Cluster 2: Summarize, represent, and interpret data on two categorical and quantitative variables. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting Cluster)Archived

This Excel spreadsheet allows the educator to input data into a two way frequency table and have the resulting relative frequency charts calculated automatically on the second sheet. This resource will assist the educator in checking student calculations on student-generated data quickly and easily.

Steps to add data: All data is input on the first spreadsheet; all tables are calculated on the second spreadsheet

1. Modify column and row headings to match your data.
2. Input joint frequency data.
3. Click the second tab at the bottom of the window to see the automatic calculations.

Type: Educational Software / Tool

Students are asked to compute, graph, and interpret the residuals associated with a line of best fit.

Type: Formative Assessment

Students are asked to use a two-way frequency table to interpret marginal and joint relative frequencies.

Type: Formative Assessment

Students are given a two-way frequency table and asked to determine if there is a relationship between the two variables.

Type: Formative Assessment

Students are asked to use data from a survey to create a two-way frequency table.

Type: Formative Assessment

Students are asked to use a two-way frequency table to interpret two different conditional relative frequencies.

Type: Formative Assessment

Students are asked to use a linear model to make and interpret predictions in the context of the data.

Type: Formative Assessment

Students are asked to informally fit a line to model the relationship between two quantitative variables in a scatterplot, write the equation of the line, and use it to make a prediction.

Type: Formative Assessment

Students are given a set of data and are asked to use technology to create a scatter plot and write a function that fits the data set.

Type: Formative Assessment

The changing climate is an important topic for both scientific analysis and worldly knowledge. This lesson uses data collected by the National Snow and Ice Data Center to create and use mathematical models as a predictive tool and do critical analysis of sea ice loss.

Type: Lesson Plan

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

This review lesson relates graphical and algebraic representations of bivariate data by giving students opportunities to 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.

Type: Lesson Plan

This lesson allows the students to connect the science of cricket chirps to mathematics. In this lesson, students will collect real data using the CD "Myths and Science of Cricket Chirps" (or use supplied data), display the data in a graph, and then find and use the mathematical model that fits their data.

Type: Lesson Plan

In this lesson, students are introduced to two-way frequency tables. They will calculate joint, marginal, and relative frequencies and draw conclusions about the relationship between two categorical variables.

Type: Lesson Plan

This activity is a lab exercise where students look at the passing of water in cups and compare it to the loss of available energy as it moves through an ecosystem. Students will collect data, calculate efficiency, graph the data and respond to reflection questions to connect the data to what happens in an ecosystem. The end of the activity includes a connection to the 10% rule where only 10% of energy from one trophic level is available at the next level.

Type: Lesson Plan

Real-life data helps students gain a better understanding of creating dot-plot and/or two-way tables. Students will collect data at the beginning of the lesson and use that data to create double dot plots and frequency tables, finding and interpreting relative frequencies.

The assignment allows students to work collaboratively and cooperatively in groups. They will communicate within groups to compare shoes sizes and ages to acquire their data. From the collection of data they should be able to predict, analyze and organize the data into categories (two-way tables) or place on a number line (dot-plot).

As the class assignment concludes, a discussion of the final class display should take place about the purchasing of shoes versus ages and the relationship that either exists or doesn't exist.

Type: Lesson Plan

This lesson will provide students with an opportunity to collect and analyze bivariate data and use technology to create scatter plots, lines of best fit, and determine the correlation strength of the data being compared. Students will have a hands on inquire based lesson that allows them to create gliders to analyze data. This lesson is an application of skills acquired in a bivariate unit of study.

Type: Lesson Plan

Today's teenager is a savvy consumer of digital music and the constantly-evolving technology that plays it. Ask a typical student what they know about iTunes versus Pandora versus Spotify—most of them will have an opinion on the "best" service for listening to songs. This lesson links students' existing interest in music with the mathematical topics of frequency and relative frequency.

The activity assumes that students know what Shuffle Mode does when they listen to digital music. Shuffle Mode is a function on digital music players that "shuffles" or randomly rearranges the order of a list of songs. Each time a person presses Shuffle Mode, the playlist is rearranged. If we assume a music player's Shuffle Mode is truly random, the chances of any particular song being played would equal 1 divided by the total number of songs (1/total #). This is analogous to rolling a fair die; each number on the die has an equal probability of being rolled (1/6 or 16.7%).

Type: Lesson Plan

This lesson will require students to calculate relative frequencies and determine if an association exists within a two-way table. The students will analyze the frequencies and write a response justifying the associations and trends found within the table.

Type: Lesson Plan

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

In this lesson plan, students will be exposed to data collection and construction of two-way frequency tables. They will also learn how to analyze the two-way frequency table by calculating the relative conditional frequency.

Type: Lesson Plan

In this lesson, students develop a strong use of the vocabulary of correlation by investigating crowd ratings for a month at Disney. Students will find weekly crowd rating regression lines and regression correlations and discuss what this means for a Disney visit.

Type: Lesson Plan

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

Type: Lesson Plan

This is an interactive lesson in which students will explore marginal and conditional distributions as they calculate relative frequency of data they have collected regarding the use of cell phones and social networking sites while in the classroom.

Type: Lesson Plan

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 best fit equation and interpret slope and y-intercept to make conclusions about interest and credit scores.

Type: Lesson Plan

Students will have guided practice, starting with assessing prior knowledge on scatterplots, line of best fit and correlation. The teacher will guide through inquiry-based learning on what is residual, how to find it and why it is used to check if the regression is a good fit. Students will work with a partner investigating the residual of the price versus seating of a soccer stadium and if and what the relationship is between the number of rows a fan is from the field and the price of their ticket.

Type: Lesson Plan

Have students get colorful in defining marginal, joint and conditional frequencies of two-way frequency tables. Students will take charge in justifying the associations they find in the tables.

Type: Lesson Plan

In this lesson, teachers will find tools that will guide learners to find the residuals of a set of two-variable data. Teachers are provided with materials that will allow them to review, present, practice, and assess students for this new topic. This is an introductory lesson and could be used prior to teaching residual plots.

Type: Lesson Plan

Students will examine drop-out rates in the United States in 2012 by gender and race using data provided by the National Center for Education Statistics. Students will create conditional relative frequency tables to interpret the data and identify associations between genders and races and drop out rates.

Type: Lesson Plan

In groups, students will analyze associations between genders in their class by constructing two-way frequency tables and relative frequency tables, and interpreting the results of the data. Students will present their findings to classmates.

Type: Lesson Plan

Students will complete a two-way frequency table to investigate whether breakfast is for champions.

Type: Lesson Plan

This is a predict, observe, explain type lesson that allows students to make predictions based on prior knowledge, observe both the teacher and their peers in order to create a discussion, and receive the opportunity to express themselves and their ideas while explaining what they learned. Students will be participating in an activity where they will collect data after making a prediction and then construct a scatter plot. From the scatterplot, students will make an interpretation of the data by calculating the correlation coefficient (r value) and deciding if there is a correlation or not in terms of its strength and magnitude, then explaining what that means.

Type: Lesson Plan

The program 60 Minutes reports that parents are intentionally holding their children back in Kindergarten to give them a competitive advantage in sports later on in life. The students are using the data collected to decide if this is really a trend in the US.

Type: Lesson Plan

Using a completed survey of male and female student interest in comedy vs. action movies, the students will create a two-way frequency table using actual data results, fraction results, and percent results. The students will then act as the movie producer and interpret the data to determine if it is in their best interest to make a comedy or action movie. As the Summative Assessment, the student will take on the job/role of an actor/actress and interpret the data to support their decision.

Type: Lesson Plan

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a coaster's height and speed. Using technology the students can determine the line of best fit, correlation coefficient and use the line for interpolation. This lesson also uses prior knowledge and has students solve systems of equations graphically to determine which type of coaster is faster.

Type: Lesson Plan

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a person's height and arm length. Using technology the students will explore in-depth how to perform a least square regression as a procedure for determining the line of best fit.

Type: Lesson Plan

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a person's height and foot length. Using technology the students can determine the line of best fit, correlation coefficient and use the line for interpolation.

Type: Lesson Plan

The students are asked to create a scatter plot of Bennie's height, determine an equation of best fit, calculate residuals and create a residual plot. The students are then asked to use the residual plot to determine if a linear model is the best predictor of the data.

Type: Lesson Plan

Students will enjoy this project lesson that allows them to choose and collect their own data. They will create a scatter plot and find their line of best 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

This lesson is an application activity in which students will use relative frequencies to support an argument. Students will be given the task of creating an argument that would support why their club/team should be awarded a monetary prize that the school has won. The students will create statistical questions, collect their own data, analyze and interpret it to support their claim, present their argument, critique other arguments, and refine their argument for a rebuttal and closing remarks. The project will be graded with the rubric found in the Summative Assessment section, and has a student packet attached as well. All attachments can be modified.

Type: Lesson Plan

This is a lesson plan takes a different approach to the regular math class because it is in a "Predict Observe Explain" format, allowing students to make predictions, inquire and formulate ideas from observations and discussions. Students will be participating in an activity that extrapolates the data and practicing how to make a scatter plot and then create a line of best fit for the data. From their graph, students will be making predictions and describing the relationships between the variables.

Type: Lesson Plan

This lesson will remind students of the differences between quantitative and qualitative data then guide the students through learning how to display quanitative data on a scatter plot then separating the data into qualitative categories to be displayed and interpreted in a frequency table.

Type: Lesson Plan

Introduction to two-way frequency tables. The lesson will be delivered using a PowerPoint presentation.

The teacher will introduce and define joint and marginal frequency, demonstrate how two-way frequency tables are constructed from a given set of data, calculate relative frequencies, and draw conclusions based on the information in the table. Students will practice these skills through guided practice with the teacher, independent practice, and complete a summative assessment to measure student learning. All resources, including the PowerPoint, have been provided.

Type: Lesson Plan

The lesson is a laboratory-based activity involving measurement, accuracy and precision, stoichiometry and a basic statistical analysis of data using a scatter plot, linear equation, and linear regression (line of best fit). The lesson includes teacher-led discussions with student participation and laboratory-based group activities.

Type: Lesson Plan

This is a lesson for teaching students how to make Two-Way Frequency and Relevant Frequency tables and to use the data collected and displayed in the tables for interpretation and prediction.

Type: Lesson Plan

In this lesson, the student will learn how to set up a two-way frequency table from two categorical variables and use the two-way frequency table to calculate frequency counts and relative frequency. The vocabulary terms learned in this lesson are two-way frequency table, relative frequency, joint frequency, marginal frequency, and conditional frequency.

This lesson covers only a portion of the standard. The teacher should complete the standard with a follow-up lesson in which students will make data tables and then use the data to explore probability.

Type: Lesson Plan

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

Type: Lesson Plan

In this lesson, students will learn how to convert a simple and two-way frequency tables to relative frequency tables through using real world data collected in the classroom.

Type: Lesson Plan

Students will learn how to read, complete, and interpret two-way frequency tables.

Type: Lesson Plan

This lesson unit is intended to help you assess how well students understand the notion of correlation. In particular this unit aims to identify and help students who have difficulty in understanding correlation as the degree of fit between two variables, making a mathematical model of a situation, testing and improving the model, communicating their reasoning clearly and evaluating alternative models of the situation.

Type: Lesson Plan

This is a model-eliciting activity where students have been asked by a new website, CollegeReview.com, to come up with a system to rank various colleges based on five categories; tuition cost, social life, athletics, education, city population and starting salary upon graduation.

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

Type: Lesson Plan

This MEA is designed to have teams of 4 students look at data in a two-way table. Teams must discuss which categorical or quantitative factors might be the driving force of a song's popularity. Hopefully, popular songs have some common thread running through them.

Each team must write down their thought process on how they will create the most popular playlist of songs for a local radio station. A major constraint for each team is to thoroughly explain how they will maximize the 11 minutes available with the most popular songs.

Students will be provided with letters from a local radio station, WMMM - where you can receive your "Daily Mix of Music and Math." WMMM has 10 songs and the researchers have collected data on each. Student teams: it is your responsibility to pick the playlist and write a letter to the station supporting why you made your particular selection. The winning team gets an opportunity to record a sound bite which introduces their playlist on the radio.

Now, just when the teams believe they have addressed WMMM's request, a twist is thrown in the midst, and the student teams must return to the drawing board and write a second letter to the station which may or may not affect the team's original playlist.

Do you have the musical swag to connect the associations?

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

Type: Lesson Plan

Students will be comparing hybrid-electric vehicles (HEV) versus gasoline-powered vehicles. They will research the benefits of owning a HEV while also analyzing the cost effectiveness.

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

Type: Lesson Plan

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

Students will model molecular motion with everyday materials (shaker bottles) then associate their model/actions to the phase transitions of water while graphing its heat curve from data collected during a structured inquiry lab.

Type: Lesson Plan

Learn to define, calculate, and interpret marginal frequencies, joint frequencies, and conditional frequencies in the context of the data with this interactive tutorial.

Type: Original Student Tutorial

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

In this video, Brad Rosenheim describes how Louisiana sediment cores are used to estimate sea level changes over the last 10,000 years. Video funded by NSF grant #: OCE-1502753.

Type: Perspectives Video: Expert

The tide is high!  How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Chip Cotton, fishery biologist, discusses his use of mathematical regression modeling and how well the data fits his models based on  his deep sea shark research.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

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

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

COAPS oceanographer Dmitry Dukhovskoy describes the process used to mathematically model eddy shedding in the Gulf of Mexico.

Type: Perspectives Video: Professional/Enthusiast

Laws and regulations that affect the public are being formed based on data from a variety of laboratories. How can we be sure that the laboratories are all standardized?

Type: Perspectives Video: Professional/Enthusiast

Dr. Bill McShea from the Smithsonian Institution discusses how regression analysis helps in his research.

This video was created in collaboration with the Okaloosa County SCIENCE Partnership, including the Smithsonian Institution and Harvard University.

Type: Perspectives Video: Professional/Enthusiast

This problem solving task asks students to make deductions about what kind of music students like by examining a table with data.

Type: Problem-Solving Task

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient.

Type: Problem-Solving Task

Students in a first Algebra course model the relationship between two variables by fitting functions to data. The focus of this tutorial is on (1) using technology to create a scatterplot of data and calculate the equation of the least squares regression line and (2) informally assessing the fit of a function fitted to data by calculating, graphing, and analyzing residuals.

Type: Professional Development

Students will first measure and plot the total mass vs liquid volume in a graduated cylinder. They will then use slope and the mathematical formula for the plot to determine the density of the liquid, the density of a solid added to the liquid, and the mass of the graduated cylinder.

Type: Teaching Idea

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

This informational text resource is intended to support reading in the content area. Pew Research Center surveyed scientists and the general public on 12 science oriented issues, including genetically modified foods, vaccines, nuclear power and evolution. Results of the survey showed large discrepancies between the thoughts, causes and recommendations on the issues of the scientists and the general public. Sample sizes and margins of errors are given on the survey results which are represented in percent form. The overall survey showed that the public and the scientists see the world very differently.

Type: Text Resource

In a variety of fields, functions are used to mathematically model bivariate data in order to describe, understand, and make predictions about the relationship between two variables. The focus of this tutorial is on (1) teaching students how to model the relationships between two variables with linear and exponential functions and (2) using models to make predictions about values of variables.

Type: Tutorial

Type: Unit/Lesson Sequence

Khan Academy tutorial video that demonstrates with real-world data the use of Excel spreadsheet to fit a line to data and make predictions using that line.

Type: Video/Audio/Animation

Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

This lesson is designed to introduce students to the difference between univariate and bivariate data, and how the two can be represented graphically. This lesson provides links to model discussions and online graphing applets, as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Virtual Manipulative

This is an online graphing utility that can be used to create box plots, bubble graphs, scatterplots, histograms, and stem-and-leaf plots.

Type: Virtual Manipulative