Today students will explore the mathematical relationship between surface area to volume ratio. Students need to understand this relationship so that they realize there is a limitation to cell size. Many students have the misconception that a cell can continue to grow forever. Here is an overview of what students will learn today.
Show the trailer for the movie The Blob. (Note: I start the video at 0:37 and end it at 1:26.)
Ask students if they think a single celled organism like an amoeba could get big enough to eat a small fish. What about a rat? What about a human? Have them explain their reasoning.
Equipment needed for each student group:
Students should wear gloves and goggles when handling the gelatin blocks. Give student a large block of gelatin that has been prepared with phenolphthalein. (See this protocol to make indicator cubes. IMPORTANT: Gelatin should be pre-made at least a day before the lab. It will take 24 hours for the gelatin to set.)
Using a ruler and scalpel, have students cut the gelatin into 1 cm^3, 2 cm^3, and 3 cm^3 gelatin cubes. Have students gently place the cubes into a disposable petri dish. Have students make sketches in their lab notebook or the provided student handout. Students could also take a picture of the gelatin cubes. Next have students calculate the total surface area in cm^2 using the formula length X width X number of sides. They should also calculate the total volume of the cube using the formula length X width X height. Students should record this data in their lab notebooks or student handout.
Students should then pour 15 mL of ammonia over the top of each cube and record any changes they may see. Cubes should then be placed in the fume hood and the fume hood should be turned on. Observations will be recorded again at the end of the period.
Students should clean up their lab areas and return to their seats.
(Note: Ammonia can give off fumes that can be irritating to some students. A 1% solution of sodium hydroxide can be substituted instead. However, it will take longer to see results.)
Use the NSTA Interactive: Cell Size and Efficiency found in the Science Object, Cell Structure and Function: Cells--The Basis of Life. (Note: This interactive can be accessed on the NSTA Learning Center and is free for teachers to use as long as they have a Learning Center account. Search for the Science Object by using the keyword surface area.)
Project the interactive and lead students through the data collection exercise. (Note: I asked for student volunteers to drag the ruler within the interactive and measure each of the cubes in the interactive. We complete the table as a class.)
Ask students how many times bigger each of the blocks are as compared to each other. (Here is a copy of the completed data Table from the interactive.)
Note: It is not necessary to use the NSTA Interactive. One can simply project a 1 cm^3, 2cm^3, 3 cm^3, and 4 cm^3 drawings of cubes. Then have students measure the length of the cubes and perform the necessary calculations to complete the data table.
After completing the Science Object interactive as a class, students should retrieve their gelatin cubes from the fume hood. Students should wear gloves and goggles while handling the gelatin cubes. They should take pictures of the gelatin cubes or make sketches in their lab notebooks. They should note the time that has elapsed since the ammonia has been added.
Students should gently remove the gelatin from the petri dish and place it into a new clean, dry petri dish. Using a scalpel, students should slice the gelatin cube and record what they see in their lab notebooks by making a sketch. They could also take pictures. (Here are a sample of the pictures that my class took of their gelatin cubes: 1 cm^3 cube bisected, 2 cm^3 cube bisected, 3 cm^3 cube bisected, and A comparison of gelatin cubes after 25 minutes).
Students should place the gelatin cubes in the chemical disposal bucket. They should pour the ammonia down the sink with copious amounts of water.
Students should then calculate the total surface area to volume ratio by dividing the surface area from the volume. Students should expressed the ratio is the simplest form. Students should record these calculations in their lab notebooks or the student handout.
Give the students copies of the gelatin cube handout which is 1-D cutout of the agar cube drawn on graph paper. Students can cut these graph cubes out and fold them on the dotted lines to make a cube. Using colored pencils have students draw on the graph paper cube how far into the gelatin block the ammonia traveled. (This distance would be where the gelatin block changed from clear to pink.) Then have students unfold the cube and glue them into their lab notebook.
Ask students what the surface area to volume ratio was for each of the gelatin blocks.
Ask students the following questions
Now have students consider what needs to happen to the cell membrane as the cell increases in size.
Give students time to record their final findings in their lab notebooks.
Check students' understanding by having them answer the following questions about the activity and lab.
(Answer: the cell membrane)
(Answer: the cytoplasm)
(Possible Answers: Diffusion of gases and liquids into and out of the cell, Removal of waste products from the cell.)
(Possible Answers: The cell can die. Certain cell processes are triggered inside the cell leading to the copying of all cell components and the dividing of the cell into two smaller cells.)
Have students look back at their responses from the beginning of class. Have students revise their predictions about whether or not a living thing like the Blob could exist. Have students support their claim with evidence from today's lab and interactive. Students should record their thoughts in their lab notebooks and turn them in for evaluation.