📋 Teacher Cheat Sheet — Session 3: Sampling Strategies

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

~60 min Ages 10–11 Session 3 of 8 ND-Friendly

⏱ Session Agenda

Time	Block	What's Happening
0–5	🎯 Hook	Show a jar of 100 beads — "How many of each color without counting all of them?" Take one guess.
5–18	📖 Lesson 1–2	Population vs. sample · Random, convenience, stratified sampling · Why sample size matters
18–45	🫙 Simulation	Bead Jar Simulation — pairs draw samples of 10, then 30; compare to true distribution; calculate percentages
45–53	📖 Lesson 3	Real-world sampling examples · Calculating sample percentage · What "representative" means
53–58	✍️ Analysis	Students analyze their simulation data: which sample size was closer to truth? why?
58–60	👋 Close	Preview S4: "Even good samples can be used to deceive — next session we see how."

Pacing note: The bead simulation is the entire heart of this session. Give it the full time. The "why" of sample size is experienced through the activity, not explained before it.

📦 Materials Needed

1 opaque jar or bag per pair (100 beads total — 4 colors) True distribution key (kept hidden from students until debrief) Worksheets (1 per student) Pencils & colored pencils for graphing Small cups for drawing beads

Jar Setup — True Distribution:
40 red · 30 blue · 20 yellow · 10 green = 100 total
(40% / 30% / 20% / 10%)

Pre-count and prep 1 jar per pair. Keep the true % secret until debrief. Beads available at craft stores; colored counters or M&Ms work too.

📚 Key Vocabulary

Population — the entire group you want to learn about

Sample — a smaller group selected from the population to represent it

Random sample — every member of the population has an equal chance of selection

Convenience sample — you pick whoever is easiest to reach (introduces bias)

Stratified sample — population is divided into groups; you sample from each group proportionally

Representative — a sample that reflects the true proportions of the population

Sample size — the number of individuals in the sample

Percentage — part ÷ whole × 100; used to compare samples of different sizes

💬 Discussion Questions + Teacher Notes

"Why can't we just ask every single person in a population?"
→ Time, cost, access. A national survey of 330 million people is impractical. A good sample of 1,000 can represent the whole accurately if chosen carefully. This is how polls, census estimates, and medical trials work.
"What's wrong with a convenience sample?"
→ It's biased toward whoever is easiest to reach — often friends, nearby people, or people who volunteer. Example: asking only your friends what music is popular gives you a biased picture of your whole grade.
"After your 10-bead draw, was your sample representative?"
→ Probably not perfectly. That's the point — small samples are noisier. After the 30-bead draw, most pairs will be closer to the true distribution. The experience IS the lesson.
"If you drew 50 beads, would it definitely be more accurate than 30?"
→ More likely, but not guaranteed. Probability means you can still get a bad sample by chance. Larger sample = better odds, not a certainty. This previews the Law of Large Numbers (S5).
"How do you know when your sample is big enough?"
→ It depends on how varied the population is, and how precise you need to be. Real statisticians use formulas; for now, the rule of thumb is: larger samples are more reliable, and a sample should be at least 10% of the population for small groups.

🫙 Bead Simulation — Full Setup Guide

Pairs work together. Each pair gets 1 jar. True distribution is hidden. Students draw without looking.

Steps:

Without looking, draw 10 beads. Record color counts. Put beads back. Shake jar.
Convert to percentages: count ÷ 10 × 100. Record on worksheet.
Without looking, draw 30 beads. Record. Convert to percentages: count ÷ 30 × 100.
Reveal the true distribution (40/30/20/10%). Students compare their two samples.
Class discussion: which sample was closer? Did anyone get a very wrong result with 10 draws?

Key debrief question: "Which sample was closer to the true distribution — your 10-bead or 30-bead draw? Why do you think that happened?"

Expected result: Most pairs' 30-bead samples will be closer to the true distribution. Some pairs will have surprising 10-bead results — use these as examples of why sample size matters.

🎯 Opening Hook

Hold up the jar of 100 beads. Ask: "Without counting every single bead — how could you figure out approximately how many of each color there are?"

Take one student guess. Then: "That's exactly what sampling is. Let's see how well it works."

→ Don't explain sampling yet. Let the curiosity about the jar drive the lesson forward.

✍️ Analysis Writing Prompt

Write on board:
"Which sample size gave you a more accurate picture of the jar — 10 beads or 30 beads? Use your data to explain. What would happen with 50 beads? 90?"

5 min writing. Students should cite their actual numbers, not just say "30 was better."

Strong response: "My 10-bead draw showed 50% red but the true amount was 40%. My 30-bead draw showed 43% red — much closer. Larger samples reduce the effect of chance."

🧠 ND-Friendly Tips

Tactile is the lesson — The physical act of drawing beads without looking IS the concept of random sampling. Don't rush to abstract definitions.
Focus on the "why" first — Before any vocabulary, establish: "We can't count everything, so we take a sample. The question is: how do we make it fair?"
Percentage calculation scaffold — Some students may struggle with the math. Write on board: count ÷ total × 100 = %. Walk through one example together before they work independently.
Allow retesting — Students who want to draw a third sample should be encouraged. Curiosity about what happens with even more draws is exactly the right instinct.
Normalize surprising results — If a pair gets wildly wrong results with 10 draws, celebrate it: "This is exactly why sample size matters — and why one bad sample can mislead us!"