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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.
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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

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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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

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.
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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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Number and Operations

Components of a Vector

9-12
In this lesson, students manipulate a velocity vector to control the movement of a car in a game setting. Students learn that vectors are composed of two components: magnitude and direction.
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Number and Operations

Sums of Vectors and Their Properties

9-12
This example illustrates how using a dynamic geometrical representation can help students develop an understanding of vectors and their properties, as described in the Number and Operations Standard. Students manipulate a two vectors to control the movement of a plane in a game-like setting. Students extend their knowledge from the first lesson to further investigate the system of vectors.