📋 Teacher Cheat Sheet — Session 5: Probability and Prediction

Data Science for Young Minds · Grade 5 · Ages 10–11

~60 min Ages 10–11 Session 5 of 8 ND-Friendly

⏱ Session Agenda

Time	Block	What's Happening
0–5	🎯 Hook	"I flipped this coin 10 times and got 8 heads. Is the coin broken?" (It's not — discuss why.)
5–18	📖 Lesson 1–2	Experimental vs. theoretical probability · P(heads) = 1/2 = 50% · Outcomes and trials
18–45	🪙 Simulation	Coin flip experiment: Round 1 (10 flips), Round 2 (50 flips). Record, calculate %, graph results.
45–53	📖 Lesson 3	Law of Large Numbers · Why more trials = closer to theoretical · Simulations in real science
53–58	✍️ Analysis	Students write: compare their experimental to theoretical; explain why 10 vs. 50 differs
58–60	👋 Close	Preview S6: "Two things can happen together without one causing the other — next time we investigate."

Key message to repeat: "Getting 8 heads out of 10 doesn't mean the coin is broken — it means probability is at work. This is exactly what probability predicts CAN happen."

📦 Materials Needed

1 coin per student (or pair) Worksheets (1 per student) Pencils & colored pencils Tally counters or tally sheets Optional: timer for 50-flip round

💡 Tip: If real coins aren't available, students can use a random number generator (odd = tails, even = heads) or a dedicated coin flip app shown on a device.

📚 Key Vocabulary

Probability — the likelihood that a specific outcome will occur; expressed as a fraction, decimal, or %

Experimental probability — probability based on actual trials you conduct

Theoretical probability — probability based on what should happen mathematically

Trial — one instance of an experiment (e.g., one coin flip)

Outcome — the result of one trial (e.g., heads or tails)

Law of Large Numbers — as the number of trials increases, experimental probability gets closer to theoretical

Simulation — using a model (coin, computer, beads) to imitate real-world probability

💬 Discussion Questions + Teacher Notes

"If theoretical probability of heads is 50%, why did you get 8 heads out of 10?"
→ Because 10 trials is a very small sample. With so few trials, random variation dominates. This is the Law of Large Numbers — more trials brings you closer to the theoretical value. Getting 8/10 heads is surprising but completely consistent with a fair coin.
"If you flipped 1,000 times and got 600 heads, would you think the coin was biased?"
→ Yes — 600/1000 = 60%, which is far from 50% with a very large sample. At large sample sizes, big deviations from theoretical become meaningful. This is why scientists use large samples.
"What's the difference between experimental and theoretical probability?"
→ Theoretical is what math says should happen (1/2 for heads). Experimental is what actually happened in your trials (8/10 or 80%). They can differ — especially with small samples. Over many trials they converge.
"Can probability tell you what will happen on the NEXT flip?"
→ No. Each flip is independent. After 8 heads, the 9th flip is still 50/50. This is the "gambler's fallacy" — the mistaken belief that past random events affect future independent ones.
"Where do scientists use simulations instead of real experiments?"
→ Testing drug safety (can't give dangerous doses to humans), climate modeling, economics, traffic planning. Simulations let you run thousands of "trials" that would be impossible or unethical in real life.

🪙 Coin Flip Experiment — Setup Guide

Each student (or pair) works independently. Two rounds. Record every flip as H or T. Calculate percentage after each round.

Steps:

Round 1: Flip coin 10 times. Tally H and T. Calculate: Heads% = heads ÷ 10 × 100.
Round 2: Flip 50 times (students can flip in groups of 10 and tally). Calculate: Heads% = heads ÷ 50 × 100.
Graph: Draw a bar chart comparing 10-flip %, 50-flip %, and 50% theoretical.
Class data: Compile class totals — add all students' 10-flip heads counts, then all 50-flip counts. Which combined total is closer to 50%?

Class compilation tip: Ask for a show of hands: "Who got more than 50% heads in their 10-flip round? Who got less?" Then: same question for 50 flips. Show how distribution tightens with more trials.

Expected result: Wide variation in 10-flip results (30%–80% common). Much tighter clustering around 50% in the 50-flip round. Class combined total of all flips should be very close to 50%.

🎯 Opening Hook

Say: "I flipped this coin before class. I got 8 heads and 2 tails. Is this coin broken?"

Take votes: broken / not broken / not sure. Then: "By the end of today, you'll know for certain — and understand WHY."

→ DO NOT reveal the answer yet. Let it drive the session forward as an unresolved question.

✍️ Analysis Writing Prompt

Write on board:
"Compare your 10-flip result to your 50-flip result. Which was closer to 50%? Use your actual percentages. Why do you think that happened?"

5 min writing. Students must cite their actual numbers. Then extend: "What would happen with 200 flips?"

Strong response: "I got 70% heads in 10 flips but 52% in 50 flips. The 50-flip result was much closer to the theoretical 50% because more trials reduce the effect of random variation."

🧠 ND-Friendly Tips

Physical coins before notation — Flip first, write fractions second. Never introduce P(H) = 1/2 before students have held and flipped a real coin.
Normalize unexpected results — Say repeatedly: "Getting 8 heads in 10 flips is completely fine. That's what probability says CAN happen — not 'won't happen.'"
50 flips in chunks — For students who lose count easily, flip in groups of 10 and tally after each group. Five groups of 10 = 50 total.
Class data compilation is powerful — When the whole class's results are combined, the Law of Large Numbers becomes visually obvious. Don't skip this step.
Connect to S4 — "Someone who only showed you the 10-flip result could use it to mislead you. A single small trial isn't reliable — we learned that last session."