# MA.912.DP.1.2

Interpret data distributions represented in various ways. State whether the data is numerical or categorical, whether it is univariate or bivariate and interpret the different components and quantities in the display.

### Clarifications

Clarification 1: Within the Probability and Statistics course, instruction includes the use of spreadsheets and technology.
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

• Categorical Data
• Numerical Data

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 7, students created and interpreted different displays of univariate numerical and categorical data. In grade 8, they created scatter plots and began to interpret them by consider lines of fit. In Algebra I, students interpret the components of data displays for numerical and categorical data, both univariate and bivariate. In later courses, they will use data displays to compare distributions of data sets to one another and to theoretical distributions.
• It is the intention of this benchmark to include cases where students must calculate measures of center/variation to interpret (MTR.3.1)
• For students to have full understanding of numerical/categorical, univariate/bivariate data sets and their displays, instruction should include MA.912.DP.1.1. These benchmarks are not intended to be separated. One is reinforced by the other.
• Numerical univariate includes histograms, stem-and-leaf plots, box plots and line plots.
• Numerical bivariate includes scatter plots and line graphs.
• Categorical univariate includes bar charts, line plots, circle graphs, frequency tables and relative frequency tables.
• Categorical bivariate includes segmented bar charts, joint frequency tables and joint relative frequency tables.
• Instruction includes identifying the measures of center and spread from different scenarios.
• Instruction includes explaining that an outlier is extremely smaller or larger than the rest of the data set.
• Teacher provides opportunities to analyze the effects on the measures of center and spread when the outlier is the minimum and maximum.
• This benchmark reinforces the importance of the use of questioning within instruction.
• Does this display univariate or bivariate data?
• Is the data numerical or categorical?
• What do the different quantities within the data display mean in terms of the context of the situational data?

### Common Misconceptions or Errors

• Students may not be able to properly distinguish between numerical and categorical data or between univariate and bivariate data.
• Students may misidentify or misinterpret the quantities in data displays.
• Students may not be able to distinguish between the measures of center (mean, median) and measures of spread (range, IQR).
• Students may not completely grasp the effect of outliers on the data set; or incorrectly conclude a point is an outlier.
• Students may not be able to distinguish the differences between frequencies and relative frequencies.
• Students misidentify the condition that determines a conditional or relative frequency in a joint table.

### Strategies to Support Tiered Instruction

• Instruction includes a graphic organizer to complete collaboratively.
• For example, teacher can provide the graphic below and have students match the vocabulary terminology with the correct definition. Then, have students create an example that can help with remembering the vocabulary terminology.

• Teacher provides students with definitions and co-creates examples for frequency and relative frequency.
• For example, have students draw a definition chart in their interactive notebook. Give them the opportunity to create an example that will help them remember the definition.

• The histogram below shows the efficiency level (in miles per gallons) of 110 cars.
• Part A. Does this display univariate or bivariate data?
• Part B. Is the data numerical or categorical?
• Part C. What do the different quantities within the data display mean in terms of the context of the situational data?
• Part D.
• How many cars have an efficiency between 15 and 20 miles per gallon?
• How many cars have an efficiency more than 20 miles per gallon?
• What percentage of cars have an efficiency less than 20 miles per gallon?

• A police department tracked the number of ticket writers and number of tickets issued for each of the past 8 weeks. The scatter plot shows the results.

• Part A. Does this display univariate or bivariate data? Is the data numerical or categorical?
• Part B. What do the different quantities within the data display mean in terms of the context of the situational data?
• Part C. Which statement is an appropriate interpretation of the data?
• a. More ticket writers result in fewer tickets being issued.
• b. There were 50 tickets issued every week.
• c. When there are 10 ticket writers, there will be 600 tickets issued.
• d. When there are more ticket writers, more tickets are being issued.

### Instructional Items

Instructional Item 1

• The scatter plot shows the amount of sleep needed per day by age.
• Part A. Does this display univariate or bivariate data? Is the data numerical or categorical?
• Part B. What is a possible trend that is shown by the data?

*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.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200380: Algebra 1-B (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond (current))
7912070: Access Mathematics for Liberal Arts (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 - 2023, 2023 and beyond (current))
7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1210305: Mathematics for College Statistics (Specifically in versions: 2022 and beyond (current))
1207350: Mathematics for College Liberal Arts (Specifically in versions: 2022 and beyond (current))
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1700600: GEAR Up 1 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))
1700610: GEAR Up 2 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))
1700620: GEAR Up 3 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))
1700630: GEAR Up 4 (Specifically in versions: 2020 - 2022, 2022 and beyond (current))
1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))
7912120: Access Mathematics for Data and Financial Literacy (Specifically in versions: 2022 - 2023, 2023 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.DP.1.AP.2: Given a univariate or bivariate data distribution (numerical or categorical), identify the different components and quantities in the display.

## Related Resources

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

## Lesson Plans

Data Speaks Part 3:

Students will analyze a data set and create a data display that best represents the data, in this integrated lesson plan.

Type: Lesson Plan

Data Speaks: Part 2:

Students will analyze and interpret data displays to explain the advantages and disadvantages of each data display, in this integrated lesson plan.

Type: Lesson Plan

Choosing The Proper Chart For Your Data Set:

Students will use previously gathered data to create a spreadsheet, choose and create a graph/chart that best diplays the data, and explain their reasoning for choosing the graph/chart, in this lesson plan.

Type: Lesson Plan

Data Speaks: Part 1:

Students will classify variables as numerical/categorical and univariate/bivariate. Graphs representing various data related to citizenship will be used in this integrated lesson plan.

Type: Lesson Plan

Got Bull?:

This MEA is a genetics based lesson for upper level biology students. Students will review the data on several bulls and help a client choose the best bulls to begin a new cattle operation.

Type: Lesson Plan

How Hot Is It?:

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

Analyzing Box Plots:

This lesson is designed for students to demonstrate their knowledge of box plots.

• Students will need to create four box plots from given data.
• Students will need to analyze the data displayed on the box plots by comparing similarities and differences.
• Students will work with a partner to complete the displays and the follow-up questions.

Type: Lesson Plan

Texting and Standard Deviation:

This lesson uses texting to teach statistics. In the lesson, students will calculate the mean, median, and standard deviation. They will create a normal distribution using the mean and standard deviation and estimate population percentages. They will construct and interpret dot plots based on the data they collected. Students will also use similarities and differences in shape, center, and spread to determine who is better at texting, boys, or girls.

Type: Lesson Plan

Heart Rate and Exercise: Is there a correlation?:

Students will use supplied heart rate data to determine if heart rate and the amount of time spent exercising each week are correlated. Students will use GeoGebra to create scatter plots and lines of fit for the data and examine the correlation. Students will gather evidence to support or refute statistical statements made about correlation. The lesson provides easy to follow steps for using GeoGebra, a free online application, to generate a correlation coefficient for two given variables.

Type: Lesson Plan

Can You Walk in My Shoes?:

Students use real-life data to create dot-plots and 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

Span the Distance Glider - Correlation Coefficient:

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

Students will compile the data gathered from measuring their resting heart rates and heart rates after exercising into box plots. Using these displays, they will analyze the data's center, shape, and spread.

Type: Lesson Plan

"What's My Grade" is a lesson that will focus on a sample student's grades to demonstrate how a final grade is calculated as well as explore possible future grades. Students will create the distributions of each grade category using histograms. They will also analyze grades using mean and standard deviation. Students will use statistics to determine data distribution while comparing the center and spread of two or more different data sets.

Type: Lesson Plan

How tall is an 8th grader?:

Ever wonder about the differences in heights between students in grade 8? In this lesson, students will use data they collect to create and analyze multiple box plots using 5-number summaries. Students will make inferences about how height and another category may or may not be related.

Type: Lesson Plan

Plane Statistics:

This lesson starts with an activity to gather data using paper airplanes then progresses to using appropriate statistics to compare the center and spread of the data. Box plots are used in this application lesson of concepts and skills previously acquired.

Type: Lesson Plan

Which One: Box plot, Dot Plot, or Histogram?:

Students will be asked to obtain data and create a human box plot, which will be analyzed and explained using statistical terms. Students will then understand the differences and advantages to using the box plot, histogram, and dot plot. Students will also practice selecting the most appropriate graphical representation for a set of data.

Type: Lesson Plan

This resource can be used to teach students how to create and compare box plots. After completing this lesson, students should be able to answer questions in both familiar and unfamiliar situations.

Type: Lesson Plan

Which is Better? Using Data to Make Choices:

Students use technology to analyze measures of center and variability in data. Data displays such as box plots, line plots, and histograms are used. The effects of outliers are taken into consideration when drawing conclusions. Students will cite evidence from the data to support their conclusions.

Type: Lesson Plan

How many licks does it take to get to the center?:

Students will create different displays, line plots, histograms, and box plots from data collected about types of lollipops. The data will be analyzed and compared. Students will determine "Which lollipop takes the fewest number of licks to get to the center: a Tootsie Pop, a Blow Pop, or a Dum Dum?"

Type: Lesson Plan

Birthday Party Decisions:

Students will create and compare four different boxplots to determine the best location for a birthday party.

Type: Lesson Plan

Outliers in the Outfield â€“ Dealing With Extreme Data Points:

Students will explore the effects outliers have on the mean and median values using the Major League Baseball (MLB) salary statistics. They will create and compare box plots and analyze measures of center and variability. They will also be given a set of three box plots and asked to identify and compare their measures of center and variablity.

Type: Lesson Plan

This lesson allows students to have a hands-on experience collecting real-world data, creating graphical representations, and analyzing their data. Students will make predictions as to the outcome of the data and compare their predictions to the actual outcome. Students will create and analyze line plots, histograms, and box plots.

Type: Lesson Plan

Comparing Data Using Box Plots:

Students will use box plots to compare two or more sets of data. They will analyze data in context by comparing the box plots of two or more data sets.

Type: Lesson Plan

How do we measure success?:

Students will use the normal distribution to estimate population percentages and calculate the values that fall within one, two, and three standard deviations of the mean. Students use statistics and a normal distribution to determine how well a participant performed in a math competition.

Type: Lesson Plan

How Old are the Players?:

For this lesson, students will research the ages of players on two basketball teams. They will find the five-number summary, the mean, and determine if there are outliers in the data set. Two box plots will be created and the measures of center and variation analyzed.

Type: Lesson Plan

The students will compare the effects of outliers on measures of center and spread within dot plots and box plots.

Type: Lesson Plan

Why do I have to have a bedtime?:

This predict, observe, explain lesson that allows students to make predictions based on prior knowledge, observations, discussions, and calculations. Students will receive the opportunity to express themselves and their ideas while explaining what they learned. Students will make a prediction, collect data, and construct a scatter plot. Next, students will calculate the correlation coefficient and use it to describe the strength and magnitude of a relationship.

Type: Lesson Plan

Baking Soda and Vinegar: A statistical approach to a chemical reaction.:

Students experiment with baking soda and vinegar and use statistics to determine which ratio of ingredients creates the most carbon dioxide. This hands-on activity applies the concepts of plot, center, and spread.

Type: Lesson Plan

Should Statistics be Shapely?:

Students will Interpret differences in shape, center, and spread of a variety of data displays, accounting for possible effects of extreme data points.

Students will create a Human Box Plot using their data to master the standard and learning objectives, then complete interactive notes with the classroom teacher, a formative assessment, and later a summative assessment to show mastery.

Type: Lesson Plan

Using Two-Way Frequency Tables to Analyze Data:

The television 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 will use data collected to decide if this is truly a trend in the United States.

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

ENSO: Friend or Foe?:

In this activity students will compare El Nino / La Nina Anomaly data and compare the data to hurricane frequency in the Atlantic Basin. The ENSO Anomaly Data has been provided. Students will then research hurricane frequency and compare both data sets. To close the activity, students will need to apply the knowledge learned in the lesson to synthesize and make a prediction in a writing prompt.

Type: Lesson Plan

Are you a CrimiNole or Gatorbait? Two rivalries in one table!:

This is an 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

Homework or Play?:

Students will be given data and then plot the data using a graphical method of choice (dot plot, bar graph, box plot, etc.) The students will work in groups and then analyze and summarize the data.

Type: Lesson Plan

Sweet Statistics - A Candy Journey:

Students will sort pieces of candy by color and then calculate statistical information such as mean, median, mode, interquartile range, and standard deviation. They will also create an Excel spreadsheet with the candy data to generate pie charts and column charts. Finally, they will compare experimental data to theoretical data and explain the differences between the two. This is intended to be an exercise for an Algebra 1 class. Students will need at least 2 class periods to sort their candy, make the statistical calculations, and create the charts in Excel.

Type: Lesson Plan

Interpreting Box Plots:

Students will analyze various real world scenario data sets and create, analyze, and interpret the components of the box plots. Students will use data from morning routines, track times, ages, etc. Lesson includes a PowerPoint, homework, and assessments.

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

The Debate: Who is a Better Baller?:

In this activity the students will use NBA statistics on Lebron James and Tim Duncan who were key players in the 2014 NBA Finals, to calculate, compare, and discuss mean, median, interquartile range, variance, and standard deviation. They will also construct and discuss box plots.

Type: Lesson Plan

Who's Better?--Using Data to Determine:

This lesson is intended for use after students are able to construct data plots (histograms, line plots, box plots). Students are tasked with not only constructing data plots, but also matching data plots to data sets. In the summative assessment, students are given two data sets and asked to select which of three data plots (histogram, line plot, or box plot) would best be used to compare the data. After choosing and constructing their plot, students are then tasked with forming a conclusion based on the plots they have constructed.

Type: Lesson Plan

Burgers to Smoothies.:

Students will create double box plots to compare nutritional data about popular food choices.

Type: Lesson Plan

Correlation or Causation: That is the question:

Students will learn how to analyze whether two events/properties demonstrate a correlation or causation or both. They will learn what factors are involved when evaluating whether correlated events demonstrate causation. If two events are claimed to be causal when they are not, they will be able to determine why, and which (if any) causal fallacies are present. At the close of the lesson students will be given situational data and develop a newscast that assumes causation when in fact there is no causal link. Students who are observing will analyze each presentation and determine which (if any) causal fallacy was used (or explain why the newscast is correct in their assumption of causality).

Type: Lesson Plan

A Bunch of Hot Air....Balloon Rides That Is!:

This is a 9th grade MEA about weather prediction and limitations thereof. This MEA will ask students to work as a team to design a plan to select the source for weather forecasts for a private hot-air balloon tour company. Students will evaluate information from various weather predictions sources to determine which one is best for a hot-air balloon ride company.

Type: Lesson Plan

Smarter than a Statistician: Correlations and Causation in the Real World!:

Students will learn to distinguish between correlation and causation. They will build their skills by playing two interactive digital games that are included in the lesson. The lesson culminates with a research project that requires students to find and explain the correlation between two real world events.

Type: Lesson Plan

Students will compare the advantages and disadvantages of dot plots, histograms, and box plots. During this lesson, students will review the statistical process and learn the characteristics of a statistical question; whether it be numerical or categorical. Students will apply the information learned in a project that involves real-world issues and make an analysis based on the data collected.

Type: Lesson Plan

The Perfect Steak Oven:

The lesson integrates language arts and physical science standards through the use of a Model Eliciting Activity. Students collaborate to create a procedure to solve a particular problem (the best steak oven).

Type: Lesson Plan

A New View: Space Exploration:

This MEA is about space exploration. Students will review data on six extrasolar planets and determine which one would be most feasible to explore first.

Type: Lesson Plan

Interpreting Statistics: A Case of Muddying the Waters:

This lesson is intended to help you assess how well students are able to:

• Interpret data and evaluate statistical summaries.
• Critique someone else's interpretations of data and evaluations of statistical summaries.

The lesson also introduces students to the dangers of misapplying simple statistics in real-world contexts, and illustrates some of the common abuses of statistics and charts found in the media.

Type: Lesson Plan

The Election Resource:

In this Model Eliciting Activity, MEA, students will analyze sets of data and draw conclusions to justify the top candidates for positions of President, Treasurer, and Secretary of the school's Student Government Association.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

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

## Perspectives Video: Expert

Histograms Show Trends in Fisheries Data Over Time:

<p>NOAA Fishery management relies on histograms to show patterns and trends over time of fishery data.</p>

Type: Perspectives Video: Expert

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

Random Walk III:

The task provides a context to calculate discrete probabilities and represent them on a bar graph.

How Is the Weather?:

This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match. The first and third graphs look very similar at first glance, but the function values are very different since the scales on the vertical axes are very different. The task could also be used to generate a group discussion on interpreting functions given by graphs.

Music and Sports:

This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.

Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.

## STEM Lessons - Model Eliciting Activity

A Bunch of Hot Air....Balloon Rides That Is!:

This is a 9th grade MEA about weather prediction and limitations thereof. This MEA will ask students to work as a team to design a plan to select the source for weather forecasts for a private hot-air balloon tour company. Students will evaluate information from various weather predictions sources to determine which one is best for a hot-air balloon ride company.

A New View: Space Exploration:

This MEA is about space exploration. Students will review data on six extrasolar planets and determine which one would be most feasible to explore first.

Got Bull?:

This MEA is a genetics based lesson for upper level biology students. Students will review the data on several bulls and help a client choose the best bulls to begin a new cattle operation.

The Election Resource:

In this Model Eliciting Activity, MEA, students will analyze sets of data and draw conclusions to justify the top candidates for positions of President, Treasurer, and Secretary of the school's Student Government Association.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

The Perfect Steak Oven:

The lesson integrates language arts and physical science standards through the use of a Model Eliciting Activity. Students collaborate to create a procedure to solve a particular problem (the best steak oven).

## Student Resources

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

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

Random Walk III:

The task provides a context to calculate discrete probabilities and represent them on a bar graph.

How Is the Weather?:

This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match. The first and third graphs look very similar at first glance, but the function values are very different since the scales on the vertical axes are very different. The task could also be used to generate a group discussion on interpreting functions given by graphs.

Music and Sports:

This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.

Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.

## Parent Resources

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

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

Random Walk III:

The task provides a context to calculate discrete probabilities and represent them on a bar graph.

How Is the Weather?:

This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match. The first and third graphs look very similar at first glance, but the function values are very different since the scales on the vertical axes are very different. The task could also be used to generate a group discussion on interpreting functions given by graphs.

Music and Sports:

This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.

Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.