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## Gallery Walk

9-12
1

This lesson is designed to allow students to view the work of other students in the class and to explain their own work. Some teachers may be tempted to skip this step in the Unit Plan, but it is very important that students be given the opportunity to verbalize what the mathematics means that they performed in Lesson Three.

This lesson should begin with what is known as “Gallery Walk.” Depending on the size of the class, the students should be given a specified amount of time to view the graphs that were taped to the wall during Lesson Three of this Unit Plan. The students are to move from graph to graph during this time and, without any talking, view the work of their classmates. While on their “Gallery Walk,” the students should think about the data their classmates plotted and whether or not the information accompanying each graph seems appropriate.

After the “Gallery Walk” is completed, each pair of students should be given the opportunity to stand next to their graphs. Each student should explain one of the graphs. Their explanations should include such topics as why they thought their data would be linear in nature; how they chose the labels for their axes; what rate of change the slope of their line represents; what the y-intercept of their line means in the context of their data; what the correlation coefficient was; and, what the correlation coefficient meant in terms of the fit of their line.

• Graphs from the previous lesson

Assessment Option

These presentations will give both the teacher and students an opportunity to assess the students' understanding of the material in the first four lessons of this Unit Plan. At this stage of the Unit Plan it is important to know if students can:

• Correctly plot data points, both by hand and on the applet
• Interpret the meaning of the slope of a line as a rate of change in the context of real-life data
• Interpret the meaning of the y-intercept of a line in the context of real-life data
• Understand the meaning of correlation coefficients as used with their data sets
• Correctly label the axes on the graph of real-life data
• Correctly scale the axes for a set of real-life data

It is important to determine the students’ understanding and appropriate use of the mathematical vocabulary used thus far in this Unit Plan. Are the students’ grasping the concept of slope as a rate of change? Can they correctly interpret the y-intercept of the least squares regression line? Do they understand the relationship between the correlation coefficient and the “fit” of the least squares regression line? Determine if students may need some other data sets to really understand the relationship between the correlation coefficient computed by the calculator and the calculator’s regression equation.

The teacher should continue to collect information about the students’ understanding of the material on the Teacher Resource Sheet, Status of the Class. The assessment information you collect can help you monitor student learning, adjust instruction, and plan future lessons for the class. Data on individual students can be used to plan strategies for regrouping students, remediation, and extension activities. This information is extremely useful when discussing progress toward learning targets with students, parents, administrators, and colleagues.

Extension

Continue on to the next lesson in the unit, Automobile Mileage: Year vs. Mileage.

Questions for Students

1. When you took the Gallery Walk, what similarities did you notice among the graphs?
2. What differences did you observe on the Gallery Walk? What caused these differences?
3. Was the information presented on the graph represented appropriately?
4. What rate of change does the slope of the line represent?
5. What is the meaning of the y-intercept in the context of the data you presented?

Teacher Reflection

1. What key words did the students use correctly?
2. What key words did the students use incorrectly?
3. What adjustments would I make in this lesson the next time I teach it?
4. What mathematical content should I stress in earlier lessons in order to make this lesson more successful?

### Traveling Distances

9-12
In this lesson, students interpret the meaning of the slope and y-intercept of the graph of real-life data. By examining the graphical representation of the data, students relate the slope and y-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the resulting least squares regression line.

### Bathtub Water Levels

9-12
This lesson is similar to Lesson One: Traveling Distances; however, this lesson is designed so students examine real-life data that illustrates a negative slope. Students interpret the meaning of the negative slope and y-intercept of the graph of the real-life data. By examining the graphical representation of the data, students relate the slope and y-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the least squares regression line.

### My Graph Is…

9-12
This lesson is designed to allow students to select their own real-life data to plot and interpret. Interpreting the meaning of the slope and y-intercept of their least squares regression lines will help reinforce the concepts introduced in Lessons One and Two of this Unit Plan. The students are then given the opportunity to display their work.

### Automobile Mileage: Year vs. Mileage

9-12
In this lesson, students plot data about automobile mileage and interpret the meaning of the slope and y-intercept in the resulting equation for 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 interpret them in the context of the real-life application. Students also make decisions about the age and mileage of automobiles based on the equation of the least squares regression line.

### 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.

### 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.

### 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.

### 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.

### Learning Objectives

Students will:

• Explain their reasoning for selecting data.
• Explain their findings about the slope and y-intercept of their own data.

### NCTM Standards and Expectations

• Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled.
• Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference.
• Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions.