Activity Template
Subject Area(s) Biology
Associated Unit
None
Associated Lesson None
Activity Title Why Cells are Small: Surface area to Volume
Ratios
Header
Image 1
ADA Description: Cells and microscope
Caption: Cells are small, but all living things are made of cells
Image file name: j0301072.wmf
Source/Rights: Copyright © Copyright © 2007 Microsoft Corporation, One
Microsoft Way, Redmond, WA 98052-6399
Grade Level 9 (9 - 11)
Activity Dependency none
Time Required 50 minutes
Group Size 4
Expendable Cost per Group US$1.25
Summary
This lab investigates why cells are generally small: as they increase in size, the surface area
increases much faster than the volume, making the surface area to volume ratio decrease as the
cell gets larger. Because of this, larger cells have a hard time getting enough nutrients in and
enough wastes out of the cell – there is too much cell to get all the “stuff” across the membrane.
Very large cells do exist, but most have novel ways of getting around this constraint – like giant
nerve cells are very big, but they are also very long and thin, increasing the surface area to
volume ratio. This lab has students build sugar cube models to help them visualize the surface
area to volume relationship, and then use hot potatoes to understand how heat is lost in small and
large potatoes.
Engineering Connection
Engineers must understand the relationship between surface areas and volumes and other
geometric relationships in many types of calculations. It is relevant in biomedical engineering,
in calculating heat exchange in many fields of engineering, and is used in principle in wastewater
engineering.
Engineering Category
(1) relates science concept to engineering
Level of Inquiry
Guided Inquiry
Keywords
cell size, potato, sugar cube, surface area to volume ratio
Educational Standards
State science: (California)
Grades 9-12 Biology / Life Sciences
1. The fundamental life processes of plants and animals depend on a variety of chemical
reactions that occur in specialized areas of the organism’s cells. As a basis for understanding
this concept:
a. Students know cells are enclosed within semipermeable membranes that regulate their
interaction with their surroundings.
9. As a result of the coordinated structures and functions of organ systems, the internal
environment of the human body remains relatively stable (homeostatic) despite changes in
the outside environment. As a basis for understanding this concept:
a. Students know how the complementary activity of major body systems provides cells with
oxygen and nutrients and removes toxic waste products such as carbon dioxide.
State math:
Grade 6
1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show
the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).
Pre-Requisite Knowledge
Students should have a basic understanding of cells, and diffusion & active transport. Lesson
also assume students have at least a basic understanding that cells get nutrients and expel
wastes through these processes, and that cells, in general, are small.
Learning Objectives
After this activity, students should be able to:
 explain the difference between surface area and volume, and how they increase in relation to
each other
 explain why cells are small
 explain why multicellular organisms may have an advantage over unicellular organisms
Materials List
Each group needs:
 100 sugar cubes

2 hot potatoes, 1 large, 1 small

2 thermometers

Paper towels or some other way to handle hot potatoes

Worksheets (one per individual or one per group)
To share with the entire class:
 One toaster oven to keep potatoes warm for classes
Introduction / Motivation
The human body is made up of a lot of different types of cells, but one thing they all have in
common, and what they have in common with most types of cells that make up any kind of
organism is that they are almost all very, very small. Why is this? Why aren’t we just one giant
cell? Why is each cell in every organism, almost without exception so very tiny?
It turns out there’s a very good reason for this. Big cells have a lot of problems that they
just can’t solve, because they can’t get enough food and get rid of enough waste. But little cells
have no problem with this. So what’s the difference? That’s what we’ll be looking at today.
Vocabulary / Definitions
Word
Definition
Surface
The area of all of the faces of an object added together. For example, for a cube,
area
the area of one side is the length x width. Since there are six sides on a cube, the
surface area is 6 x length x width.
Procedure
Before the Activity
 Bake potatoes before school so they are soft. This can be done the night before, but ideally
would be done the morning of so they are easy to warm in class.
 It helps to count out the sugar cubes for the groups, though this is tedious. If students don’t
eat the cubes, you can reuse them for subsequent classes. Try to have a few spares on hand.
 In school, reheat enough potatoes so each group can have one small and one large potato.

With the Students
1. Divide students into groups.
2. Start students with sugar cube exercise. It helps to lead them through the first example, so
they understand what they are expected to fill in for the chart. Give them a few minutes to build
the structures and do calculations. Tell them to build the structures. Some groups will need a
little more guidance than others on this part, so make sure everyone understands the point, and
that they are calculating the numbers correctly. Point out that they have enough cubes to build
each structure without dismantling the previous one.
2. Once the majority of students have finished this section (~10-15 min), quickly go over that
part of the exercise, pointing out what happened to the surface area as the cubes got bigger, what
happened to the volume, and what happened to the ratio. Also – what happened with that last
column? Interesting…
3. Now move onto the hot potato section. Explain to the students that they are going to act as
scientists today, and they will conduct their own experiment trying to understand why cells are
small, based on the results they got from the first part.
4. Remind them that cells have to bring in food from the outside world, and get rid of cellular
waste somehow. Perhaps this surface area to volume ratio is important. Explain they will be
using a potato as a model for a cell. Heat is the cellular waste that they have to monitor. Which
potato will be better at getting rid of that waste?
5. Have students create a hypothesis about which potato will get rid of heat better, and come up
with an experiment to test it. They should include in their experimental design what they are
testing, how they will test it, how often they will test it. Most will come up with something like
measure the temperature of the potato – but make sure they know where they will put the
thermometer! Will they measure the temperature once or at intervals, or start and end? Make
sure they record their data, not just in the graph they are supposed to make.
Attachments
Embedded_assessment.doc
Embedded_assessment.pdf
Post_activity_assessment.doc
Post_activity_assessment.pdf
Preassessment_Questions.doc
Preassessment_Questions.pdf
teachers_manual.doc
teachers_manual.pdf
Safety Issues
 Thermometer breakage: Students may try to poke the hole in the potato for the thermometer
with the thermometer. This is a bad plan. Remind them that thermometers break easily and
point out that it works well to poke a hole in the potato with a pencil, and then place the
thermometer in the hole. Once the thermometer is in place, it is best to leave it, but place the
potato on a table, so that the thermometer lies on its side and can’t tip.
 Hot potatoes and hot toaster oven are potential burn hazards. Do not allow students to handle
things in the toaster oven, and only allow them to handle hot potatoes with paper towels.
Note the limits of your alcohol thermometers – potatoes needn’t be extremely hot.
Troubleshooting Tips
Potatoes must be precooked (by microwave or oven) to be soft enough to get the thermometer
into them. If they are not, and simply microwaved in class, they will be too hot for the
experiment.
Assessment
Pre-Activity Assessment
Title: Preassessment_Questions
A preliminary assessment to see how much students understand about cell size before the
activity.
Activity Embedded Assessment
Title: Embedded_assessment
A worksheet which guides them through the activity and includes follow-up questions to gauge
understanding of the concepts and how well students can extrapolate concepts to larger contexts.
These questions can also be used in class discussion.
Post-Activity Assessment
Title: post_activity_assessment
A warm-up which can be copied onto an overhead transparency for use the following day to
initiate conversation about the previous day’s lab and check for comprehension and retention.
Activity Scaling
 For lower grades, use only the hot potato portion, and let them understand the concepts of
which size potato will hold heat longer.
References
Other
Ideas based loosely on labs created by Judy Sanderson, teacher at Culver City High School.
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Owner
UCLA SEE-LA GK-12 Program, University of California, Los Angeles.
Contributors
Kristine Kaiser
Copyright
© 2009 University of California, Los Angeles. This digital library content was
developed by the GK12 SEE-LA program under National Science Foundation grant no..