preliminary math lesson

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Preliminary Graphing Lesson Plan

VOCABULARY:

scatter plot: a graph that shows the relationship between two sets of data using points. Each point represents a pair of numbers.
correlation: the relationship between two sets of data.
line of best fit: a straight line that is drawn through the scatter plot that estimates the relationship between two sets of data.

OVERVIEW

The purpose of this lesson is for students to become familiar with the applications of graphing techniques, specifically scatter plots, in data analysis.

Click HERE for Core Curriculum Standards.

Learning Objectives

In this lesson, students will learn to:

systematically collect, organize, and describe data
construct, read, and interpret tables and graphs
make inferences and convincing arguments based on data analysis

Materials Needed

graph paper
rulers

Procedures

Discuss physical growth and have students hypothesize about one's height in relation to the lengths of arms, legs, feet, etc.
Have students survey a set group of people, noting each individual's height and arm span (length from left middle fingertip to right middle fingertip when arms are outstretched).
Students will then organize the collected data in a three column table whereby the first column represents the person's name, the second column will represent that person's height, and the third column will represent their arm span in cm.
Using graph paper, guide students in making a graph with a vertical and a horizontal axis, with the vertical axis (Y) representing arm span, and the horizontal axis (X) representing height.
Refer to tables and guide students in plotting a point where the two sets of data for each person meet. For example, find Mary's height on "x", and Mary's arm span on "y". Trace each line and place a point where the lines intersect. Graph all points. This is a scatter plot.
When all points have been plotted, students will observe a TREND, or pattern. To determine what kind of correlation they are looking at it, students should try to draw a straight line, or a line of best fit, through the points so that the line is as close to all points as possible. Note: If the students have trouble doing this, have them visualize the line as an arrow pointing either upward or downward to the right, showing the direction in which the data point.
Note the three types of correlation and what they mean:

       a) positive correlation - when one set increases, so does the other (as Mary's height increases, her arms will get longer).
       b) negative correlation - when one set increases, the other decreases (the further North latitude, the lower the temperature)
       c) no correlation - there is no relationship between the two sets of data ( as Mary's height increase, it does not change her IQ)

Assessment

Have the students draw conclusions based on their graphs and explain any correlations they find. Students may also make predictions about a person's arm span based on that person's height. Students might prepare a presentation or a final paper according to a teacher made outline.

Some suggested questions to consider:

Describe the trend you see in the scatter plot.
Which shows the trend better, the table or scatter plot?
Which point(s) fit the trend the least? Why do you think that is?
Would you ever expect to see all points on a perfectly straight line? Why or why not?

This lesson could be modified and done for different sets of data which would enable students to observe all three types of correlation.

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