Odds On - Free Classroom Simulation

Math (Probability & Statistics) Grades 9-12 8 roles 45 min 1 class period

The school nurse's office, the Monday after the homecoming football game. About half the student section is sick. Everyone recovers.

Half the student section is sick the day after homecoming. The class is the investigation team, and the clearest way to name the food is to put the sick students' numbers next to the healthy students'.

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Class Time

45 minutes

Designed For

1 class period

Roles

8 roles

Class Sizes

Core (4 teams), Wide (6 teams), Full class (8 teams)

Learning Objectives

5 objectives

Standards

4 standards aligned

Where This Fits in Your Curriculum

This is the two-way-table probability unit of Geometry and Integrated Math 2, run as a room. Students need to be able to divide a count by a total and read a percentage; they do not need to have met conditional probability, Bayes, or any AP Statistics vocabulary, and none of those words appear anywhere a student works. Underneath the outbreak story the class is doing three things the S-CP and S-MD standards point at and textbooks rarely make felt: comparing a rate among cases to the same rate among controls (S-CP), revising a belief when new and fallible evidence arrives, and paying a real cost for being more certain than the evidence supports (S-MD.B.7). It also fits a Health Science or Psychology unit on how a finding gets made, and an Algebra 1 or Integrated Math 1 class that has finished percentages and needs a reason to care about them. Everything is calculated on paper; the devices only capture what each team decided.

What Students Will Learn

Compute the rate of exposure to each food among students who got sick and among students who did not, using the correct denominator for each column.
Compare the two rates and explain why a food eaten just as often by both groups is not evidence, even when it tops the sick list.
Revise a stated confidence when a fallible test result arrives, using a printed rule rather than a hunch.
Build a two-way table for one food and decide whether eating it and getting sick are independent.
Weigh the cost of acting early against the cost of waiting, and state the reason for the call in one sentence.

Cases Included

CCSS.MATH.CONTENT.HSS.CP.A.4 - construct and interpret two-way frequency tables and use them to decide if events are independent. MET: the separate Two-Way Table sheet builds a 2x2 for the team's top food (ate / did not eat x sick / well) - two cells copied, two subtracted from printed totals - and asks, using the printed comparison line, whether eating it and getting sick are independent.
CCSS.MATH.CONTENT.HSS.CP.A.5 - explain conditional probability and independence in everyday language and everyday situations. MET: a food that both groups ate just as often is independence, the class meets one in round two, and it says so out loud in the debrief.
CCSS.MATH.CONTENT.HSS.ID.B.5 - summarize categorical data for two categories in two-way frequency tables and interpret relative frequencies in context. PARTLY MET: the Sick % and Well % columns are conditional relative frequencies and recognising a possible association is the whole game; joint and marginal relative frequencies appear only on the Two-Way Table sheet.
CCSS.MATH.CONTENT.HSS.MD.B.7 (+) - Front Office seat only: analyze decisions and strategies using probability concepts. MET at that seat: the sheet puts the payout for a correct pull this round beside the -120 for a wrong one and asks how sure the team is.

Social & Emotional Learning (CASEL)

Aligned to the CASEL framework's core competencies. These are the SEL skills students actively practice while playing.

Responsible Decision-Making Front Office makes a call every round that costs something either way - shut a stand that may be innocent, or leave one open while more students get sick - and writes the reason down before the room hears it.
Relationship Skills The swap is structured, timed and unavoidable: neither survey team can finish its own sheet without the other team's column, and each team knows by name who it is going to.
Self-Awareness The 100-point spread is a public statement of how sure a team is, and the swing test asks whether that team is more sure than ten interviews can make anybody.

Flexible Class Sizes

Core (4 teams)

One survey pair plus Lab and Front Office. 8 to 20 students, 2 to 5 per team.

Wide (6 teams)

Two survey pairs plus Lab and Front Office. 20 to 28 students. The two pairs interview different students, so their numbers will not match.

Full class (8 teams)

Three survey pairs plus Lab and Front Office. 28 to 34 students. Three different batches of interviews, and the class board is where they get reconciled.

How the Game Plays Out

Turn 1: Round 1: The First Ten

Ten interviews and nothing to compare them to

"What can ten sick students tell you on their own?"

Turn 2: Round 2: The Well Column

The healthy students finally get asked

"Which foods did the sick students eat MORE often than the healthy ones?"

Turn 3: Round 3: Narrowing

Bigger samples, and the story starts to hold still

"Has the leader changed, and what changed it?"

Turn 4: Round 4: Last Call

The biggest samples, and the last chance to act

"Is the class sure enough to act, and what is being risked either way?"

Roles Your Students Will Play

8 roles across 3 factions. Each has different information, different goals, and different leverage. Click any role to see their background and what they are trying to accomplish.

Sick Survey 1

pair 1

You sit with the students who got sick and ask one question: what did you eat at the game? Your team holds the only list of what the sick students ate, and a new batch of interviews arrives every round. Nobody else in the room has your column.

You get the counts of what the SICK students ate, and only those. Your total is printed at the top of every round and it changes every round. Your numbers come from your own batch of interviews, not from the other pairs'. A count on its own means nothing until it sits next to the healthy students' count.

Goals

Turn your counts into Sick % for all eight foods, every round.
Carry your sheet to Well Survey 1 in the swap and fill in the columns each sheet is missing.
Spread your 100 points by the Difference column if your team has one, or by your own column if not. Use the ladder on your card if it has one.

Well Survey 1

pair 1

You sit with the students who went to the game and did not get sick, and ask them the same question. Your team is the control group. Without your column, a food that everybody ate looks guilty.

You get the counts of what the WELL students ate, and only those. Your total is printed at the top of every round and it is never the same as the sick total. Your first interviews arrive in round two; round one has none. Your numbers come from your own batch of interviews.

Goals

From round two, turn your counts into Well % for all eight foods.
Host Sick Survey 1 in the swap and fill in the columns each sheet is missing.
Spread your 100 points by the Difference column if your team has one, or by your own column if not. Use the ladder on your card if it has one.

Sick Survey 2

pair 2

You sit with a different set of sick students from Sick Survey 1 and ask the same question. Your batch is not their batch, so your numbers will not match theirs. That is not a mistake, and reconciling the two is the room's job.

You get the counts of what the SICK students in YOUR batch ate, and only those. Your total is printed at the top of every round. Sick Survey 1 interviewed different students and will report different counts. The class board on the projector is where the two get averaged.

Goals

Turn your counts into Sick % for all eight foods, every round.
Carry your sheet to Well Survey 2 in the swap and fill in the columns each sheet is missing.
Spread your 100 points by the Difference column if your team has one, or by your own column if not. Use the ladder on your card if it has one.

Well Survey 2

pair 2

You are the control group for pair two. Your healthy students are not the same students Well Survey 1 spoke to, so the two well columns will disagree. From round two you also host the Lab's runner.

You get the counts of what the WELL students in YOUR batch ate, and only those. Your first interviews arrive in round two. The Lab sends a runner to your table in the last minute of every swap to copy your Difference column.

Goals

From round two, turn your counts into Well % for all eight foods.
Host Sick Survey 2 in the swap and fill in the columns each sheet is missing.
Have your Difference column finished before the runners arrive at one minute. If you have no Sick Survey partner, have your Well % column ready.

Sick Survey 3

pair 3

You are the third batch. Three pairs, three different sets of interviews, one outbreak. When all three spreads go up on the board, the class finds out how much two honest teams can disagree.

You get the counts of what the SICK students in YOUR batch ate, and only those. Your total is printed at the top of every round. The other two pairs interviewed different students and will report different counts.

Goals

Turn your counts into Sick % for all eight foods, every round.
Carry your sheet to Well Survey 3 in the swap and fill in the columns each sheet is missing.
Spread your 100 points by the Difference column if your team has one, or by your own column if not. Use the ladder on your card if it has one.

Well Survey 3

pair 3

You are the control group for pair three, and from round two you host the Front Office's runner. The person who decides whether to close a stand reads their evidence off your sheet.

You get the counts of what the WELL students in YOUR batch ate, and only those. Your first interviews arrive in round two. Front Office sends a runner to your table in the last minute of every swap to copy your Difference column and run the swing test there.

Goals

From round two, turn your counts into Well % for all eight foods.
Host Sick Survey 3 in the swap and fill in the columns each sheet is missing.
Have your Difference column finished before the runner arrives at one minute. If you have no Sick Survey partner, have your Well % column ready.

Lab

You run the rapid swab. You pick which foods get tested, you get the result before anyone else, and you read it to the room. The swab is quick and it is wrong often enough to matter: it misses bad food about three times in ten, which is a false negative, and it calls clean food positive about fifteen times in a hundred, which is a false positive.

You pick the swabs and you see the result first. A swab picked this round reads out at the start of the next round. The last round's pick is read out at the reveal. Nothing appears on the projector until you tap We announced it. From round two you have no interview column of your own - you send a runner to copy one. A food may be swabbed again; each swab is a fresh test.

Goals

Pick the swabs that would tell the room the most, not the ones that confirm what it already thinks.
Read every result to the room when your screen says to, then tap We announced it.
Send one person to the Well Survey table named on your card when the clock reads one minute.

Front Office

You decide, on behalf of the whole class, how this outbreak gets handled - whether a food comes off the stand today or stays on for another round. Closing the right stand early is worth the most and gets worth less every round you wait. Closing the wrong one costs the class, and nothing on any screen will tell you which you did until the end.

You get nothing from the interviews after round one - you send a runner. A correct pull pays 200, minus 50 for every round you waited. A wrong pull costs 120. One food a round at most, and a pull cannot be undone. No screen tells you whether you were right until the reveal. Ten interviews is a small sample size, and the swing test is how you find out whether it can be trusted.

Goals

Fill in the waiting-cost block every round before you decide.
Send one person to the Well Survey table named on your card at one minute, copy the Difference column, and run the swing test there.
Make the call and write one sentence saying why.

Hand Each Student Their Own Sheet

One click on the teacher dashboard prints a dossier for every role - background, goals, key facts, and their confidential briefing - plus the primary-source packet and a vocabulary sheet. Print them, or save as PDF, so each student reads their role on paper instead of huddling around one screen. The app still runs the votes and the action; the paper just carries the reading.

Primary Sources

Every role includes real historical documents. Students read them because they need the information to make their case.

Key Terms Students Will Learn

outbreakcasecontrol groupsick ratewell ratetwo-way tableindependencebase ratesample sizefalse positivefalse negativeswabconfidencepullswing test

After the Game: Debrief Questions

The free water was at the top of the Sick % column in every round. Why was it never the answer?
Which food did your team have in the lead after round two, and is it still your answer? If it changed, name what changed it. If it did not, name what made you more sure.
Front Office, read your round-2 swing test, or read it off the reveal. How many well interviews was the leader's Well % built on? Did moving one interview change the leader?
Your pairs interviewed different students. Did they land on the same leader after round two? The class board averages the spreads of every team that locked. Why does the board usually do better than a typical team?

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