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!"