Automobile Mileage: Years Since 1990 vs. Mileage

This lesson is a third representation of the automobile mileage data used in Lessons Five and Six of this Unit Plan. This lesson provides another opportunity for the students to analyze how changing the independent variable in a set of data can result in a different least squares regression line. Students can then use the new equation to make some of the same predictions they made in Lessons
Five and Six.

Automobile Mileage: Comparing and Contrasting

In this lesson, students compare and contrast their findings in Lessons Five, Six, and Seven of this Unit Plan. This lesson allows students the time they need to think about and discuss what they have done in the previous lessons. This lesson will provide the teacher with another opportunity to listen to student discourse and assess student understanding.

Make a Conjecture

Doctors and veterinarians are interested in a quantity called the "cardiac output" which is a measure of the rate of blood flow being pumped by the heart. To measure the cardiac output, a catheter (tube) is inserted through the heart. The catheter measures the temperature of the surrounding blood near the tip of the probe. The catheter has a small balloon at the tip which is inflated to help the probe move through the heart and then deflated. Once the catheter is inserted, ice water is injected through the catheter and emerges from a small hole approximately 12 inches before the end of the catheter.

Analyze the Data

Students will analyze and graph the data taken.

Reflecting On Your Work

The methods explored in the measuring of cardiac output can be applied to other situations. Two of these situations are described here. The first examines the sediments flowing from the Des Moines River near Saylorville, Iowa. The second situation investigates the measurement of blood flow through the brain.

Light in the Ocean

In the first lesson, students make a conjecture about how the intensity of light changes as a function of the depth of the ocean. A video clip is used to prompt thinking, and students propose a graph that represents light intensity vs. depth.

Gather Data

To test their conjectures, students gather data using one of three different methods: using a simulated online dive; covering a tank with plexiglass to simulate ocean water; or, incrementally filling a column with water to simulate increasing depth.

Reflect On Your Work

This lesson contains extension activities that can be used as follow-ups to the light intensity investigation. The extensions rely on exponential models, but each uses a different context.

Northwestern Crows

Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. The crows appear to be selective; they pick up only large-sized whelks. They are also persistent. For instance, one crow was observed to drop a single whelk 20 times. Scientists have suggested that this behavior is an example of decision-making in optimal foraging.