### Examples

*Example:*Jaylyn is collecting data about the relationship between grades in English and grades in mathematics. He represents the data using a scatter plot because he is interested if there is an association between the two variables without thinking of either one as an independent or dependent variable.

*Example:* Samantha is collecting data on her weekly quiz grade in her social studies class. She represents the data using a line graph with time as the independent variable.

### Clarifications

*Clarification 1:*Instruction includes recognizing similarities and differences between scatter plots and line graphs, and on determining which is more appropriate as a representation of the data based on the context.

*Clarification 2:* Sets of data are limited to 20 points.

**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

- Bivariate Data
- Scatter Plot

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grades 6 and 7, students worked with both numerical and categorical univariate data. Additionally, students have had experience developing statistical questions since grade 6. In grade 8, students encounter bivariate data, and it is restricted to numerical data, which is often displayed with a scatter plot, but in some circumstances, may also be displayed with a line graph. In Algebra 1, students will continue working with scatter plots and line graphs for bivariate numerical data, but expand their knowledge to bivariate categorical data, displayed with frequency tables.- Bivariate data refers to the two-variable data, with one variable graphed on the $x$-axis and the other variable on the $y$-axis. Instruction includes flexibility in the understanding of the dependent and independent variables. Students can represent situations in terms of $x$ or in terms of $y$.
- Instruction includes proper labeling of graphical representations, including axes, scales and a title.
- Line graphs are a way to map independent and dependent variables. Line graphs showcase data by connecting each data point together. The rate of change from a single data point to another data point can be measured. An overall trend can be described, but the trend is between individual or small groups of points. A line graph allows for the interpretation of the rate of change, or slope, between individual data points. The independent variable can be either numerical or categorical.
- For example, independent variables can be shown as months of the year.

- For example, independent variables can be shown as months of the year.
- Scatter plots are another way to show the relationship between two variables having individual points that will not be connected directly together. Often neither variable is thought of as the independent or dependent variable, so it is a matter of choice of which variable will be represented on the $x$-axis and which will be represented on the $y$-axis. Trends can be seen through the distribution of points. Scatter plots are used to collect a large number of data points to illustrate patterns in the data including linear or non-linear trends, clusters and outliers.
- Instruction includes the understanding that with bivariate data, a single $x$-value can be associated with more than one $y$-value. When this is the case, a scatter plot should be used as the graphical display rather than a line graph.
- Instruction includes providing opportunities for students to interact with scatter plots through the development of statistical questions.
- Students should label and determine appropriate scales when completing work with bivariate numerical data.

### Common Misconceptions or Errors

- When discussing and interpreting the data, students may incorrectly identify an association when the scatter plot shows no association. To address this misconception, provide examples for students that would help them understand that some data will not have association.
- For example, the height of a person and their number of pets.

- Students may confuse the dependent and independent variables when creating line graphs.
- Students may incorrectly believe bivariate data can only be displayed as a scatter plot.

### Strategies to Support Tiered Instruction

- Teacher provides instruction on different types of associations, then provides clear examples of associations of scatter plots for students who need additional assistance identifying associations.
- Teacher provides instruction on independent and dependent variables and the difference between them. Instruction includes the use of real-world situations to accurately identify independent and dependent variables.
- Teacher co-creates anchor chart/graphic organizer showing different ways to display data.
- Teacher provides examples for students to help them understand that some data will not have association.
- For example, the height of a person and their number of pets.

### Instructional Tasks

*Instructional Task 1 (MTR.2.1, MTR.4.1, MTR.6.1)*

Scientists at the new company, BunG, tested their bungee cords, used for bungee jumping, with weights from 10 to 200 pounds. They identified a random sample of cords and measured the length that each cord stretched when different weights were applied. The table displays the average stretch length for the sample of cords for each weight.

- Part A. Construct a scatter plot and a line graph for this set of data.
- Part B. Which representation is most appropriate for displaying and describing the relationship between the weights applied to a bungee cord and the length the cord stretches? Explain your reasoning.

### Instructional Items

*Instructional Item 1*

A pool cleaning service drained a full pool. The following table shows the number of hours it drained and the amount of water remaining in the pool at that time.

**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 Tutorial

## Perspectives Video: Experts

## Perspectives Video: Professional/Enthusiast

## Teaching Idea

## Virtual Manipulative

## MFAS Formative Assessments

Students are given a set of data and are asked to choose the scale for the axes, graph the data, and explain why they chose the scales they used.

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

Students are asked to describe potentially important variables that can be used in a model to predict the amount of damage caused by a thunderstorm.

Students are asked to describe potentially important variables that can be used in a model to predict the amount of time required to get to school.

## Original Student Tutorials Mathematics - Grades 6-8

Learn how to graph bivariate data in a scatterplot in this interactive tutorial.

This is part 1 in 6-part series. Click below to open the other tutorials in the series.

## Student Resources

## Original Student Tutorial

Learn how to graph bivariate data in a scatterplot in this interactive tutorial.

This is part 1 in 6-part series. Click below to open the other tutorials in the series.

- Scatterplots Part 2: Patterns, Associations and Correlations
- 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