# Standard 1: Represent and interpret numerical and categorical data.

General Information
Number: MA.7.DP.1
Title: Represent and interpret numerical and categorical data.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.7.DP.1.AP.1
Use context to determine the appropriate measure of center (mean or median) or range to summarize a numerical data set with 10 or fewer elements, represented numerically or graphically.
MA.7.DP.1.AP.2
Given two numerical or graphical representations of data in the same form, compare the mean, median or range of each representation.
MA.7.DP.1.AP.3
Given data from a random sample of the population, select from a list an appropriate prediction about the population based on the data.
MA.7.DP.1.AP.4
Use proportional reasoning to interpret data in a pie chart.
MA.7.DP.1.AP.5
Given a data set, select an appropriate graphical representation (histogram, bar chart, or line plot).

## Related Resources

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

## 3D Modeling

Wind Farm Design Challenge:

In this engineering design challenge, students are asked to create the most efficient wind turbine while balancing cost constraints. Students will apply their knowledge of surface area and graphing while testing 3D-printed wind farm blades. In the end, students are challenged to design and test their own wind farm blades, using Tinkercad to model a 3D-printable blade.

Type: 3D Modeling

## Formative Assessments

Prediction Predicament:

Students are asked to use sample data to make and assess a prediction.

Type: Formative Assessment

Cranberry Counting:

Students are asked to assess the validity of an inference regarding two distributions given their box plots.

Type: Formative Assessment

TV Ages - 1:

Students are asked to informally determine the degree of overlap between two distributions with the same interquartile range (IQR) by expressing the difference between their medians as a multiple of the IQR.

Type: Formative Assessment

TV Ages - 2:

Students are asked to informally determine the degree of overlap between two distributions with the same interquartile range (IQR) by expressing the difference between their medians as a multiple of the IQR.

Type: Formative Assessment

Overlapping Trees:

Students are asked to compare two distributions given side-by-side box plots.

Type: Formative Assessment

School Days:

Students are asked to use data from a random sample to estimate a population parameter and explain what might be done to increase confidence in the estimate.

Type: Formative Assessment

Movie Genre:

Students are asked to use data from a random sample to draw an inference about a population.

Type: Formative Assessment

Height Research:

Students are asked to describe a method for collecting data in order to estimate the average height of 12 year old boys in the U.S.

Type: Formative Assessment

## Lesson Plans

The Watergate Effect part 3:

Students will create a circle graph to display categorical data of the public presidential approval rates after the Supreme Court Case United States v. Nixon. Students will graph results independently and compare them to the circle graphs created during the Watergate Effect Part 1 Lesson (Resource ID#: 208926) and the Watergate Effect Part 2 Lesson (Resource ID#: 210122) to discuss the trend of the data over the entirety of the Supreme Court case.

Type: Lesson Plan

The Watergate Effect part 2:

Students will create a circle graph to display categorical data of the public presidential approval rates during the Supreme Court Case United States v. Nixon. Students will graph results in pairs/groups and compare them to the circle graph created during the Watergate Effect Part 1 Lesson (Resource ID#: 208926).

Type: Lesson Plan

A MEANingful Discussion about Central Tendency:

Using relatable scenarios, this lesson explores the mean and median of a data set and how an outlier affects each measure differently.

Type: Lesson Plan

Create a Circle Graph to Represent Percentages:

Students will compare each region's percentage of seats in the U.S. House of Representatives to other regions and the whole. Students will calculate central angle degrees and create a circle graph to represent the percentages. The civics standard will be the real-world example used to apply the concept of displaying data to the Legislative Branch of government in this integrated lesson plan.

Type: Lesson Plan

The Watergate Effect Part 1:

Students will create a circle graph to display categorical data of the public presidential approval rates of Richard Nixon before the Supreme Court Case United States v. Nixon. Students will calculate percentages and central angle degrees to graph results in pairs/groups and analyze the results in this integrated lesson plan.

Type: Lesson Plan

Budgeting and Decision-Making: Integrating Math and Civics:

This lesson will help students understand the concept of percentages within the context of government budgets. Students will explore how percentages are used to allocate funds in government budgets and how they can be effectively communicated using graphs. The lesson will involve collaborative learning, discussions, and problem-solving to foster critical thinking and application of math concepts in a civics context.

Type: Lesson Plan

Understanding Taxation and Civic Obligation:

Students will use their knowledge of percentages to calculate federal income tax and local sales tax. They will explore the obligation of citizens to pay taxes and how taxes fund public services. Students will evaluate different tax models by comparing percentages of income taxed at different income levels.

Type: Lesson Plan

Use Circle Graphs to Analyze International Organizations:

Students will analyze international organizations using proportional reasoning to construct circle graphs while examining the purpose of international organizations and the United States’ participation in this integrated lesson plan.

Type: Lesson Plan

Analyzing Government Spending: Integrating math & civics:

Students will practice their skills in interpreting data and creating graphical representations in this integrated civics lesson. Students will apply graphing skills to analyze government spending data and reflect on the importance of mathematics in communicating complex numerical information visually so the public can better stay informed.

Type: Lesson Plan

Graphing Local Voting Data:

This is lesson 3 in a mini unit of 3 lessons. Students will analyze voting data from a Florida county. Students will use the given data to choose and create an appropriate graphical representation.

Type: Lesson Plan

Graphing Data:

This is lesson 2 in a mini unit of 3 lessons. Students will analyze data collected from students, teachers, and principals to decide whether cell phone usage should be allowed in the classroom. They will be receiving data from fictional surveys of teachers and principals. Students will use the given data to choose and create an appropriate graphical representation.

Type: Lesson Plan

Introduction to Voting and Graphing Data:

The students will vote on whether cell phones should be allowed in the classroom or not. They will use this data to select the appropriate way of graphing the results. The teacher will give sample data from other teachers and principals for students to review. The correlation will be relating students to local voting in this integrated lesson plan.

Type: Lesson Plan

Students will utilize historical trade flow data (import and export) to interpret, create, and draw conclusions about foreign policy, specifically the World Trade Organization. Students will write a claim using the data to make suggestions regarding foreign trade import and export in this integrated lesson plan.

Type: Lesson Plan

Clean the pier- To fish or not to fish?:

Students will examine the impact humans can have on the water quality at a popular public fishing pier and ways that citizens can interact with the government to address cleaning the pier in this integrated MEA. Students will analyze the revenue from the fishing pier, peak visiting times, and amounts of marine debris accumulated to determine the pros/cons of closing the fishing pier more frequently to clean the marine debris. Students will research which government agency must be contacted with a proposal.

Type: Lesson Plan

Build a New School:

Students will calculate, interpret, and use measures of center and spread of different populations to determine in which city in Manatee County new schools should be built. Students will also use percentages to estimate the future population of school-aged children which will be used to determine where new schools should be built.

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: https://www.cpalms.org/cpalms/mea.aspx to learn more about MEAs and how they can transform your classroom.They resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. 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.

Type: Lesson Plan

Election Predictions:

Students will examine poll results from three cities to predict a voting outcome on a local level. They will make inferences about a population based on the poll results and develop a written statement to present their findings to the board of county election commissions. Students will then use the peojected election results to determine the impact of citizens in the community.

Type: Lesson Plan

Measurement Data Error:

In this interdisciplinary lesson, students will practice the skill of data collection with a variety of tools and by statistically analyzing the class data sets will begin to understand that error is inherent in all 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

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

Bowling for Box Plots:

Students will learn about the effects of an outlier and interpret differences in shape, center, and spread using a bowling activity to gather data. The students will learn to score their games, report their scores, and collectively measure trends and spread by collaborating to create a box plot. They will analyze and compare box plots, and determine how much of an effect an extreme score (outlier) can have on the overall box plot of the data.

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

The Distance a Coin Will Travel:

This lesson is a hands-on activity that will allow students to collect and display data about how far different coins will travel. The data collected is then used to construct double dot plots and double box plots. This activity helps to facilitate the statistical implications of data collection and the application of central tendency and variability in data collection.

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 long did you study?:

Students will create and analyze histograms based on student study time when preparing for the Algebra EOC. Students will be given a set of data and guided notes

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 – 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

Digging the Plots:

Students construct box plots and use the measure(s) of center and variability to make comparisons, interpret results, and draw conclusions about two populations.

Type: Lesson Plan

A Walk Down the Lane:

Students will collect data, and create box plots. Students will make predictions about which measurement best describes the spread and center of the data. Students will use this information to make predictions.

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

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

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

Is My Backpack Too Massive?:

This lesson combines many objectives for seventh grade students. Its goal is for students to create and carry out an investigation about student backpack mass. Students will develop a conclusion based on statistical and graphical analysis.

Type: Lesson Plan

Cricket Songs:

Using a guided-inquiry model, students in a math or science class will use an experiment testing the effect of temperature on cricket chirping frequency to teach the concepts of representative vs random sampling, identifying directly proportional relationships, and highlight the differences between scientific theory and scientific law.

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

Exploring Box plots:

This lesson involves real-world data situations. Students will use the data to create, explore, and compare the key components of a box plot.

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

Is It a Guess or Statistics?:

This lesson teaches random sampling which leads to making inferences about a larger group or population. Students will determine the best measure of center to use for a data set. Students will collect data, select a data display and then analyze the data.

Type: Lesson Plan

5E Natural Selection Module:

This resource uses a variety of techniques to address the factors that contribute to natural selection. Included in the lesson is a hook to engage students, a weblab exercise, a poster activity for expression and a hands-on simulation.

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

Inferences:

This lesson shows students how to conduct a survey and display their results. The lesson takes the students through:

1. What is a statistical question?
2. General population versus sample population.
3. What is a hypothesis?
4. What is a survey?
5. How to make inferences.

Type: Lesson Plan

Box Plots:

An introduction lesson on creating and interpreting box plots.

Type: Lesson Plan

Computer Simulated Experiments in Genetics:

A computer simulation package called "Star Genetics" is used to generate progeny for one or two additional generations. The distribution of the phenotypes of the progeny provide data from which the parental genotypes can be inferred. The number of progeny can be chosen by the student in order to increase the student's confidence in the inference.

Type: Lesson Plan

Water Troubles:

This Model Eliciting Activity (MEA) presents students with the real-world problem of contaminated drinking water.  Students are asked to provide recommendations for a non-profit organization working to help a small Romanian village acquire clean drinking water.  They will work to develop the best temporary strategies for water treatment, including engineering the best filtering solution using local materials.  Students will utilize measures of center and variation to compare data, assess proportional relationships to make decisions, and perform unit conversions across different measurement systems.

Type: Lesson Plan

A MEANingful Discussion about Central Tendency:

Using relatable scenarios, this lesson explores the mean and median of a data set and how an outlier affects each measure differently.

Type: Lesson Plan

## Original Student Tutorial

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Experts

Chronic Pain and the Brain:

<p>Florida State researcher Jens Foell discusses the use of fMRI&nbsp;and statistics in chronic pain.</p>

Type: Perspectives Video: Expert

Statistical Sampling Results in setting Legal Catch Rate:

Fish Ecologist, Dean Grubbs, discusses how using statistical sampling can help determine legal catch rates for fish that may be endangered.

Type: Perspectives Video: Expert

fMRI, Phantom Limb Pain and Statistical Noise:

<p>Jens Foell&nbsp;discusses how statistical noise reduction is used in fMRI&nbsp;brain imaging to be able to determine which specifics parts of the brain are related to certain activities and how this relates to patients that suffer from phantom limb pain.</p>

Type: Perspectives Video: Expert

Assessment of Antarctic Ice Sheet Movement Rate by Sediment Core Sampling:

<p>Eugene Domack, a geological oceanographer, describes how sediment cores are collected and used to estimate rates of&nbsp;ice sheet movement in Antarctica.&nbsp;Video funded by&nbsp;NSF&nbsp;grant #:&nbsp;OCE-1502753.</p>

Type: Perspectives Video: Expert

Mathematically Modeling Hurricanes:

<p>Entrepreneur and meteorologist Mark Powell discusses the need for statistics in his mathematical modeling program to help better understand hurricanes.</p>

Type: 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

Mathematically Exploring the Wakulla Caves:

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?

Type: Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

<p>It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.</p>

Type: Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

<p>How do scientists collect information from the world? They sample it! Learn how scientists take samples of phytoplankton not only to monitor their populations, but also to make inferences about the rest of the ecosystem!</p>

Type: Perspectives Video: Expert

Managing Lionfish Populations:

<p>Invasive lionfish are taking a bite out of the ecosystem of Biscayne Bay. Biologists are looking for new ways to remove them, including encouraging recreational divers to bite back!</p>

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Nestle Waters & Statistical Analysis:

<p>Hydrogeologist&nbsp;from Nestle Waters discusses the importance&nbsp;of statistical tests in monitoring&nbsp;sustainability and in maintaining consistent&nbsp;water quality in bottled water.</p>

Type: Perspectives Video: Professional/Enthusiast

Fishery Independent vs Dependent Sampling Methods for Fishery Management:

<p>NOAA&nbsp;Scientist Doug Devries discusses the differences between fishery independent surveys and fishery independent surveys. &nbsp;Discussion&nbsp;includes trap sampling as well as camera sampling. Using&nbsp;graphs to show changes in population of red snapper.</p>

Type: Perspectives Video: Professional/Enthusiast

Statistical Art: Four Words:

<p>Graphic designer and artist,&nbsp;Drexston&nbsp;Redway&nbsp;infuses statistics into his artwork to show population distribution and overlap of poverty and ethnicity in Tallahassee, FL.</p>

Type: Perspectives Video: Professional/Enthusiast

Camera versus Trap Sampling: Improving how NOAA Samples Fish :

<p>Underwater sampling with cameras has made fishery management more accurate for NOAA&nbsp;scientists.</p>

Type: Perspectives Video: Professional/Enthusiast

Making Inferences about Wetland Population Sizes:

<p>This ecologist from the Coastal Plains Institute discusses sampling techniques that are used to gather data to make statistical inferences about amphibian populations in the wetlands of the Apalachicola National Forest.</p>

Type: Perspectives Video: Professional/Enthusiast

Sampling Amphibian Populations to Study Human Impact on Wetlands:

<p>Ecologist Rebecca Means discusses the use of statistical sampling and comparative studies in field biology.</p>

Type: Perspectives Video: Professional/Enthusiast

Mean Data and Striking Deviations in Sea Turtle Research:

<p>Dive in and learn about how statistics can be used to help research sea turtles!</p>

Type: Perspectives Video: Professional/Enthusiast

Statistical Analysis of a Randomized Study:

<p>This education researcher uses measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.</p>

Type: Perspectives Video: Professional/Enthusiast

Random Sampling to Estimate Wildlife Populations:

<p>Dr. Bill McShea from the Smithsonian Institution discusses sampling and inference in the study of wildlife populations.</p> <p>This video was created in collaboration with the Okaloosa County SCIENCE Partnership, including the Smithsonian Institution and Harvard University.</p>

Type: Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

<p>Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.</p>

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Ideas

Using Visual Models to Determine Mode, Median and Range:

Unlock an effective teaching strategy for teaching median, mode, and range in this Teacher Perspectives Video for educators.

Type: Perspectives Video: Teaching Idea

Pitfall Trap Classroom Activity:

<p>Patrick&nbsp;Milligan&nbsp;shares a teaching idea for collecting insect samples.</p>

Type: Perspectives Video: Teaching Idea

Atlatl - Differences in Velocity and Distance:

<p>An archaeologist describes how an ancient weapons technology can be used to bring home dinner or generate data for a math lesson.</p>

Type: Perspectives Video: Teaching Idea

Rubber Band Races for Testing Measurement Accuracy:

<p>This activity will send your measurement lab to new distances.</p>

Type: Perspectives Video: Teaching Idea

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.

Mr. Brigg's Class Likes Math:

In a poll of Mr. Briggs's math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.

Offensive Linemen:

In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.

Election Poll, Variation 1:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). There are two important goals in this task: seeing the need for random sampling and using randomization to investigate the behavior of a sample statistic. These introduce the basic ideas of statistical inference and can be accomplished with minimal knowledge of probability.

## Teaching Ideas

Pump Up the Volume:

This activity is a statistical analysis of recorded measurements of a single value - in this case, a partially filled graduated cylinder.

Type: Teaching Idea

A Certain Uncertainty:

Students will measure the mass of one nickel 10 times on a digital scale precise to milligrams. The results will be statistically analyzed to find the error and uncertainty of the scale.

Type: Teaching Idea

All Numbers Are Not Created Equal:

Although a sheet of paper is much thinner than the divisions of a ruler, we can make indirect measurements of the paper's thickness.

Type: Teaching Idea

## Text Resource

Cell Phone Ownership Hits 91% of Adults:

This informational text resource is intended to support reading in the content area. A Pew Research Center survey indicates that cell phone ownership is at an all-time high, with 91% of Americans owning a cell phone in 2013. Statistical tests show that cell phone usage is significantly higher in men, college-educated people, the wealthy, and those living in urban/suburban areas. This rise in ownership is associated with a variety of positive impacts of cell phone use, but previous research shows there are several negative impressions and impacts of cell phones as well.

Type: Text Resource

## Student Resources

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

## Original Student Tutorial

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Experts

Mathematically Exploring the Wakulla Caves:

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?

Type: Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

<p>It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.</p>

Type: Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

<p>How do scientists collect information from the world? They sample it! Learn how scientists take samples of phytoplankton not only to monitor their populations, but also to make inferences about the rest of the ecosystem!</p>

Type: Perspectives Video: Expert

Managing Lionfish Populations:

<p>Invasive lionfish are taking a bite out of the ecosystem of Biscayne Bay. Biologists are looking for new ways to remove them, including encouraging recreational divers to bite back!</p>

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

<p>Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.</p>

Type: Perspectives Video: Professional/Enthusiast

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.

Mr. Brigg's Class Likes Math:

In a poll of Mr. Briggs's math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.

Offensive Linemen:

In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.

Election Poll, Variation 1:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). There are two important goals in this task: seeing the need for random sampling and using randomization to investigate the behavior of a sample statistic. These introduce the basic ideas of statistical inference and can be accomplished with minimal knowledge of probability.

## Parent Resources

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

## Perspectives Video: Experts

Using Statistics to Estimate Lionfish Population Size:

<p>It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.</p>

Type: Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

<p>How do scientists collect information from the world? They sample it! Learn how scientists take samples of phytoplankton not only to monitor their populations, but also to make inferences about the rest of the ecosystem!</p>

Type: Perspectives Video: Expert

Managing Lionfish Populations:

<p>Invasive lionfish are taking a bite out of the ecosystem of Biscayne Bay. Biologists are looking for new ways to remove them, including encouraging recreational divers to bite back!</p>

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

<p>Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.</p>

Type: Perspectives Video: Professional/Enthusiast

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.

Mr. Brigg's Class Likes Math:

In a poll of Mr. Briggs's math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.