Week 4 — How Big Can a Cell Get? The Cell-Size Report

Assignment 4 of the term — compute how a cell's surface, volume, and pump work scale, and explain to someone new to biology why cells stay small.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, evidence-based report on cell size and transport. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. This week's lecture tutorial, quiz, discussion, and Biology Lab & Inquiry practise the same ideas from other angles; this assignment is where you put the cube cell, the membrane, and the pump together. It builds on Week 3, where you met the phospholipid that the membrane is made from.

The task

The cube cell is an illustrative model built for this course (not real data). Four model cube cells have sides of 1, 2, 3, and 4 units. For a cube of side s, surface area = 6s², volume = s³, and the surface-area-to-volume ratio simplifies to 6 ÷ s, so the four ratios are 6:1, 3:1, 2:1, and 1.5:1. The sodium-potassium pump spends 1 ATP in each cycle to move 3 sodium ions (Na⁺) out of the cell and 2 potassium ions (K⁺) in.

Work these four problems, showing your arithmetic:

1. A model cube cell has a side of 2 units. Using surface area = 6 × side × side, what is its surface area in square units?
2. The side-4 model cube cell has a surface area of 96 square units and a volume of 64 cubic units. What is its surface-area-to-volume ratio?
3. The sodium-potassium pump moves 3 sodium ions out of the cell in each cycle and spends 1 ATP per cycle. How many sodium ions does it move out in 4 cycles?
4. When the model cube cell's side doubles from 2 to 4 units, its surface area goes from 24 to 96 square units. How many times larger is the new surface area?

Beside each answer, add one brief interpretation:

• Problem 1: say what surface area stands for in a real cell, and explain what it means that the plasma membrane is selectively permeable.
• Problem 2: write the ratio in simplest form, compare it with the side-1 cube's 6:1, and explain why a falling ratio limits how big a cell can get.
• Problem 3: explain why the pump counts as active transport, and contrast it with facilitated diffusion.
• Problem 4: compare this growth in surface area with the growth in volume (8 to 64 cubic units), and name one way real cells cope, giving an organelle that uses it.

Explain it to a non-expert

Your younger sibling, after a science video, asks, "Why can't one cell grow as big as a basketball?" Write a 3–5 sentence message that explains the size limit in everyday words using your results, and names one limit of the evidence, including that the cube cell is an illustrative model and that real cells are not cubes. Explain any technical term in everyday words. More than one good answer is possible.

For a different, ungraded example, imagine a friend asking why crushed ice cools a drink faster than one big ice cube. Model answer: "Ice cools a drink only where it touches the drink, at its surface. Crushing one big cube into many small pieces keeps the same amount of ice but gives it far more surface touching the drink, so heat moves faster. That is why the crushed ice works quicker even though there is no more of it. Ice is not alive, so this comparison shows the surface idea but not how a living cell takes in food or water."

Use that pattern for the cell-size question, with your own wording and evidence.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to your sibling before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show calculations when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach for an introductory biology course. Draw out and challenge MY thinking about this week's cell structure, membrane transport, and cell size. Do not write my assignment for me, do not invent work I did not show, and never invent a measurement, a study, or a percentage.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The data: the cube cell, an illustrative model built for this course (not real data). Four model cube cells have sides of 1, 2, 3, and 4 units. For a cube of side s, surface area = 6 x s x s, volume = s x s x s, and the surface-area-to-volume ratio simplifies to 6 / s, so the four ratios are 6:1, 3:1, 2:1, and 1.5:1. The sodium-potassium pump spends 1 ATP in each cycle to move 3 sodium ions (Na+) out of the cell and 2 potassium ions (K+) in.
PROBLEM P1: A model cube cell has a side of 2 units. Using surface area = 6 × side × side, what is its surface area in square units?
PROBLEM P2: The side-4 model cube cell has a surface area of 96 square units and a volume of 64 cubic units. What is its surface-area-to-volume ratio?
PROBLEM P3: The sodium-potassium pump moves 3 sodium ions out of the cell in each cycle and spends 1 ATP per cycle. How many sodium ions does it move out in 4 cycles?
PROBLEM P4: When the model cube cell's side doubles from 2 to 4 units, its surface area goes from 24 to 96 square units. How many times larger is the new surface area?
After the four answers, I must briefly interpret each one: for P1, what surface area stands for in a real cell and what it means that the plasma membrane is selectively permeable; for P2, the ratio in simplest form compared with the side-1 cube's 6:1, and why a falling ratio limits how big a cell can get; for P3, why the pump counts as active transport, contrasted with facilitated diffusion; for P4, this growth in surface area compared with the growth in volume (8 to 64 cubic units), and one way real cells cope with an organelle that uses it. I must then write a 3-5 sentence message to my younger sibling explaining in everyday words why one cell cannot grow as big as a basketball, using my results, and naming one limit, including that the cube cell is an illustrative model and real cells are not cubes. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: correct computations (40 points), biological reasoning (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 computation points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my message to my sibling only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct surface area, ratio, ion count, or surface growth factor = 2; the right values and operation with only an arithmetic slip = 1; a missing result or the wrong values or operation = 0. Do not penalize an alternative valid method, such as the shortcut 6 / s for the ratio, or equivalent correct notation such as 1.5:1 or 3:2.
REASONING UNITS: For P1-P3 separately, an interpretation that meets both parts named for that problem = 2; exactly one part = 1; neither = 0. For P4, BOTH an accurate comparison of volume growth with surface growth that names one way cells cope AND a sibling message that explains the size limit in everyday words with a named limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0; saying a bigger cell works better because it has more surface, saying osmosis moves the salt, calling facilitated diffusion active transport, or dividing volume by surface is not accurate. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to biology, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the sibling message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable values and steps = 2; a relevant but incomplete value or step = 1; a result alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my message to my sibling AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised cell-size report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised cell-size report with all four answers, their brief interpretations, and your message to your sibling — written, or recorded as audio or video with a transcript, or as a labelled sketch of the cube cells with a short note; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 4 skills — computing the surface area and the surface-area-to-volume ratio of a model cube cell, counting the ions the sodium-potassium pump moves, explaining active and passive transport, and using the falling ratio to explain why cells stay small — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message to your sibling. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised cell-size report, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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