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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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Data Analysis and Probability

Northwestern Crows

9-12
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.
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Data Analysis and Probability

Analyze the Data

9-12
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.
Data Analysis and Probability

Looking Back and Moving Forward

9-12
As you review student work in this unit, it is important to remember the mathematical objectives/expectations of this Unit Plan that are stated in Principles and Standards for School Mathematics.