# Cluster 1: Summarize, represent, and interpret data on a single count or measurement variable. (Algebra 1 - Additional Cluster) (Algebra 2 - Additional Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information
Number: MAFS.912.S-ID.1
Title: Summarize, represent, and interpret data on a single count or measurement variable. (Algebra 1 - Additional Cluster) (Algebra 2 - Additional Cluster)
Type: Cluster
Subject: Mathematics
Domain-Subdomain: Statistics & Probability: Interpreting Categorical & Quantitative Data

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.912.S-ID.1.AP.1a
Complete a graph given the data, using dot plots, histograms or box plots.
MAFS.912.S-ID.1.AP.2a
Describe a distribution using center and spread
MAFS.912.S-ID.1.AP.4a
Use descriptive stats like range, median, mode, mean and outliers/gaps to describe the data set.
MAFS.912.S-ID.1.AP.2b
Use the correct measure of center and spread to describe a distribution that is symmetric or skewed.
MAFS.912.S-ID.1.AP.2c
Identify outliers (extreme data points) and their effects on data sets.
MAFS.912.S-ID.1.AP.2d
Compare two or more different data sets using the center and spread of each.
MAFS.912.S-ID.1.AP.3a
Use statistical vocabulary to describe the difference in shape, spread, outliers and the center (mean).

## Related Resources

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

## Formative Assessments

How Many Jeans?:

Students are asked to select a measure of center to compare data displayed in dot plots and to justify their choice.

Type: Formative Assessment

Texting During Lunch Histograms:

Students are asked to select measures of center and spread to compare data displayed in histograms and to justify their choices.

Type: Formative Assessment

Texting During Lunch:

Students are asked to select a measure of center to compare data displayed in frequency tables and to justify their choice.

Type: Formative Assessment

Total Points Scored:

Students are given a set of data and are asked to determine how the mean is affected when an outlier is removed.

Type: Formative Assessment

Using Spread to Compare Tree Heights:

Students are asked to compare the spread of two data distributions displayed using box plots.

Type: Formative Assessment

Using Centers to Compare Tree Heights:

Students are asked to compare the centers of two data distributions displayed using box plots.

Type: Formative Assessment

Comparing Distributions:

Students are given two histograms and are asked to describe the differences in shape, center, and spread.

Type: Formative Assessment

Students are asked to find the probability that an outcome of a normally distributed variable is greater than a given value.

Type: Formative Assessment

Students are asked to find the probability that an outcome of a normally distributed variable is between two given values.

Type: Formative Assessment

Label a Normal Curve:

Students are asked to scale and label a normal curve given the mean and standard deviation of a data set with a normal distribution.

Type: Formative Assessment

Area Under the Normal Curve:

Students are asked to find the probability that an outcome of a normally distributed variable is between two given values using both a Standard Normal Distribution Table and technology.

Type: Formative Assessment

Algebra Test Scores:

Students are asked to select a histogram for which it would be appropriate to apply the 68-95-99.7 rule.

Type: Formative Assessment

Winning Seasons:

Students are asked to construct a histogram corresponding to a given set of data.

Type: Formative Assessment

Trees in the Park:

Students are asked to construct a box plot corresponding to a given set of data.

Type: Formative Assessment

Flowering Trees:

Students are asked to determine whether each of two given dot plots are consistent with a given histogram.

Type: Formative Assessment

A Tomato Garden:

Students are asked to construct a dot plot corresponding to a given set of data.

Type: Formative Assessment

## Lesson Plans

Sea Ice Analysis Algebra:

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 statistical analysis as a tool to evaluate the sea ice loss. Students will use technology to quickly generate graphs for each month looking for trends, patterns, or deviations over time.

Type: Lesson Plan

Sensoring Data:

In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.

Type: Lesson Plan

Sea Ice Analysis:

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 statistical analysis as a tool to evaluate the sea ice loss. Students will use technology to quickly generate graphs for each month looking for trends, patterns or deviations over time.

Type: Lesson Plan

Show Me the Money! Selecting Student Athletes for Scholarships:

Students will use data to decide the ideal candidate for a college scholarship by computing the mean and the standard deviation. The student will present the data using the normal distribution and make recommendations based on the findings. Students will recognize that not all data can be presented in this format.

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 mean, median, and standard deviation. They will construct and interpret dot plots based on 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

Can You Walk In My Shoes?:

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

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 center, shape, and spread of the data.

Type: Lesson Plan

Comparing Standard Deviation:

Students will predict and compare standard deviation from a dot plot. Each data set is very different, with a small variation vs. larger variation. The students are asked to interpret the standard deviation after calculating the range and mean of the each data set.

Type: Lesson Plan

Close to the Crossbar with Standard Deviation:

The lesson will allow students to make the connection of prior knowledge of mean absolute deviation and central tendencies to standard deviation and variance. Students will learn how to calculate and analyze variance and standard deviation. With a partner, students will collect data from kicking a ball into a goal mark. Students will collect data and find the mean, then calculate standard deviation and variance, and compare the data between boys and girls. They will analyze the data distribution in terms of how many students are within certain numbers of standard deviations from the mean.

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 affect 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 of grade category using histograms. They will also analyze grades using mean and standard deviation. Students will use statistics to determine data distribution while comparing center and spread of two or more different data sets.

Type: Lesson Plan

College Freshman Entrance Data:

This lesson is designed to introduce students to possible sets of normally distributed data. Students will informally assess the normality of fit. Sample data including average SAT and ACT scores and GPA's is drawn from 36 universities around the United States. First, students will be given the data in table form, and they predict why they do or do not believe their data set is normally distributed. The students will then be given the same data set as a histogram and they observe whether or not the data appears normally distributed, skewed left or skewed right. Finally, they explain their results.

Type: Lesson Plan

How tall is an 8th grader?:

Ever wonder about the differences in heights between boys and girls in grade 8? In this lesson, students will use data they collect and analyze with multiple box plots and 5-number summaries to make inferences about how height and gender 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 center and spread of the data. This is meant to be an application lesson of concepts and skills previously acquired.

Type: Lesson Plan

Standard Deviation and the Normal Curve in Kahoot!:

In this three day lesson, students learn about standard deviation, the normal curve, and how they are applied. Your students will be engaged and learning when they collect and analyze data using a free Kahoot! quiz.

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 be able to identify which one should be used for a specified set of data.

Type: Lesson Plan

Picturing the Normal World:

This is an introductory lesson on normally distributed data. Students will collect their own height data and view the data distribution for their class. They analyze this data and decide if they are normal or not.

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:

This lesson gives students the opportunity to use technology to investigate variability in data. Students will draw conclusions and cite evidence from the data to support their conclusions.

Type: Lesson Plan

How long did you study?:

Students will be presented with a set of data and guided notes to compare study time for the Algebra EOC for different classes.

Type: Lesson Plan

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

This lesson will have students collect data through an investigative manner and compile them into a larger spreadsheet. From there students will create different data displays and do a compare and contrast of the data sets to determine "Which one do you think takes the fewest amount of licks to get to the center: a Tootsie Pop, a Blow Pop, or a Dum Dum lollipop?"

Type: Lesson Plan

Birthday Party Decisions:

This lesson has students interpret four different boxplots and has them comparing them to find a solution.

Type: Lesson Plan

Outliers in the Outfield – Dealing With Extreme Data Points:

Students will explore the effects outliers have on mean and median values using MLB salaries stats.

Type: Lesson Plan

In terms of soccer: Nike or Adidas?:

This is a lesson where the students will interpret the standard deviation for two data sets.

Type: Lesson Plan

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

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 are asked to construct given data in a data plot to analyze and determine if the data is symmetric, skewed, or uniform with an appropriate explanation. Students will give a visual display of interpreted results.

Type: Lesson Plan

A Walk Down the Lane:

Students will measure a pre-determined distance between 2 points in a hallway, classroom, or courtyard using 2 different measures (strides or rulers and tailor tape measures.) Once data is collected, return to the classroom to compile data and create box plots. Students should make predictions of which measurement will be most accurate, and how they will determine accuracy. From the box plots created, students should discuss and create a summary of the data collected, median and quartiles, and what conclusions they were able to infer from their graphs about their predictions.

Type: Lesson Plan

One man's success is another man's failure or How do we measure success?:

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

Type: Lesson Plan

How Old are the Players?:

For this lesson, students will use computers to research the ages of players on two basketball teams in pairs. They will find the five number summary, as well as the mean, interquartile range, and determine if there are outliers in the data set. At the end of the lesson, the students will have understood how to appropriately use statistics to compare the median, mean, and the interquartile range of two or more different data sets. This lesson will be guided by several principles: assigning short, meaningful amounts of practice, assigning practice to increase overlearning, and making appropriate use of massed and distributed practice.

Type: Lesson Plan

Who is the world's best ball player?:

Students will use box and whisker plots to determine who is the better basketball player, Lebron James or Michael Jordan.

Type: Lesson Plan

If The Shoe Fits – A "Normal" Cinderella Story:

Using a normal distribution manipulative and a calculator, students will explore the normal distribution curve to determine the area between each standard deviation from the mean using the empirical rule. Students will use the mean and standard deviation to predict outcomes in real world situations and finally answer the age old question: What size was Cinderella's glass slipper?

Type: Lesson Plan

The students will compare the center and spread of data sets as well as find the effects of outliers.

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?:

This resource is a lesson plan developed for students to master MAFS.912.S.1.3 (Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points).

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

Type: Lesson Plan

Sensoring Data:

In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.

Type: Lesson Plan

Hot Coffee Coming Through:

In this lesson, students will explore data collection using the temperature probe sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation to determine which coffee mug is the best. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a problem based STEM challenge. Due to the multiple skills there are many standards that are covered.

There are two options for this lab. The first student handout is for students at an average high school statistics level (Algebra 1) and will allow for standard deviation and graphical analyses of the data. The second option is for advanced students that have been exposed to hypothesis testing of claims (Algebra 2 or AP Stats).

Type: Lesson Plan

Grapevine Fabrication Part 2:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to collect data to perform basic statistical operations to analyze and make comparisons on variability within a certain brand of raisins. Part 1 must be completed prior to starting Part 2. This investigation can elicit discussion about manufacturing and quality control.

Type: Lesson Plan

Bubble Gum Bubbles Lab:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to collect data by blowing bubble gum bubbles and perform statistical analysis, including standard deviation. This lesson provides students an applied setting to use their previously acquired statistical skills.

Type: Lesson Plan

Grapevine Fabrication Part 1:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to collect data to perform basic statistical operations to analyze and make comparisons on variability within a certain brand of raisins. Part 1 may be completed without Part 2. This investigation can elicit discussion about manufacturing and quality control.

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 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

Exploring Box plots:

This lesson involves real world data situations. Students will take the data and 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.:

"You are what you eat." In this lesson students will use box plots and double box plots to analyze nutritional data about popular food choices.

Type: Lesson Plan

Florida's Manatee Population:

Students will use box plots to identify data on the past and present manatee populations on both coasts of Florida during the winter months, January through March. This lesson is designed to use technology to create box plots and analyze data. As an alternate lesson without technology, the manatee data in this lesson can be used to create box plots with graph paper and pencils. Students will use data about the past and current manatee populations in Florida and display and analyze the data using Excel and Geogebra.

This lesson is intended to be an enrichment experience and should be used after students have mastered box plots as described in the standard MAFS.912.S-ID.1.1.

Type: Lesson Plan

This lesson is intended to teach students to 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. Also, students will learn about the different advantages and disadvantages of dot plots, histograms, and box plots. After this lesson, students are expected to apply the information learned in a project that involves real-world issues and making an analysis based on data collected.

Type: Lesson Plan

Box and Whisker Plots:

Introduction lesson on how to create and interpret box and whisker plots.

Type: Lesson Plan

House Hunting!:

Students will use criteria such as median home price, neighborhood safety, and likelihood of evacuation during a hurricane to rank a list of neighborhoods in which to shop for a home.

Type: Lesson Plan

Representing Data 1: Using Frequency Graphs:

This lesson unit is intended to help you assess how well students are able to use frequency graphs to identify a range of measures, make sense of this data in a real-world context, and understand that a large number of data points allow a frequency graph to be approximated by a continuous distribution.

Type: Lesson Plan

Representing Data 2: Using Box Plots:

This lesson unit is intended to help you assess how well students are able to interpret data using frequency graphs and box plots. In particular, this unit aims to identify and help students who have difficulty figuring out the data points and spread of data from frequency graphs and box plots. It is advisable to use the first lesson in the unit, Representing Data 1: Frequency Graphs (32498), before this one.

Type: Lesson Plan

CollegeReview.com:

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.

Type: Lesson Plan

A MEANingful Discussion about Central Tendency:

This is a discovery lesson to deepen the understanding of central tendency (mean, median) by posing relevant scenarios that students must examine and explore. It is the exploration of the salary negotiations for the Los Angeles Lakers and the use of a see-saw to physically model what the algorithm for an average truly finds. This will lead students to understand the pairing of the measures of central tendency and spread dictated by the shape of the distribution. A detailed explanation of the answers is provided with the guided discovery questions so that the teacher will be able to deepen student knowledge by eliciting the nuances of the information presented.

Type: Lesson Plan

## Lesson Study Resource Kit

Measurement Matters:

This Lesson Study Resource Kit is an introductory unit on measurement for a Chemistry I course.

Type: Lesson Study Resource Kit

## Perspectives Video: Experts

Birdsong Series: Statistical Analysis of Birdsong:

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

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

Statistics and Scientific Data:

Hear this oceanography student float some ideas about how statistics are used in research.

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

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

Normal? Non-Normal Distributions & Oceanography:

What does it mean to be normally distributed?  What do oceanographers do when the collected data is not normally distributed?

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

Winning the Race with Data Logging and Statistics:

Data logging has transformed competitive racing! These SCCA drivers discuss how they use computers to compare multiple sets of data after test runs.

Type: Perspectives Video: Professional/Enthusiast

Graphs Help Identify Cost-Effective Sea Turtle Conservation Strategies:

This marine biologist discusses her use of graphical representations to help determine the most cost-effective management strategies for sea turtle conservation.

Type: Perspectives Video: Professional/Enthusiast

Revolutionize Wing Design with Equations and Statistics:

Brandon Reese, a PhD candidate in the FAMU-FSU College of Engineering, discusses the significance of both Bernoulli's equation and statistical analysis for the design of a "smart wing."

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

Smile Statistics:

This quantitative measurement and statistics activity will allow you to save face.

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.

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

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.

Should We Send Out a Certificate?:

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.

Do You Fit in This Car?:

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.

Random Walk III:

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

## Professional Development

Representing Data With Graphs: Box Plots:

Strategies to help students in a first Algebra course learn to summarize, represent, and interpret one-variable data. The focus of this tutorial is on representing data with box plots.

Type: Professional Development

## Teaching Ideas

Now That is a Dense Graph:

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

Pump Up the Volume:

This activity challenges students to analyze the statistical distribution of volume measurements from a partially filled graduated cylinder. The free app, GeoGebra is used to create a box plot to aid in the analysis.

Type: Teaching Idea

An Ecological Field Study with Statistical Analysis of Two Populations:

Students will design an investigation that compares a characteristic of two populations of the same species. Students will collect data in the field and analyze the data using descriptive statistics.

Type: Teaching Idea

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

Now That is a Dense Graph:

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

Stem-and-Leaf Plots:

This lesson is designed to introduce students to stem-and-leaf plots as a graphical way to represent a data set. The lesson also reviews measures of central tendency with directions for finding mean, median, and mode are given. This lesson provides links to discussions and activities related to stem-and-leaf plots 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: Teaching Idea

## Text Resource

Scientists See the World Differently:

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

## Unit/Lesson Sequence

Sample Algebra 1 Curriculum Plan Using CMAP:

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

### Using this CMAP

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

Type: Unit/Lesson Sequence

## Virtual Manipulatives

Histogram vs. Box Plot:

This simulation allows the student to create a box plot and a histogram for the same set of data and toggle between the two displays. Maximum, minimum, median and mean are shown for the data set. The student can change the cell width to explore how the histogram is affected.

Type: Virtual Manipulative

Box Plot:

In this activity, students use preset data or enter in their own data to be represented in a box plot. This activity allows students to explore single as well as side-by-side box plots of different data. 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

Normal Distribution Interactive Activity:

With this online tool, students adjust the standard deviation and sample size of a normal distribution to see how it will affect a histogram of that distribution. This activity allows students to explore the effect of changing the sample size in an experiment and the effect of changing the standard deviation of a normal distribution. Tabs at the top of the page provide access to 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

Univariate and Bivariate Data:

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

Histogram Tool:

This virtual manipulative histogram tool can aid in analyzing the distribution of a dataset. It has 6 preset datasets and a function to add your own data for analysis.

Type: Virtual Manipulative

Histogram:

In this activity, students can create and view a histogram using existing data sets or original data entered. Students can adjust the interval size using a slider bar, and they can also adjust the other scales on the graph. This activity allows students to explore histograms as a way to represent data as well as the concepts of mean, standard deviation, and scale. 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

Multi Bar Graph:

This activity allows the user to graph data sets in multiple bar graphs. The color, thickness, and scale of the graph are adjustable which may produce graphs that are misleading. Users may input their own data, or use or alter pre-made data sets. 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

## Student Resources

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

## 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

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.

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

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.

Should We Send Out a Certificate?:

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.

Do You Fit in This Car?:

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.

Random Walk III:

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

## Virtual Manipulatives

Histogram vs. Box Plot:

This simulation allows the student to create a box plot and a histogram for the same set of data and toggle between the two displays. Maximum, minimum, median and mean are shown for the data set. The student can change the cell width to explore how the histogram is affected.

Type: Virtual Manipulative

Box Plot:

In this activity, students use preset data or enter in their own data to be represented in a box plot. This activity allows students to explore single as well as side-by-side box plots of different data. 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

Normal Distribution Interactive Activity:

With this online tool, students adjust the standard deviation and sample size of a normal distribution to see how it will affect a histogram of that distribution. This activity allows students to explore the effect of changing the sample size in an experiment and the effect of changing the standard deviation of a normal distribution. Tabs at the top of the page provide access to 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 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

Histogram Tool:

This virtual manipulative histogram tool can aid in analyzing the distribution of a dataset. It has 6 preset datasets and a function to add your own data for analysis.

Type: Virtual Manipulative

Histogram:

In this activity, students can create and view a histogram using existing data sets or original data entered. Students can adjust the interval size using a slider bar, and they can also adjust the other scales on the graph. This activity allows students to explore histograms as a way to represent data as well as the concepts of mean, standard deviation, and scale. 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

Multi Bar Graph:

This activity allows the user to graph data sets in multiple bar graphs. The color, thickness, and scale of the graph are adjustable which may produce graphs that are misleading. Users may input their own data, or use or alter pre-made data sets. 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

## Parent Resources

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

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.

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

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.

Should We Send Out a Certificate?:

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.

Do You Fit in This Car?:

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.

Random Walk III:

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