**
Summer Research
Program for Science Teachers**

*JHS 126, Brooklyn*

*
2000*

Why Are Cells So Small?

**Goal:** to help students to develop an understanding
of the relationship between cell surface area, cell volume and
the ability of materials to diffuse throughout a cell.

**Materials:** agar block infused with
phenolpthalein , metric ruler , scalpel, mild base ( ammonium
hydroxide-very dilute is acceptable), gloves, goggles, beakers,
flat plates, lab notebooks, calculators, pencils.

**Overview:** phenolpthalein
is an indicator that turns pink in a basic environment. [5-8 Content Standard
B-
Properties of matter] Ammonium
hydroxide is a basic solution that easily diffuses throughout a
congealed agarose block.

The depth to which the
solution diffuses is easily determined by simple observation of
the areas inside of the block where a color change is visible.
Through a series of simple calculations the student can see that
the % of diffusion is clearly linked to the ratio of surface area
to volume. [Content Standard
Unifying Concepts- Change, constancy, and measurment] This offers students an opportunity
to understand the need for

**Procedure:** prepare a solution of agar which
will sufficiently fill a baking pan to a depth of 3 cm. , mix
into the solution 1 ml. of phenolpthalein. Allow the agar to
congeal into a hardened block. The block will have the
consistency of gelatin. Have each group cut and remove a piece
of the block that measures (approx.) 10cm. X 4cm.
X 3 cm. . The responsibility of each of the lab teams will
be to prepare cubes of the following dimensions: 1cm. X 1 cm. X
1cm. , 2 cm. X 2 cm. X 2 cm. , and finally 3cm. X
3cm. X 3 cm. Each group will calculate the volume and
surface area of each cube, as follows:

**volume
= s x s x s (cubic centimeters)
**

** **

** surface area = 6 x s x s
(square centimeters) **

Each group will then calculate the
s.a./vol. Ratio for each of the individual cubes. A q&a
session should follow this step to see if any of the groups have
come to a conclusion about the ratio as the length of a the side
of the cube increases. Each group will place each cube into the
basic solution for approximately 1 minute. Immediately upon
removal of each cube from the solution a group member will bisect
(accuracy in this step is not essential- as long as the interior
of the cube is exposed) each cube. Depth of penetration of the
solution can easily be determined by observation of the depth to
which a color change can be observed. We can assume that
diffusion has occurred equally in all directions due to the cubic
shape. Students will measure the depth of penetration

And subtract that distance
from the side of the original cube. This procedure will be
repeated for each of the three original cubes. Accuracy in
measurement and accuracy in the accumulation and recording of the
data is essential and should be rotated among team members. Once
the length of the un-penetrated side has been calculated
the volume of the un-penetrated cube can be calculated for each
of the three original samples. The volume of each of the
penetrated regions can be found by subtracting the volume
of the un-penetrated region from the volume of the original cube.
The final set of calculations will be to calculate the % of
diffusion , as follows:

**% of diffusion = volume of pink area/
original volume x 100 **

each group will be responsible
for calculating the % of diffusion for each of the original
cubes.

**Follow-up: **if all procedures have been followed
correctly , the students should observe an inverse relationship
between the length of the cube side and the % of diffusion of
the basic solution. The students should also be able to conclude
that there is an inverse relationship between the length of the
side of the cube and the s.a./vol. Ratio. [5-8 Content Standard
A-
Use evidence to explain]Students
might be asked to draw conclusions about the design plan followed
by most organisms. Follow-up assignments might center about
the feasibility of designing an organism with the body plan of
“the blob “ ( a very large unicellular organism) .