Week 10 — Lab / Scientific Inquiry · "Modeling Meiosis: Counting the Combinations"

Course: Introduction to Biology — General Biology I (BIOL 101) · Silver Oak University (fictional sample) · Prof. Castellano
Objective: Objective 5 — model meiosis and independent assortment; count genetically distinct gametes; connect variation to its 2ⁿ count · SLO A (model-based reasoning and quantitative interpretation)
Worth 50 points · Labs group = 15% of the grade · Lab 10
Format: a hands-on at-home modeling activity with simple paper "chromosomes" (no special equipment) — you'll build gametes, count the combinations, compare them to the 2ⁿ prediction, and then catch the AI's mistakes when it interprets your results. A free virtual meiosis explainer is linked as a backup/extension.

This is the course's signature weekly component. Every instructional week has one lab. This week's is a simple at-home model; you can run it with paper and markers (or colored beads/coins) in about fifteen minutes. All lab resources are links to external sites — nothing to buy or download.

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Part 1 — The Big Picture

This week you learned that meiosis doesn't just halve the chromosome number — it shuffles the genes so thoroughly that essentially every gamete is one of a kind. One of the two shuffling mechanisms, independent assortment, is beautifully countable: when the chromosome pairs line up in metaphase I, each pair orients randomly and independently, so the number of genetically different gametes from independent assortment alone is 2ⁿ, where n = the number of chromosome pairs.

In this lab you'll model a small cell with n = 3 chromosome pairs, physically generate the possible gametes, and confirm that there are exactly 2³ = 8 — then scale the idea up to humans (2²³ = 8,388,608). The point isn't the craft project; it's seeing why the 2ⁿ formula is true and putting a number on biology's engine of variation.

Background (optional, ~6 min): Amoeba Sisters — "Mitosis vs. Meiosis: Side by Side Comparison" (watch the crossing-over and independent-assortment portion): 🔗 https://www.youtube.com/watch?v=zrKdz93WlVk
Virtual backup/extension: Learn.Genetics (Utah), "Mitosis, Meiosis, and Fertilization": 🔗 https://learn.genetics.utah.edu/content/basics/diagnose/

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Part 2 — Your Scientific Question & Hypothesis

The question: For a model cell with 3 pairs of chromosomes (n = 3), how many genetically different gametes can independent assortment produce — and does the count match the 2ⁿ prediction?

Before you start, write your hypothesis (an "if… then…" statement is perfect):

If a cell has 3 chromosome pairs, then independent assortment can make __ genetically different gametes, because ____.

Write it down now — you'll compare it to your count at the end. (Use the 2ⁿ idea to predict; a "wrong" prediction is completely fine — testing it is the point.)

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Part 3 — Materials & Procedure

You need (all common household items):
- 6 small strips of paper, beads, or coins to act as chromosomes · two colors (e.g., blue = from Mom, red = from Dad) · a marker · a flat surface. (Coins work too: heads = Mom's copy, tails = Dad's copy.)

Set up your model cell (n = 3, so 2n = 6):
- Make 3 pairs of chromosomes. Label them by size: a Long pair, a Medium pair, and a Short pair.
- In each pair, one chromosome is blue (Mom's) and one is red (Dad's). So you have: Long-blue + Long-red, Medium-blue + Medium-red, Short-blue + Short-red.

Procedure — generate the gametes:
1. A gamete gets exactly one chromosome from each of the 3 pairs (one Long, one Medium, one Short). For each pair, independent assortment means it's a free choice of the blue or the red copy.
2. List every distinct gamete by writing each as three letters — its Long, Medium, and Short copy — using B (blue/Mom) or R (red/Dad). Example: a gamete that took Mom's Long, Dad's Medium, and Mom's Short is B-R-B.
3. Work systematically so you don't miss any or double-count: start with all-Mom (B-B-B), then change one letter at a time. Record each new combination in the data table.
4. Stop when you can't make any new distinct combination. Count how many you found.
5. (Optional) Test independence with coins: flip 3 coins (one per pair; heads = blue, tails = red) to "build" a random gamete, repeat 16 times, and tally how often each of the 8 types appears — over many flips, all 8 show up.

No paper handy? You can run the equivalent step-through on the linked Learn.Genetics meiosis page, or just use the model gamete list in Part 8 to practice the analysis — but the paper version takes fifteen minutes and makes the 2ⁿ pattern obvious.

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Part 4 — Data Table (fill this in)

List every distinct gamete for your n = 3 model (each is a Long/Medium/Short combination of B or R):

#	Long copy (B/R)	Medium copy (B/R)	Short copy (B/R)	Gamete (e.g., B-R-B)
1	______	______	______	______
2	______	______	______	______
3	______	______	______	______
4	______	______	______	______
5	______	______	______	______
6	______	______	______	______
7	______	______	______	______
8	______	______	______	______

Total distinct gametes found: __ 2ⁿ prediction (n = 3): 2³ = ____

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Part 5 — Identify Your Model's Parts

Answer in a sentence each:
1. What does "n" stand for in the 2ⁿ formula (and what is n in this model)? __
2. Which meiosis event does choosing blue-or-red for each pair represent? _
3. Independent variable in the count (what you varied across the 8 gametes):
4. Why is it "independent" assortment — what makes each pair's orientation independent of the others? ___

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Part 6 — Analysis Questions

1. How many distinct gametes did you find, and does it equal 2³? If you found fewer than 8, which combinations did you miss?
2. Use the formula to predict the count for a cell with n = 4 pairs and for n = 5 pairs. (Show 2⁴ and 2⁵.)
3. Humans have n = 23 pairs. How many genetically different gametes from independent assortment alone? Why is the answer not 23 or 46?
4. This count is from independent assortment only. Name the other source of variation in meiosis and explain why it makes the true number of possible gametes even larger.
5. Connect it: how does this variation relate to evolution — why is a population of genetically varied offspring an advantage when the environment changes? (Tie back to natural selection from Week 1.)

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Part 7 — AI-Critique Moment (required — this is the BYOAI step)

Now bring in your approved chatbot (Gemini, Claude, or ChatGPT) and be the scientist who checks its work.

1. Paste your data table (or just describe the n = 3 model) into the chatbot and ask it: "For a cell with 3 chromosome pairs, how many genetically different gametes can independent assortment make, and what's the formula? Then tell me the number for humans (23 pairs). Also, is this mitosis or meiosis?"
2. Check everything it says against your own work:
   - Did it get 2³ = 8 for the n = 3 model — or did it give a wrong number?
   - Did it report the human count as 2²³ = 8,388,608 — or did it slip and say "23," "46," or "2 × 23"? (Chatbots mis-handle this exponent surprisingly often.)
   - Did it correctly identify this as meiosis (gametes, halving, independent assortment) and not confuse it with mitosis?
3. Write 2–3 sentences reporting what the AI got right and at least one thing you had to correct or watch carefully. (If it happened to get everything right, say how you verified each claim — recompute 2²³ yourself — that's the skill.)

The habit all term: the tool drafts, you judge. A chatbot will confidently botch the 2ⁿ count or mix up mitosis and meiosis — catching it is the point.

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Part 8 — What to Submit

Submit a single document (or text entry) with: your hypothesis, your completed data table listing all 8 gametes with the 2³ prediction, your Part 5 model labels, your Part 6 answers (including the n = 4, n = 5, and human counts), and your Part 7 AI-critique paragraph. Due Sunday, Nov 8, 11:59 p.m. (50 points).

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Instructor answer key & model data — REMOVE BEFORE PUBLISHING TO STUDENTS

The n = 3 model has a single correct, complete set of 8 gametes (below). All numbers are pre-computed and independently verified (re-derived by a Python check: n=2→4, n=3→8, n=4→16, n=23→8,388,608).

Model data table — the complete set of 2³ = 8 gametes (B = blue/Mom, R = red/Dad; order Long-Medium-Short):

#	Long	Medium	Short	Gamete
1	B	B	B	B-B-B
2	B	B	R	B-B-R
3	B	R	B	B-R-B
4	B	R	R	B-R-R
5	R	B	B	R-B-B
6	R	B	R	R-B-R
7	R	R	B	R-R-B
8	R	R	R	R-R-R

• Count = 8, and 2³ = 2 × 2 × 2 = 8. ✓ (Each of the 3 pairs independently contributes a factor of 2.)
• n = 4 → 2⁴ = 16. ✓ n = 5 → 2⁵ = 32. ✓
• Humans, n = 23 → 2²³ = 8,388,608 (over eight million). ✓ — not 23 and not 46; each pair doubles the count.

Expected answers:
- Part 5: (1) n = the number of chromosome pairs (haploid number); here n = 3. (2) Independent assortment (the random orientation of each tetrad in metaphase I). (3) which parental copy (B or R) each of the three chromosomes carries. (4) each pair lines up at the metaphase plate on its own random 50/50 orientation, with no influence from the other pairs — that independence is what multiplies into 2ⁿ.
- Part 6: (1) 8 = 2³; common misses are forgetting a "mixed" combination like B-R-B or R-B-R. (2) 2⁴ = 16; 2⁵ = 32. (3) 2²³ = 8,388,608, because each of the 23 pairs independently doubles the number of combinations — so you raise 2 to the 23rd power, not add or multiply by a small number. (4) Crossing over (prophase I) swaps segments between homologs, creating chromosomes with new gene mixes, so the real number of possible gametes is effectively unlimited. (5) Varied offspring mean a population is more likely to contain individuals that survive a new disease, predator, or climate shift; those survivors reproduce, so variation is the raw material for natural selection — the Week 1 lens.
- Part 7 (AI-critique): full credit for a specific catch — most commonly the AI giving the human count as 23 or 46 instead of 2²³ = 8,388,608, or confusing meiosis with mitosis. Full credit also if the student verified each AI claim by recomputing 2²³.

Grading rubric — 50 points

Criterion	Full	Partial	None
Hypothesis — a clear, testable "if…then…" prediction using the 2ⁿ idea, with a reason (8)	8	4–6	0–2
Data table — all 8 distinct gametes listed correctly + the 2³ prediction shown (15)	15	8–12	0–6
Model parts (Part 5) — n defined, independent assortment named, independence explained (12)	12	6–10	0–4
Analysis (Part 6) — correct n=4/n=5/human counts + the crossing-over and evolution connections (10)	10	5–8	0–4
AI-critique (Part 7) — names a specific thing checked/corrected in the AI's interpretation (5)	5	3	0–2

Quality gate (self-checked): every number in this lab is pre-computed and independently re-verified — the n = 3 model yields exactly 8 gametes (enumerated above and re-derived as 2³ = 8); 2⁴ = 16; 2⁵ = 32; human 2²³ = 8,388,608. The biology is correct (independent assortment in metaphase I is the modeled source; crossing over is the additional source), and mitosis vs. meiosis is kept distinct (this models meiosis). Quantitative gate: PASS. No student-collected number is asserted as "the" answer beyond the deterministic 2ⁿ counts — the key grades the reasoning and the enumeration, both of which have a single correct value here.