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Data Analysis and Probability

Automobile Mileage: Age vs. Mileage

9-12

In this lesson, students plot data about automobile mileage and interpret the meaning of the slope and y-intercept of the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and y-intercept of the line and put those meanings in the context of the real-life application.

The activity is very similar to that in Lesson Five of this Unit Plan. However, by graphing the data in a different format, the students will produce a line with a positive slope in this activity, while the line in Lesson Five had a negative slope. Doing both lessons allows students to investigate how changing the independent variable affects the resulting graph and equation.

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Data Analysis and Probability

Automobile Mileage: Years Since 1990 vs. Mileage

9-12
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.
LPgeneric
Data Analysis and Probability

Automobile Mileage: Comparing and Contrasting

9-12
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.
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Data Analysis and Probability

Make a Conjecture

9-12
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.
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Data Analysis and Probability

Gather Data

9-12

Students will construct a simple experiment, using a catheter, which can measure cardiac output.

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Data Analysis and Probability

Analyze the Data

9-12
Students will analyze and graph the data taken.
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Data Analysis and Probability

Reflecting On Your Work

9-12
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.
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Algebra

Light in the Ocean

9-12
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.
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Algebra

Gather Data

9-12
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.
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Algebra

Reflect On Your Work

9-12
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.