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."