that today you will be modeling the how the body's kidneys filter
blood. Pour 1 liter of water into a pitcher, and explain that the water
represents some of the blood in your body. To start the discussion,
ask, "About how much blood do you have in your body?" [5 liters.]
Put several drops of food coloring into the water. Explain that this
food coloring represents 1000 mg of a drug (such as acetaminophen or
ibuprofen) that you have taken. Mix the food coloring well with the
water. Tell students that after four hours the kidneys will filter out
about 25% of this drug. Ask, "How can this be modeled?" Allow students
to offer suggestions, and then remove 250 ml of the mixture and replace
it with 250 ml of clear water. Then ask, "How many milligrams of the
drug remain in my blood?"
Before removing any more colored water, ask, "How could the kidney's
work be modeled after another four hours?" Many students will respond
that you should remove another 250 ml of colored water and replace it
with another 250 ml of clear water. Then ask, "If we did this, how many
milligrams of the drug would remain in my blood?" Allow students to
make a prediction, often 500 mg, without correction. Ask again for one
more four‑hour period. Most often students will say that again 250 mg
of the drug are removed. Finally, ask, "So, if I repeat this process
four times, will the drug be completely out of my system?" Most often
students will answer, "Yes."
Now, remove 250 mg of the colored water a second time, and replace
with 250 ml of clear water. Repeat and ask, "If I do this once more,
will all the color will be gone, leaving clear water?" The students can
now see that this will not happen. Have students debate whether it was
the model or the prediction that was incorrect. Students may realize
that the second time you removed 250 mg of colored water there was only
750 mg of the drug in the blood, so replacing a fourth of it only
removed 1/4 × 750 = 187.5 mg.
Distribute the Drug Filtering
activity sheet. Students may work alone or with a partner. Circulate
around the room to make sure everyone is engaged in the activity. Help
students connect their data to the demonstration. Make sure that
students are graphing the model correctly. Check that their data is
correct and that they are reading the scale of the graph correctly.
Ask students if the graph representing this situation is a linear
graph. [No. It is exponential.] Explain that drug filtering is not
linear, because the same amount of the drug is not removed during each
four‑hour period. Have students look at their graphs. Explain that this
is an exponential decay model. Ask students to suggest other scenarios
that can be represented by exponential decay models.
Review the answers with the Drug Filtering Answer Key.