Cell Size and Division or How Big Would You Want To Be If You Were A Cell

Nicholas DiGiovanni            Naperville Central High School
                               440 W. Aurora Rd
                               Naperville IL 60540
                               708-420-6417

Objectives:

1. For all grades: to illustrate the usefulness of models to represent things 
which are too small (cells or molecules) or too large in science.
 
2. For primary grades: to learn to measure with a ruler, to cut a cube, and 
determine smaller particles react faster than larger particles.

3. For middle grades: to determine surface area and volume of a cube in addition 
to the above. 

4. For upper grades: to determine the surface area to volume ratio and relate 
this to cell size, to determine why cells divide and 1-3 above.

Materials:

2500 ml 2% agar solution (sufficient for 15-20 set-ups or pairs)
a cake pan
phenolphthalein powder
1  250 ml beaker or cup 
50 ml .4%  NaOH solution
a metric ruler, stirrer or spoon, plastic knife, and paper towels

Strategy:

1.Advance Preparation:
Mix enough agar powder in boiling water to make a 2% agar solution.  Use enough 
water to fill a cake pan to a depth of 3 cm (approximately 2500 ml).  Stir until 
all the powder is dissolved.  As the agar cools, add 1 g of phenolphthalein (if 
solid is unavailable, add several ml of liquid phenolphthalein indicator) per 
liter of solution and stir thoroughly.  If the color is pink, add dilute acid 
drop by drop until the solution turns colorless.  Pour the mixture into the cake 
pan to solidify.  This will provide the agar for the model of the cells.  If 
agar is unavailable, substitute potatoes, but then razor blades must be used and 
a dye found which will penetrate the potato in a short time. 

2. Discuss models and their importance with the class.  In this activity we will 
use agar blocks to represent cells. 

3. Give the students a 6x3x3 cm block of agar cut from the cake pan, a plastic 
knife, and metric ruler.  Ask them to cut three separate cubes 1x1x1, 2x2x2, and 
3x3x3 cm from the block. 

4. Ask the students, "If you were a cell which cell would you rather be (small, 
medium, or large) and why?"  Write this down.

5. Ask the students to place the cubes into the beaker.  Then the teacher pours 
the NaOH into the beaker to just cover the cubes.  (CAUTION:  Sodium hydroxide 
is caustic and can burn the skin and eyes.)  

6. The cubes should remain in the solution for 10 minutes.  They should be 
stirred occasionally with the spoon.  When the NaOH comes into contact with the 
agar blocks, the blocks and perhaps the solution will turn a pink color.  The 
students enjoy this. 

7. Depending on the grade level, students should be given a task to do while the 
cubes are "soaking".  Primary grades may be asked if this were a cell, what type 
of things might move into it.  Older students may be asked the same as well as 
to explain diffusion since this is what is happening.  They should also be asked 
to set up a data table in which they determine the surface area, volume, and 
surface area to volume ratio for each cube. 

8. After 10 minutes the cubes are taken out of the beaker with a spoon and dried 
off with a paper towel.  The students should cut the cubes in half and measure 
the distance from the outer edge inward that has turned pink and record this. 

9. Students will discover that the distance that the solution travelled in each 
cube is the same (5 mm).  There is a pink border around the 2x2x2 cm and 3x3x3 
cm cube, but the 1x1x1 cm cube is pink throughout.  Ask if the pink represented 
food, water or something else needed by the cell to survive, which "cell" got 
the needed substance distributed to all its parts.  They should see that the 
smallest cell is most efficient since it is pink throughout.  

10. Mathematically, students should observe that the smallest cube has the 
largest surface area to volume ratio (SA:VOL).  Therefore this illustrates that 
a large SA:VOL promotes better efficiency in moving things into and out of cells 
and thus survival.  This can also be related to smaller particles reacting 
faster than larger particles in chemical reactions (i.e. Granular sugar 
dissolves easier than sugar cubes.) 

Assessment:

    Students can be asked which type cell they think would have a better chance 
for survival, one which is 1x1x1 cm or one which is .1x.1x.1 cm.  They need to 
justify their response.  5 points for a proper mathematical as well as written 
explanation.  4 points for an explanation which is a little unclear.  3 points 
for a proper explanation but improper or no math.  2 points for an unclear 
explanation but shows thought.  1 point for an honest attempt.  

Sources:

Adapted from Biological Sciences: An Ecological Approach.  Kendall Hunt.  1987