### Clarifications

*Clarification 1:*Descriptions include outliers; positive or negative association; linear or nonlinear association; strong or weak association.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**8

**Strand:**Data Analysis and Probability

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Association
- Outlier
- Scatter Plot

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### 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

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.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Experts

## Perspectives Video: Professional/Enthusiasts

## Problem-Solving Task

## MFAS Formative Assessments

Students are asked to construct a scatterplot corresponding to a given set of data.

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Students are given a scatter plot in a real-world context and asked to describe the association between the variables.

## Original Student Tutorials Science - Grades K-8

Continue an exploration of kinematics to describe linear motion by focusing on position-time measurements from the motion trial in part 1. In this interactive tutorial, you'll identify position measurements from the spark tape, analyze a scatterplot of the position-time data, calculate and interpret slope on the position-time graph, and make inferences about the dune buggy’s average speed

## Original Student Tutorials Mathematics - Grades 6-8

Explore the different types of associations that can exist between bivariate data in this interactive tutorial.

This is part 2 in 6-part series. Click below to open the other tutorials in the series.

Explore informally fitting a trend line to data graphed in a scatter plot in this interactive online tutorial.

This is part 3 in 6-part series. Click below to open the other tutorials in the series.

## Student Resources

## Original Student Tutorials

Continue an exploration of kinematics to describe linear motion by focusing on position-time measurements from the motion trial in part 1. In this interactive tutorial, you'll identify position measurements from the spark tape, analyze a scatterplot of the position-time data, calculate and interpret slope on the position-time graph, and make inferences about the dune buggy’s average speed

Type: Original Student Tutorial

Explore informally fitting a trend line to data graphed in a scatter plot in this interactive online tutorial.

This is part 3 in 6-part series. Click below to open the other tutorials in the series.

- Scatterplots Part 1: Graphing
- Scatterplots Part 2: Patterns, Associations and Correlations
- Scatterolots Part 4: Equation of the Trend Line
- Scatterplots Part 5: Interpreting the Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

Type: Original Student Tutorial

Explore the different types of associations that can exist between bivariate data in this interactive tutorial.

This is part 2 in 6-part series. Click below to open the other tutorials in the series.

- Scatterplots Part 1: Graphing
- Scatterplots Part 3: Trend Lines
- Scatterolots Part 4: Equation of the Trend Line
- Scatterplots Part 5: Interpreting the Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

Type: Original Student Tutorial

## Problem-Solving Task

Students are asked to examine a scatter plot and then interpret its meaning. Students should identify the form of the relationship (linear, curved, etc.), the direction or correlation (positive or negative), any specific outliers, the strength of the relationship between the two variables, and any other relevant observations.

Type: Problem-Solving Task

## Parent Resources

## Problem-Solving Task

Students are asked to examine a scatter plot and then interpret its meaning. Students should identify the form of the relationship (linear, curved, etc.), the direction or correlation (positive or negative), any specific outliers, the strength of the relationship between the two variables, and any other relevant observations.

Type: Problem-Solving Task