Week 4 Biology Lab & Inquiry: How Big Can a Cell Get?

Part 1 — The Big Picture

This week you learned that a cell trades with the world through its plasma membrane but has to feed its whole inside. In this lab you test that idea with numbers. You start by exploring a free interactive that zooms from everyday objects down to cells, so you can see where a bacterium and one of your own cells sit on the scale. Then you build a small spreadsheet of model cube cells, compute surface area, volume, and the surface-area-to-volume ratio for each, and read the trend. You test one way real cells cope, dividing into smaller cells, and finish by checking a chatbot's account of your lab for a backwards ratio, a mislabeled structure, a scrambled order, or an invented number.

Time budget: Plan for about 120 minutes.

Part 2 — The Task

Guiding question: As a model cube cell grows from a side of 5 units to a side of 10 units, what happens to its surface area for each unit of volume, and how does cutting it into smaller cubes change that?

Before you begin — hypothesis: Before you compute anything, write one hypothesis in the if… then… because… form: if a model cube cell's side gets longer, then its surface-area-to-volume ratio will rise, fall, or stay the same, because of a reason about how surface area and volume grow that you can state. Then predict which of the four cubes will have the highest ratio.

Workshop data: Your own model cube-cell calculations, with the cube sides printed in the lab

Source: Four model cube cells with sides of 5, 6, 8, and 10 units, plus one cut-up comparison, which you calculate yourself with the procedure in Part 3; the cubes are a classroom model constructed for this lab, not measurements of real cells.

• Rows: 4 model cube cells, one row each in the calculation table, with sides of 5, 6, 8, and 10 units; a second table compares 2 arrangements of the same volume, and the first table has 4 rows that name the parts of the test rather than data
• Columns: side length, surface area, volume, the ratio of surface area to volume, and the ratio in simplest form
• Units: side lengths in units, surface areas in square units, volumes in cubic units; the ratio has no unit

Part 3 — Materials & Procedure

Tools and materials

• Free virtual labs and simulations (PhET, HHMI BioInteractive, Learn.Genetics), a virtual microscope, and a spreadsheet (Google Sheets or any free spreadsheet)
• A calculator, or pencil and paper, for checking the arithmetic by hand
• A document or notebook for your written answers

Ways of working

• virtual-simulation-inquiry
• at-home-protocol-and-data-table
• figure-and-diagram-interpretation

Procedure

1. Open the Learn.Genetics Cell Size and Scale interactive in a web browser. Drag the slider slowly from the largest objects toward the smallest. Stop when you find a bacterium and when you find one of your own body's cells, such as a skin cell, and note in words which one is larger and which unit the scale uses for each. Tool: Free virtual labs and simulations (PhET, HHMI BioInteractive, Learn.Genetics), a virtual microscope, and a spreadsheet (Google Sheets or any free spreadsheet). Check: Two notes in the last table of Part 4: the object, the unit shown, and which is larger.
2. Before you calculate anything, write your hypothesis and your prediction in the first table of Part 4, and name what you change (the side length), what you calculate (the ratio), and what you keep the same (the cube shape and the formulas). Tool: A document or notebook for your written answers. Check: The first table has an if… then… because… hypothesis and a prediction for the cube with the highest ratio.
3. Open a blank spreadsheet. Type the headers Side, Surface area, Volume, and Ratio into cells A1 to D1. Type the four sides 5, 6, 8, and 10 into cells A2 to A5. In B2 type =6*A2^2, in C2 type =A2^3, and in D2 type =B2/C2, then fill the three formulas down to row 5. Tool: Free virtual labs and simulations (PhET, HHMI BioInteractive, Learn.Genetics), a virtual microscope, and a spreadsheet (Google Sheets or any free spreadsheet). Check: Columns B, C, and D fill with a surface area, a volume, and a ratio for every side, and the ratio column shrinks as you read down.
4. Copy the four rows into the calculation table in Part 4. For one row of your choice, redo the surface area, the volume, and the division by hand, writing each multiplication out, and check that 6 divided by the side gives the same ratio. Tool: A calculator, or pencil and paper, for checking the arithmetic by hand. Check: One row checked by hand, matching the spreadsheet, and the shortcut 6 ÷ s agreeing with column D.
5. Now test the divide strategy. Treat the side-10 cube as one big cell, then imagine cutting it into eight cubes with sides of 5 units. In the second table of Part 4, compute the total surface area, the total volume, and the ratio for each arrangement, multiplying the side-5 values by 8 for the cut-up version. Tool: A document or notebook for your written answers. Check: The total volume is the same for both arrangements, while the total surface area and the ratio differ.
6. Answer the analysis questions in your document, then paste your completed tables into an approved chatbot with the prompt in Part 6 and check its answer against the scripted checks. Tool: A document or notebook for your written answers. Check: Written answers and a list of the chatbot's errors with corrections.

Fallback route

When to use it: Use this route if the Cell Size and Scale interactive will not load or you cannot open a spreadsheet.

Skip the interactive and the spreadsheet. Write the course's size ranges in the last table of Part 4 in place of the scale notes, and compute every row of the model cube cells below by hand with a calculator or pencil and paper, showing each multiplication. Then complete every scaffold table, analysis question, and the critique step and submit the same items for equal credit.

This route earns the same credit as the primary route.

The four model cube cells to compute by hand, with the sides filled in and the results left for you.

Fallback model data

Side (units)	Surface area 6s² (square units)	Volume s³ (cubic units)	Ratio, surface area ÷ volume	Ratio in simplest form
5
6
8
10

Part 4 — The Scaffold

Name every part of the test before you calculate, so the comparison is fair from the start.

Student scaffold table 1

Part of the test	Your answer
Hypothesis (if… then… because…)
What you change from row to row
What you calculate and compare
What you keep the same for every cube

Record each model cube cell, surface area first, then volume, then the ratio.

Student scaffold table 2

Side (units)	Surface area 6s² (square units)	Volume s³ (cubic units)	Ratio, surface area ÷ volume	Ratio in simplest form
5
6
8
10

Compare one big cube with the same volume cut into smaller cubes, to test the divide strategy.

Student scaffold table 3

Arrangement	Total surface area (square units)	Total volume (cubic units)	Ratio, surface area ÷ volume
One cube with a side of 10 units
Eight cubes with a side of 5 units

Note what the Cell Size and Scale interactive shows, in words, before you compare it with the course's size ranges.

Student scaffold table 4

Object you found	Unit the scale used	Larger or smaller than the other object
A bacterium
One of your own cells, such as a skin cell

Part 5 — Analysis Questions

1. Complete the calculation table, show the full arithmetic for one row, and check every ratio with the shortcut 6 ÷ s. Which cube has the highest ratio, and which has the lowest?
2. Does your evidence support or fail to support your hypothesis? Write one conclusion sentence that uses supports or fails to support rather than proves, and explain the trend by comparing how fast surface area and volume grow as the side gets longer.
3. Use your second table to explain how dividing into smaller cells changes the ratio without changing the total volume. Then name one other way real cells add surface, folding or flattening, and give one structure from this week that uses folding.
4. Compare what you saw in the Cell Size and Scale interactive with the course's ranges: prokaryotic cells about 0.1 to 5.0 μm across and eukaryotic cells about 10 to 100 μm. Which kind of cell is the bacterium, which kind is your own cell, and how does the size difference fit your ratio results? Remember that the plasma membrane is selectively permeable, so every substance a cell trades must cross it.
5. Choose one and answer it in 3–4 sentences. (a) Real cells are not cubes: name one way a real cell's shape differs from your model and say whether that would raise or lower its ratio compared with a cube of the same volume. (b) A ratio compares surface with volume but says nothing about what crosses the membrane: name one thing your model leaves out about the plasma membrane and how you would add it to a better model.

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

I've pasted my completed Week 4 Biology Lab & Inquiry tables above. They model cells as cubes with sides of 5, 6, 8, and 10 units. Please do seven things. First, for each cube, compute the surface area, the volume, and the surface-area-to-volume ratio, and write each ratio in simplest form. Second, tell me which cube would be the best cell at trading materials with its surroundings, and why. Third, say what happens to the ratio when a side-10 cube is cut into eight side-5 cubes. Fourth, name the folds inside a mitochondrion and say which membrane they belong to. Fifth, list in order the organelles a protein passes through on its way out of a cell. Sixth, give the largest size a real animal cell can reach, with a source. Seventh, as two stretch questions for later in the course, say how many cells a body cell makes when it divides for growth, and what phenotype ratio a cross of two Tt parents gives.

Test the response for these likely failures:

• Chatbots often say the biggest cube is the best trader because it has the most surface area, reading total surface instead of surface for each unit of volume, or they divide volume by surface and get the trend backwards.
• Chatbots sometimes place the cristae on the outer membrane of the mitochondrion, or say plant cells have chloroplasts instead of mitochondria.
• Chatbots sometimes send an exported protein to the Golgi apparatus before the rough endoplasmic reticulum, or skip the ribosome.
• Asked for the largest size of a real animal cell, chatbots often invent one precise maximum and cite a study that was never given.
• Asked the stretch question, chatbots sometimes say a dividing body cell makes four cells or makes cells that differ from each other.
• Asked the stretch question, chatbots sometimes give the phenotype ratio of a Tt by Tt cross as 1:2:1, and on this lab they may leave a cell ratio unsimplified, such as 384:512.

Write 3–5 sentences naming one thing the chatbot got right and at least two places it went wrong or overreached, quoting its words and correcting each with evidence from your own tables or this week's chapter; mark the stretch answers as ones to check later.

Equivalent route (no AI required)

No AI account is required for this lab. Instead of the chatbot, critique this flawed analysis, printed here in full: "In my cube-cell lab, I divided volume by surface area, so the side-10 cube scored 1000 ÷ 600, the highest, which proves that bigger cells trade materials best because they have the most surface. The side-8 cube's ratio is 384:512, which is already simple enough. Cutting the big cube into small cubes changes nothing, because the volume stays the same. A mitochondrion folds its outer membrane into cristae, and a protein leaving the cell goes from the Golgi apparatus to the rough endoplasmic reticulum and then out. Real animal cells can never grow past 37 μm, as one study showed. As a preview of later weeks, a body cell dividing for growth makes four different cells, and a cross of two Tt parents gives a 1:2:1 phenotype ratio." Mark it up: quote each flawed sentence, name what is wrong (an oversimplified mechanism, a ratio garbled or divided backwards, a mislabeled structure, an order scrambled, an invented figure, or a preview fact stated wrong), cite the evidence from your tables or this week's chapter, and write a corrected sentence beneath it; for the two preview sentences, say which later week will check them. This route assesses the same objectives (Objective 2 and Objective 3) as the chatbot critique, takes comparable effort (about 30 minutes and 200–300 words), is scored by the same scoring criteria for the same credit, and its own submission artifact is the marked-up flawed analysis, posted in place of the chatbot share link and report.

Part 7 — What to Submit

• All four completed scaffold tables, filled from your spreadsheet or your hand calculations
• Written answers to all five analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Biology Lab & Inquiry report on cell size: four completed tables (the named parts of the test, the four model cube cells, the divide comparison, and the scale notes), written answers to five analysis questions, and a critique of a chatbot's account of your lab, or, on the equivalent route, a marked-up correction of the printed flawed analysis. 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. Choose a written, recorded, or visual form for your answers; every form is graded by the same scoring criteria.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Testable hypothesis and named parts of the test	A falsifiable if… then… because… hypothesis and a prediction for the highest ratio appear before any calculation, and what is changed, what is calculated, and what is kept the same are all named.	A hypothesis appears but is not falsifiable or lacks a prediction, or one part of the test is missing.	No hypothesis, or the parts of the test are not named.
Completed calculation tables	All four cube rows and both divide arrangements carry a surface area, a volume, and a ratio computed as surface area ÷ volume and written in simplest form, with one row worked by hand and checked against 6 ÷ s.	The tables are filled, but one or two values are wrong, a ratio is divided backwards or left unsimplified, or the hand check is missing.	No calculations are recorded, or the values are copied rather than computed.
Analysis of size, surface, and the membrane	Questions 1 to 4 are answered accurately: the highest and lowest ratios are identified, the conclusion uses supports or fails to support and compares square and cube growth, dividing is shown to raise the ratio at the same volume with a folding structure named, and the bacterium and the student's own cell are placed as prokaryotic and eukaryotic.	The questions are attempted, but one or two answers read total surface instead of the ratio, claim the result proves the hypothesis, omit the folding structure, or swap prokaryotic and eukaryotic.	The analysis questions are missing or do not address the results.
Critique of the chatbot or of the printed flawed analysis	On either route, at least two errors are quoted and corrected with evidence from the student's own tables or the chapter, stretch answers are marked to check later, and one correct point is acknowledged; both routes earn this band equally.	On either route, errors are named but corrected without evidence, or only one error is caught.	No critique appears, or pasted output is submitted without any checking.
Reflection on the limits of the model	The chosen reflection option is answered in 3–4 sentences that tie a specific gap between the cube model and a real cell to a concrete change in the model or in what can be claimed.	The reflection is answered but stays general or names no specific change.	No reflection is submitted.

Quality Gate

• Every number in the tables comes from your own spreadsheet or hand calculation, never from memory or a chatbot.
• Each ratio divides surface area by volume, in that order, and is written in simplest form.
• The hypothesis was written before the first calculation and has the if… then… because… form.
• The scale notes describe what the interactive shows in words and do not add sizes it does not show.
• No measurement, maximum size, percentage, study, or source is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence from your tables or the chapter.