MA.8.DP.1.1

Given a set of real-world bivariate numerical data, construct a scatter plot or a line graph as appropriate for the context.

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.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

Benchmark Instructional Guide

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.

• 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 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.

Construct a line graph or scatter plot for the data above based on which is most appropriate for the context.

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

Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.DP.1.AP.1: Graph bivariate data using a scatter plot.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Aquarium Visitors:

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.

Type: Formative Assessment

Time to Get to School:

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.

Type: Formative Assessment

Rain Damage Model:

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.

Type: Formative Assessment

Bungee Cord Data:

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

Type: Formative Assessment

Lesson Plans

Why Correlations?:

This lesson is an introductory lesson to correlation coefficients. Students will engage in research prior to the teacher giving any direct instruction. The teacher will provide instruction on how to find the correlation coefficient by hand and using Excel.

Type: Lesson Plan

Why Correlations?:

This lesson is an introductory lesson to correlation coefficients. Students will engage in research prior to the teacher giving any direct instruction. The teacher will provide instruction on how to find the correlation coefficient by hand and using Excel.

Type: Lesson Plan

Students will explore trends in voter turnout during the early 20th century, create a line graph to represent voter turnout data, and make comparisons to draw conclusions about the impact of the 19th Amendment, in this integrated lesson plan.

Type: Lesson Plan

Which graph is most appropriate?:

In this lesson plan, students will create and compare a scatterplot and line graph to determine which is the most appropriate representation of voter turnout and voting age population data from past presidential elections. Students will use both graphs to explore how the Reconstruction Amendments broadened the opportunity for civic participation.

Type: Lesson Plan

Clean Up, Collect Data, and Conserve the Environment!:

Students will participate in collecting trash either on campus or another location. They will compare the distance traveled and the weight of the trash bag collected. Students will explore the use of mean and median in finding the ratios of the data set. They will discuss the use of mean and median in finding the relationship between the independent and dependent variables. Students will examine their scatter plot and determine if any patterns of association exist. They will compare their data to a coastal cleanup report. Finally, students will use the data to help determine interventions at the local, state and national level regarding environmental issues.

Type: Lesson Plan

Compacting Cardboard:

Students investigate the amount of space that could be saved by flattening cardboard boxes. The analysis includes linear graphs and regression analysis along with discussions of slope and a direct variation phenomenon.

Type: Lesson Plan

A Day at the Park:

In this activity, students investigate a set of bivariate data to determine if there is a relationship between concession sales in the park and temperature. Students will construct a scatter plot, model the relationship with a linear function, write the equation of the function, and use it to make predictions about values of variables.

Type: Lesson Plan

You Can Plot it! Bivariate Data:

Students create scatter plots, calculate a regression equation using technology, and interpret the slope and y-intercept of the equation in the context of the data. This review lesson relates graphical and algebraic representations of bivariate data.

Type: Lesson Plan

Basketball - it's a tall man's sport - or is it?:

The students will use NBA player data to determine if there is a correlation between the height of a basketball player and his free throw percentage. The students will use technology to create scatter plots, find the regression line and calculate the correlation coefficient.

Basketball is a tall man's sport in most regards. Shooting, rebounding, blocking shots - the taller player seems to have the advantage. But is that still true when shooting free throws?

Type: Lesson Plan

Scatter Plots:

This lesson is an introduction to scatterplots and how to use a trend line to make predictions. Students should have some knowledge of graphing bivariate data prior to this lesson.

Type: Lesson Plan

Students will gather and use data to calculate a line of fit and the correlation coefficient with their classmates' height and hand size. They will use their line of fit to make approximations.

Type: Lesson Plan

What Will I Pay?:

Who doesn't want to save money? In this lesson, students will learn how a better credit score will save them money. They will use a scatter plot to see the relationship between credit scores and car loan interest rates. They will determine a line of fit equation and interpret the slope and y-intercept to make conclusions about interest and credit scores.

Type: Lesson Plan

An Introduction to Finding Residuals:

Students will calculate the residuals of two-variable data. Teachers are provided with materials to review, present, practice, and assess students for this new topic. This is an introductory lesson and could be used before teaching residual plots.

Type: Lesson Plan

Is My Model Working?:

Students will enjoy this project lesson that allows them to choose and collect their own data. They will create a scatter plot and find the line of fit. Next they write interpretations of their slope and y-intercept. Their final challenge is to calculate residuals and conclude whether or not their data is consistent with their linear model.

Type: Lesson Plan

Students will make a scatter plot and then create a line of fit for the data. From their graph, students will make predictions and describe relationships between the variables. Students will make predictions, inquire, and formulate ideas from observations and discussions.

Type: Lesson Plan

Quantitative or Qualitative?:

This lesson examines the differences between quantitative and qualitative data and guides students through displaying quantitative data on a scatter plot and then separating the data into qualitative categories to be displayed and interpreted in a two-way frequency table.

Type: Lesson Plan

Star Scatter Plots:

In this lesson, students plot temperature and luminosity data from a provided star table to create a scatter plot. They will analyze the data to sequence the colors of stars from hottest to coolest and to describe the relationship between temperature and luminosity. This lesson does not address differentiation between absolute and apparent magnitude.

Type: Lesson Plan

Scatter Plots and Correlations:

Students create scatter plots, and lines of fit, and then calculate the correlation coefficient. Students analyze the results and make predictions. This lesson includes step-by-step directions for calculating the correlation coefficient using Excel, GeoGebra, and a TI-84 Plus graphing calculator. Students will make predictions for the number of views of a video for any given number of weeks on the charts.

Type: Lesson Plan

This lesson uses real-world examples to practice interpreting the slope and y-intercept of a linear model in the context of data. Students will collect data, graph a scatter plot, and use spaghetti to identify a line of fit. A PowerPoint is included for guidance throughout the lesson and guided notes are also provided for students.

Type: Lesson Plan

If the line fits, where's it?:

In this lesson students learn how to informally determine a "best fit" line for a scatter plot by considering the idea of closeness.

Type: Lesson Plan

Doggie Data: It's a Dog's Life:

Students use real-world data to construct and interpret scatter plots using technology. Students will create a scatter plot with a line of fit and a function. They describe the relationship of bivariate data. They recognize and interpret the slope and y-intercept of the line of fit within the context of the data.

Type: Lesson Plan

Scrambled Coefficient:

Students will learn how the correlation coefficient is used to determine the strength of relationships among real data. Students use card sorting to order situations from negative to positive correlations. Students will create a scatter plot and use technology to calculate the line of fit and the correlation coefficient. Students will make a prediction and then use the line of fit and the correlation coefficient to confirm or deny their prediction.

Students will learn how to use the Linear Regression feature of a graphing calculator to determine the line of fit and the correlation coefficient.

The lesson includes the guided card sorting task, a formative assessment, and a summative assessment.

Type: Lesson Plan

Spaghetti Trend:

This lesson consists of using data to make scatter plots, identify the line of fit, write its equation, and then interpret the slope and the y-intercept in context. Students will also use the line of fit to make predictions.

Type: Lesson Plan

Help, My Data is Scattered!!!:

This lesson provides activities for students to conceptually understand how to gather, organize, and interpret data using a scatter plot. They will be required to work cooperatively to complete certain tasks. They will use estimation strategies to complete a experiment that compares the the length of their hand to the number of centimeter cubes they can grab in order to make predictions about data with a larger sample size. Students will be assessed formally and informally throughout lesson via slide notes and data collection tool.

Type: Lesson Plan

This lesson will get your student up to speed with constructing and interpreting scatter plots using bivariate data. With this lesson, patterns of association are investigated between two quantities and positive or negative association as well as linear and non-linear association is determined through the use of data from the NFL as reported by ESPN. Data from Consumer Reports is used to determine associations between shoe price and quality.

Type: Lesson Plan

Slope and y-Intercept of a Statistical Model:

Students will sketch and interpret the line of fit and then describe the correlation of the data. Students will determine if there’s a correlation between foot size and height by collecting data.

Type: Lesson Plan

Line of Fit:

Students will graph scatterplots and draw a line of fit. Next, students will write an equation for the line and use it to interpret the slope and y-intercept in context. Students will also use the graph and the equation to make predictions.

Type: Lesson Plan

Finding the Hottest Trend:

In this lesson, students will graph a scatter plot and learn how to recognize patterns. The students will learn that correlation may still exist even though the points are not in a perfectly straight line (linear function). Students will be able to identify outliers, describe associations, and justify their reasoning.

Type: Lesson Plan

Why Correlations?:

This lesson is an introductory lesson to correlation coefficients. Students will engage in research prior to the teacher giving any direct instruction. The teacher will provide instruction on how to find the correlation coefficient by hand and using Excel.

Type: Lesson Plan

Guess the Celebrities' Heights!:

In this activity, students use scatter plots to compare the estimated and actual heights of familiar celebrities and athletes. They will determine how their answers impact the correlation of their data, including the influence of outliers. Finally, they will compare their correlation to that provided in a scatter plot with a larger data sample.

Type: Lesson Plan

Scatter plots, spaghetti, and predicting the future:

Students will construct a scatter plot from given data. They will identify the correlation, sketch an approximate line of fit, and determine an equation for the line of fit. They will explain the meaning of the slope and y-intercept in the context of the data and use the line of fit to interpolate and extrapolate values.

Type: Lesson Plan

Original Student Tutorial

Scatterplots Part 1: Graphing:

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.

Type: Original Student Tutorial

Perspectives Video: Experts

Birdsong Series: Statistical Analysis of Birdsong:

Wei Wu discusses his statistical contributions to the Birdsong project which help to quantify the differences in the changes of the zebra finch's song.

Type: Perspectives Video: Expert

Birdsong Series: STEM Team Collaboration :

Researchers Frank Johnson, Richard Bertram, Wei Wu, and Rick Hyson explore the necessity of scientific and mathematical collaboration in modern neuroscience, as it relates to their NSF research on birdsong.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Slope and Deep Sea Sharks:

Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.

Type: Perspectives Video: Professional/Enthusiast

Teaching Idea

Now That is a Dense Graph:

In this activity, the density of ethanol is found by graphical means. In the second part, the density of sodium thiosulfate is found, also by graphical means. The values found are then analyzed statistically.

Type: Teaching Idea

Virtual Manipulative

KidsZone: Create a Graph:

Create bar, line, pie, area, and xy graphs.

Type: Virtual Manipulative

MFAS Formative Assessments

Aquarium Visitors:

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.

Bungee Cord Data:

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

Rain Damage Model:

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.

Time to Get to School:

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

Scatterplots Part 1: Graphing:

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

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Scatterplots Part 1: Graphing:

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.

Type: Original Student Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.