before you write anything.
What is the mode of the Spinner Stall’s ratings? What is the mode of the Treasure Bag’s?
What is the range of each set? Write both.
How many Preps gave a 3 or a 4 at each stall?
Both sets have a range of 3. Look at your two charts. Does that mean the two stalls got the same reaction? Explain what the charts show.
Write one sentence that compares the two stalls. Name the thing that is different, give both numbers, and say what it means.
Which stall did the Preps like more? Give two separate pieces of evidence for your answer.
A teacher looks at the two ranges and says “they are both 3, so the Preps liked the two stalls about the same”. What would you say back?
2. Both 3. Both sets run from 1 to 4, so both ranges are 4 minus 1. Watch for “1 to 4” — that is the spread described, not the range, and the range is a single number.
3. Spinner Stall 16 of 20. Treasure Bag 9 of 20. Because both groups are twenty, these two counts can be compared directly — that is why the numbers were chosen this way.
4. The point of the lesson. No. The range only uses the highest and the lowest value, and both stalls happen to have a 1 and a 4 in them. It says nothing about the twenty Preps in between. The charts show the Spinner Stall’s ratings bunched up at the top end while the Treasure Bag’s sit lower and more spread out.
5. Looking for the structure, not just a true statement. The Spinner Stall’s ratings were higher — 16 of its 20 Preps gave a 3 or a 4, against 9 of the Treasure Bag’s — so the Preps enjoyed the Spinner Stall more. Two sentences joined by “and”, each describing one stall, is not a comparison.
6. Any two of: the mode is higher (3 against 2); 16 against 9 gave a top-two rating; only one Prep disliked the Spinner Stall against four at the Treasure Bag; the whole Spinner Stall chart leans right. Insist the two pieces are genuinely different, not the same fact said twice.
7. The response worth an A says what the range actually measures. Something like: the range only looks at the highest and lowest rating, and both stalls had a 1 and a 4 in them. It ignores everybody else. If you look at where most of the Preps are, the two stalls are not alike at all. A student who just says “no, look at the chart” has the right instinct without the reason — push once for why the range missed it.
Choose your path
Look at the printed tally. Which rating did the most Preps give at the Spinner Stall?
How many Preps gave a 3 or a 4 at each stall? Which stall has more?
Finish the sentence on your sheet to compare the two stalls.
Frame: “The Preps liked ______ more, because ______ out of 20 gave it a 3 or a 4, and only ______ out of 20 did at the other stall.”
Stuck on 5? Say the difference out loud first, then write down exactly what you said.
Invent a third stall where the mode is 3, but most of the twenty Preps did not enjoy it. Is that even possible? Show your tally.
For these two stalls, the range turned out to be a poor way to compare them. Explain why, and say what you would compare instead.
Back to the warm-up question
“Forty minutes ago I asked whether two sets with the same range are the same. What do you say now?
Both of these go from 1 to 4. Both have twenty Preps. And they are not remotely alike.”
| What it tells you | Mode | Range |
|---|---|---|
| What it measures | The value that came up most often. | How far apart the highest and the lowest are. |
| What it misses | Everything except the tallest bar. | Everybody except two people. |
| Here | 3 against 2 — a real difference. | 3 against 3 — tells you nothing. |
give both values, and say what it means.
The sentence to listen for, and the one to stop
Stop: “The Spinner Stall’s mode was 3. The Treasure Bag’s mode was 2.” Two facts with a full stop between them. Ask: so which did they like more, and how do you know?
Listen for: “higher”, “more of them”, “bunched up at the top”. Those are comparison words and they are what the achievement standard is asking for.
Keep the shaded charts
Lesson 11 opens with these same two numbers — 16 and 9 — drawn dishonestly. Having their own honest charts to hold it against is most of the argument.
Exit ticket
Two more stalls, twenty Preps at each.
| Rating | Set X | Set Y |
|---|---|---|
| 1 | 0 | 5 |
| 2 | 2 | 4 |
| 3 | 12 | 8 |
| 4 | 6 | 3 |
What is the mode of each set?
The modes are the same. Write one sentence saying how the two sets are still different.
Someone says “same mode, so same reaction”. Use a number from the table to show they are wrong.
The answers
1. Both 3. Chosen so the mode matches and the shapes do not — the same trap as the range, one lesson on.
2. Set X is bunched near the top with nobody at all giving a 1; Set Y is spread right across with five Preps at the bottom. Any sentence that names where the bulk sits.
3. The cleanest number is 18 of 20 against 11 of 20 giving a 3 or a 4. Also fine: nobody gave Set X a 1, against five for Set Y. A student who reaches for a number without being told to has understood the lesson.
Back to your goal
Read what you wrote on the Intentions tab. Did you do it? One sentence.
What you need for this lesson
| File | Who gets it |
|---|---|
| l9-01-worksheet-core.pdf | One per student. The data, both chart grids and all seven questions on the one sheet. |
| l9-02-worksheet-support.pdf | First chart already shaded, three questions, sentence frame. |
| Compare Two Sets | On the board. Press Ratings — Lesson 9 and leave it up. |
| Games Day — what to print | The collection sheet and the rating card, and how to run the day. Games Day sits between this lesson and Lesson 10. |
| Coloured pencils | For shading the bars. One colour per chart is plenty. |
Where this sits in the achievement standard
AC9M6ST01 — interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables, and compare distributions in terms of mode, range and shape. Today is ordinal categorical data: a rating scale where the order means something but the gaps are not measured.
The achievement standard sentence says students compare distributions using digital tools. Compare Two Sets is that tool, and the same two charts drawn on one shared scale is the evidence.
What is deliberately not here
Different group sizes. Both stalls have twenty Preps so that a count can be compared with a count and the lesson stays on shape. Unequal groups are the Going Further prompt in Lesson 10 and are worth meeting once — but not while students are still learning what shape means.
Australian Curriculum content descriptions and achievement standard extracts © ACARA 2010–present, licensed under CC BY 4.0. ACARA does not endorse this material.