# 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.

## 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

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

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

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

## 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:

Florida State researcher Jens Foell discusses the use of fMRI and statistics in chronic pain.

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:

Jens Foell discusses how statistical noise reduction is used in fMRI 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.

Type: Perspectives Video: Expert

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

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

Type: Perspectives Video: Expert

Mathematically Modeling Hurricanes:

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

Type: Perspectives Video: Expert

Histograms Show Trends in Fisheries Data Over Time:

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

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:

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

Type: Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

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!

Type: Perspectives Video: Expert

Managing Lionfish Populations:

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!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Nestle Waters & Statistical Analysis:

Hydrogeologist from Nestle Waters discusses the importance of statistical tests in monitoring sustainability and in maintaining consistent water quality in bottled water.

Type: Perspectives Video: Professional/Enthusiast

Fishery Independent vs Dependent Sampling Methods for Fishery Management:

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

Type: Perspectives Video: Professional/Enthusiast

Statistical Art: Four Words:

Graphic designer and artist, Drexston Redway infuses statistics into his artwork to show population distribution and overlap of poverty and ethnicity in Tallahassee, FL.

Type: Perspectives Video: Professional/Enthusiast

Camera versus Trap Sampling: Improving how NOAA Samples Fish :

Underwater sampling with cameras has made fishery management more accurate for NOAA scientists.

Type: Perspectives Video: Professional/Enthusiast

Making Inferences about Wetland Population Sizes:

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.

Type: Perspectives Video: Professional/Enthusiast

Sampling Amphibian Populations to Study Human Impact on Wetlands:

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

Type: Perspectives Video: Professional/Enthusiast

Mean Data and Striking Deviations in Sea Turtle Research:

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

Type: Perspectives Video: Professional/Enthusiast

Statistical Analysis of a Randomized Study:

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.

Type: Perspectives Video: Professional/Enthusiast

Random Sampling to Estimate Wildlife Populations:

Dr. Bill McShea from the Smithsonian Institution discusses sampling and inference in the study of wildlife populations.

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

Type: Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

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

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Ideas

Pitfall Trap Classroom Activity:

Patrick Milligan shares a teaching idea for collecting insect samples.

Type: Perspectives Video: Teaching Idea

Atlatl - Differences in Velocity and Distance:

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

Type: Perspectives Video: Teaching Idea

Rubber Band Races for Testing Measurement Accuracy:

This activity will send your measurement lab to new distances.

Type: Perspectives Video: Teaching Idea

## 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:

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

Type: Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

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!

Type: Perspectives Video: Expert

Managing Lionfish Populations:

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!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

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

Type: Perspectives Video: Professional/Enthusiast

## 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:

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

Type: Perspectives Video: Expert

Tow Net Sampling to Monitor Phytoplankton Populations:

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!

Type: Perspectives Video: Expert

Managing Lionfish Populations:

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!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

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

Type: Perspectives Video: Professional/Enthusiast