Teacher’s Page

Scatterplots

Carrie Wiederholz, 12/2015

Abstract & Essential Question

In this webquest students will be analyzing the relationship between two variables using scatterplots.  In order to understand what they are creating, each group will first individually research scatterplot correlation types, lines of best fit and determine how scatterplots are created using technology.  Then they will chose from one of five professions in either sports, the food industry, Olympics, movie production or the environment where they will work together as a team to collect data to develop a scatterplot and then make predictions based upon their results.

Performance Objectives

  1.  Students will work in groups to collect information about their desired topic from which they can create a scatterplot and then make predictions using their graph and their line of best fit.

  2. Students will present their graph and findings using Google Slides.

Outcomes

  1. Students will be able to describe the relationship of a scatter plot and determine if there is a correlation between the two variables.

  2. Students will be able to construct a scatter plot on Google Sheets and on a graphing calculator.

  3. Students will be able to draw a line of best fit and write the equation for the line.

  4. Students will be able to interpret and analyze their graph.

  5. Students will be able to use their line of best fit to make predictions.

  6. Students will be more aware of how scatterplots are used in many professions.

Scaffolding Knowledge

Essential Question:  How can you make predictions based on a scatter plot?

Bloom’s Taxonomy Levels

Level

Activities
Remember Students will define scatter plot and describe its correlations.

Students will describe trend lines and lines of best fit.

Students will recall how to determine the equation for a line.

Students will define interpolation and extrapolation.
Understand Students will explain the information that they learned about scatter plots during their individual research to their team.

Students will follow steps to demonstrate how to graph a scatter plot on a graphing calculator and on Google Sheets.
Apply Students will apply the information that they learned about scatter plots to create their own scatter plot about a chosen profession.
Analyze Students will compare and contrast the types of correlations of scatter plots.

Students will compare and contrast two variables related to a profession and determine their type of correlation.
Evaluate Students will make predictions based upon their scatter plot.
Create Students will create a Google Sheets presentation demonstrating their knowledge of scatter plots and how they are used outside of the math classroom.

Students will create a scatter plot and its line of best fit on Google Sheets based upon the information that they gathered.

Multiple Intelligences

Naturalist Students will research how the average temperature per month in New York City has changed over the years.
Linguistic Students will be reading about scatter plots to collect information and will then create a Google Slide based upon the information that they found. Students will also write predictions based upon their line of best fit.
Logical-Mathematical Students will think logically to look for a pattern between the two variables, plot data points on a coordinate plane, describe correlations and calculate the equation for the line of best fit.
Existential Students are making predictions about various topics and thinking about the bigger picture.  Based upon their results, they can make conjectures about the trend of temperatures in years to come.
Bodily-Kinesthetic Students will be using laptops to actively visit websites, practice problems and create a Google Slide presentation.
Spatial As students work through this web quest, they will be engaged through various graphics and videos. Students will also create a visually stimulating Google Slide presentation based upon all of the information that they have individually gathered as well as the data that they have analyzed as a team.
Interpersonal Students will work in groups to research two variables within a particular profession, create a scatterplot and make predictions based upon their line of best fit.
Intrapersonal Students will work independently to research an aspect of scatter plots; correlations, technology and predictions.

Learning Styles

Concrete Sequential These students will enjoy the detailed steps of this webquest and the specific steps outlined for completion of each role.  These students will make sense of the evaluation rubric and understand how they are being assessed.
Concrete Random These students will enjoy developing their own scatterplot and collecting information from the real-world that interests them.  In addition, they will enjoy being creative with their presentation.
Abstract Random  These students will enjoy working in a group to discuss scatter plots, collect real-world information and collaborating on the best way to make the scatterplot and line of best fit.
Abstract Sequential These students will enjoy the individual portion of this web quest where they get to gather information and analyze their results.

Sense & Meaning

In order for the brain to move information to long term memory, sense and meaning need to be in place so that the hippocampus can encode that information and send it to long term storage. By connecting this lesson to previous lessons on graphing on the coordinate plane, graphing linear equations and slope, students are able to make sense of the topic being covered, scatter plots. They find meaning for this lesson by applying scatter plots to real-world professions by comparing two variables, creating a scatter plot and making predictions based upon their line of best fit.

Motivation

In order to keep students on-task and learning, they need to be motivated to do well and focus on their project.  Through the use of various professions, many students will be intrinsically motivated because they are interested in researching variables within a particular profession and then making predictions based upon their findings.  The students will also be extrinsically motivated to correctly complete the webquest because their grade depends upon it.  Furthermore, since the students are responsible for individually researching a part of the project and then sharing with their group, they will be extrinsically motivated because their group is relying on them to do a good job.

Standards Addressed

Algebra Common Core Standards:

S.ID.6.c  Fit a linear function for a scatter plot that suggests a linear association.

N.Q.1  Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

S.ID.6.a  Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of data.

S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

S.ID.9 Distinguish between correlation and causation.

Technology Standards:

8.1.8.A.1 – Demonstrate knowledge of a real world problem using digital tools.

8.1.8.A.4 – Graph and calculate data within a spreadsheet and present a summary of the results.

8.1.8.D.1 – Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.

8.1.8.F.1 – Explore a local issue, by using digital tools to collect and analyze data to identify a solution and make an informed decision.

Teacher Preparation

This webquest should be assigned after students have worked on linear equations and slope.  The first day of the assignment should be spent discussing the steps of the webquest by going to each of the pages and giving the students a “tour.” It is also important to review the Evaluation Rubric so that the students understand how they are being assessed.

Materials:

  • Chromebooks
  • Internet Access
  • IXL logon
  • Headphones

Key Terms

Scatter plot A graph that relates two different sets of data by displaying them as ordered pairs.
Positive Correlation The relationship between two sets of data in which both sets of data increase together.
Negative Correlation The relationship between two sets of data, in which one set of data decreases as the other set of data increases.
No Correlation There does not appear to be a relationship between two sets of data.
Trend Line A line on a scatter plot drawn near the points.  It shows a correlation.
Interpolation The process of estimating a value between two known quantities.
Extrapolation The process of predicting a value outside the range of known values.
Line of Best Fit The most accurate trend line on a scatter plot showing the relationship between two sets of data.
Correlation Coefficient A number from -1 to 1 that tells you how closely the equation of the line of best fit models the data.
Causation When a change in one quantity causes a change in a second quantity.  A correlation between quantities does not always imply causation.

Alternate Outline – Accommodations

Example:

  • Students who are below/above grade level will be assigned to appropriate role that best meets their needs and they will be able to work in a group of mixed levels.
  • Students can borrow chromebooks from the library if they do not have their individual chromebook or the class can be taken to the computer lab.
  • English Language Learners can use translation dictionaries to help them better understand the directions.

Suggested Follow-Up

If students need more practice on skills, visit supplemental math websites, such as IXL.com or MeasuringUpLive.com that help to reinforce skills.

To extend the webquest further, students can research two variables on their own and look for a relationship between them or they can survey their peers to create data and then make a scatter plot of the data.