Overview

Using information from the game Monopoly, students compare the distance from “Go” and the cost of the property using a scatter plot, make a median fit line and determine why certain points are away from the line. Students can also determine if this line could be used for prediction.

Objective

Students will show that they can create a scatter plot and make a median fit line.

Standards Address

Mathematics — Data Analysis

Grade 7

Data Collection, Benchmark A

01. Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate.

 

Grade 8

Data Collection, Benchmark A

01. Use, create and interpret scatter plots and other types of graphs as appropriate.

Statistical Methods, Benchmark F

06. Make conjectures about possible relationship in a scatter plot and approximate line of best fit.

09. Construct convincing arguments based on analysis of data and interpretation of graphs.

 

Materials

• Graph paper

• Rulers

Procedure

1. Ask how many students have played Monopoly and what they know about the game board.

2. Allow the students to work with a partner or in groups of three, but make sure each student makes his or her own graph.

3. Distribute the Monopoly Madness handout and ask the students to make scatter plots that compare the distance of a property from “Go” and the cost of the property. (Distance is the independent variable because cost is determined by distance; therefore, distance will be on the x-axis.)

4. Once graphs are completed, share them with the class. Find out if everyone used the same intervals and how the graphs with different intervals might look different even though the same data are displayed. Have students look for points that look “out of whack” with the rest of the data. They should be able to identify these points as the railroads and the utilities.

5. Review the steps in making a median fit line:

Divide the number of points by three and draw a line showing each third. If the number of points is not divisible by three, the middle group will have the different number of points.

Find the median of each third vertically.

Find the median of each point horizontally.

Lay your ruler on the intersection of the two means in the first and last third. Move the ruler one-third of the way to the middle intersection and draw your line.

6. Advanced students can find the slope of the line.

Evaluation

Rubric for Scatter Plot

Category	4	3	2	1
Scatter Plot Construction	Student constructed the scatter plot correctly and paid attention to scale, labels, etc.	Student constructed the scatter plot correctly but missed attention to details.	Scatter plot had mistakes or unclear scale; there is minimal attention to detail.	Student does not understand scatter plot construction or how to form the scale.
Central Tendency	Student correctly calculated all three measures of central tendency and understood the change to the mean with an outlier present.	Student calculated the scatter plot correctly but misinterpreted change to the mean, or student made an error in calculation.	Student made a significant error in calculation and does not understand effect of outliers on mean.	Student does not understand how to calculate measures of central tendency and does not understand outliers effect on mean.
Line of Best Fit	Student correctly constructs line of best fit and is able to interpolate correctly.	Student made a minor error in line of best fit, but understands the process.	Student made an error in line of best fit and is not able to interpolate correctly.	Student does not understand how to find line of best fit and cannot interpolate correctly with the line.
Concepts	Student has a clear understanding of scatter plots and line of best fit and has communicated that effectively.	Student has satisfactory understanding of the major concepts, but has small misunderstandings.	Student has major misunderstandings of the concepts and cannot complete work on his own.	Student does not display understanding of the major concepts or did not complete the assignment.
Line	Line was correct. Thirds were correctly placed. Vertical and horizontal medians were correct in each third.	Line was correct and thirds were correct, but vertical and horizontal medians were not correctly placed.	Line was okay. Thirds and vertical and horizontal medians were not accurate.	Line was incorrect.