Standard #: MA.8.DP.1.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.8.AR.3

 

Terms from the K-12 Glossary

• Association
• Outlier
• Scatter Plot

 

Vertical Alignment

Previous Benchmarks

• MA.6.DP.1
• MA.7.DP.1

Next Benchmarks

• MA.912.DP.2.4
• MA.912.DP.2.6
• MA.912.DP.3.1

 

Purpose and Instructional Strategies

In grades 6 and 7, students described and interpreted, quantitatively and qualitatively, both numerical and categorical univariate data. In grade 8, students encounter bivariate data, and they use scatter plots to determine whether there is any association between the variables. In Algebra 1, students will continue working with scatter plots to display association, but expand their knowledge to consider association in bivariate categorical data, displayed with frequency tables.

• Instruction includes students communicating the relationships between two variables. Students should analyze scatter plots to determine the type and degree of association.
  
  
  
• Outliers in scatter plots are different than outliers in box plots. There is no special rule determining if a data point is an outlier in a scatter plot. Instead, students need to consider why the outlier does not fit the pattern. Students should examine if outliers are valid or represent a recording or measurement error. Students should identify outliers and clusters and give possible reasons for their existence (MTR.4.1, MTR.7.1).
• Instruction includes opportunities to discuss the effects of changing the data slightly and how the changes impact the scatter plots (MTR.4.1).

 

Common Misconceptions or Errors

• Students may invert positive and negative correlations.
• Students may incorrectly assume that associations can only have one descriptor.
  • For example, students may only say that the correlation is a positive association instead of describing it as a strong, positive linear association.
• Students may misinterpret an outlier and why it may occur in a set of data.

 

Strategies to Support Tiered Instruction

• Teacher provides clear examples of associations of scatter plots (representing both strong and weak associations). Teacher facilitates discussion about whether each association is positive or negative.
  
  
  
• Teacher provides examples of different outliers and discusses with students why this occurred. Creating this dialogue will help students begin to understand how outliers can be used differently depending on the type of data collected, and what the data is intended for.
• Instruction includes co-creating a graphic organizer to include examples of different patterns to association. Categories include trends in association (positive, negative, no), strength of association (strong, weak) and pattern of association (linear or nonlinear).

 

Instructional Tasks

Instructional Task 1 (MTR.4.1, MTR.7.1)
The graphs below shows the test scores of the students in Dexter's class. The first graph shows the relationship between test scores and the amount of time the students spent studying, and the second graph shows the relationship between test scores and shoe size.

 

• Part A. Describe and explain the pattern of association for each of the graphs.
• Part B. If you were to add an outlier to the first graph, describe the data point and what it would mean in context.

Instructional Task 2 (MTR.4.1, MTR.7.1)
Population density measures are approximations of the number of people per square unit of area. The following scatter plot represents data from each of the 50 states comparing population (in millions) to land area (in 10,000 square miles) in 2012.

• Part A. Describe the type and degree of association between population and land area.
• Part B. Discuss with a partner possible interpretations of your answer to Part A. Do you think this would hold true for other countries?

 

Instructional Items

Instructional Item 1
The scatter plot below compares middle school students' scores on the Epworth Sleepiness Scale (ESS) to their scores on a recent math test. The Epworth Sleepiness Scale measures excessive daytime sleepiness with zero being least sleepy. Describe the type and degree of association between scores on the Epworth Sleepiness Scale and scores on the math test.

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.