### Clarifications

*Clarification 1:*Instruction focuses on the connection to linear functions.

*Clarification 2:* Instruction includes using a variety of tools, including a ruler, to draw a line with approximately the same number of points above and below the line.

**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
- Line of Fit
- Scatter Plot

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grades 6 and 7, students created graphical representations for both numerical and categorical univariate data. In grade 8, students encounter bivariate data displayed with scatter plots, and they use their knowledge of graphing lines to determine approximate lines of fit. In Algebra 1, students will continue working with scatter plots and lines of fit to display association, but expand their knowledge to consider association in bivariate categorical data, displayed with frequency tables.- Instruction includes the understanding that a straight line can used to display a linear association in a scatter plot. This line allows predictions of other potential data points. Instruction includes students discussing what it means to be above and below the line of fit
*(**MTR.4.1*). - Instruction includes providing opportunities to look at multiple lines of fit and determine which would be the best model for the scatter plot. The use of manipulatives are a way for students to make adjustments on their informal fit of a line. Students should compare and contrast their models and explain why their models best represent the fit of the data
*(**MTR.4.1*). - Instruction includes the use of linear models to represent the line of fit. Students should describe the $x$-intercept and slope in terms of the context within the scatter plot.

### Common Misconceptions or Errors

- Students may incorrectly believe the line of fit should go through all the data points. To address this misconception, provide examples to students to show some lines that do go through data points and examples that may go through very few or no data points.
- Students may incorrectly think the line of fit should go through the first and last data point on the scatter plot. To address this misconception, provide examples to students to show some lines that do not go through the first and last data point.

### Strategies to Support Tiered Instruction

- Using digital tools to model graphing a line of fit will provide clarity for misunderstanding that a line of fit needs to either start with the first and end with the last point or go through all points.
- Teacher provides examples to showing lines of fit that go through data points and examples that may go through very few or no data points.
- Teacher provides examples to show lines of fit that do not go through the first and last data point.

### Instructional Tasks

*Instructional Task 1*

**(MTR.6.1,***MTR.7.1*)Each graph shows the same set of data and a line that has been fitted to the data.

- Part A. Determine which line, $a$, $b$ or $c$, most appropriately fits the data and explain why.
- Part B. What statistical question could be asked to represent the set of data?

### Instructional Items

*Instructional Item 1*

The scatter plot below shows the relationship between the ages and weights of 50 female infants. Draw a line on the scatter plot that fits the data.

*Instructional Item 2*

A scatter plot is shown in the coordinate plane. Draw a line on the scatter plot that fits the data.

**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: Professional/Enthusiasts

## Teaching Idea

## STEM Lessons - Model Eliciting Activity

Students will apply skills (making a scatter plot, finding Line of Best Fit, finding an equation and predicting the y-value of a point on the line given its x-coordinate) to a fuel efficiency problem and then consider other factors such as color, style, and horsepower when designing a new coupe vehicle.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal studentsâ€™ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

## MFAS Formative Assessments

Students are asked to informally fit a line to model the relationship between two quantitative variables and to assess how well that line fits the data.

Students are asked to informally fit a line to model the relationship between two quantitative variables and to assess how well that line fits the data.

Students are asked to informally assess three lines fitted to data to determine which fit is the best.

Students are asked to compare two lines fitted to data to determine which fit is better.

## Original Student Tutorials Mathematics - Grades 6-8

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.

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

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

## Student Resources

## Original Student Tutorials

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

This is part 6 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
- Scatterplots Part 3: Trend Lines
- Scatterplots Part 4: Equation of the Trend Line
- Scatterplots Part 5: Interpreting the Equation of the Trend Line

Type: Original Student Tutorial

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 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
- Scatterplots Part 3: Trend Lines
- Scatterplots Part 5: Interpreting the Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

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