# Cluster 1: Develop understanding of statistical variability. (Additional Cluster)Archived

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.6.SP.1
Title: Develop understanding of statistical variability. (Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Statistics & Probability

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.6.SP.1.AP.1a
Identify statistical questions and make a plan for data collection.
MAFS.6.SP.1.AP.2a
Find the range of a given data set.
MAFS.6.SP.1.AP.2b
Explain or identify what the mode represents in a set of data.
MAFS.6.SP.1.AP.3a
Solve for mean of a given data set using whole numbers.
MAFS.6.SP.1.AP.3b
Explain or identify what the mean represents in a set of data.

## Related Resources

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

## Formative Assessments

Explain Measures of Variability:

Students are asked to list measures of variability and explain what they indicate about a set of data.

Type: Formative Assessment

Explain Measures of Center:

Students are asked to list measures of center and explain what they indicate about a set of data.

Type: Formative Assessment

Compare Measures of Center and Variability:

Students are asked to explain the difference between measures of center and measures of variability.

Type: Formative Assessment

Students are asked to determine whether or not questions are statistical and justify their responses.

Type: Formative Assessment

TV Statistics:

Students are asked to write a statistical question and explain why it is statistical.

Type: Formative Assessment

Math Test Center:

Students are asked to describe and compare the centers of two data sets given their dot plots.

Type: Formative Assessment

Pet Frequency:

Students are asked to describe the distribution of data given in raw form.

Type: Formative Assessment

Students are asked to describe and compare the spread of the distribution of two data sets given their dot plots.

Type: Formative Assessment

Math Test Shape:

Students are asked to describe the shapes of three distributions given their dot plots and to explain the shapes in terms of the context.

Type: Formative Assessment

## Lesson Plans

Climate and Careers!:

Students will explore chosen outdoor careers and how the careers connect to certain climates based on temperature and precipitation. The guiding question states "How might you use evidence from weather data and dot plot displays to allow you to identify which location's climate would be best for your career and why?" Students will collect data online and display the data using dot plots on posters with analysis using the mean. Students will engage in collaboration throughout. A power point is included with all necessary resources.

Type: Lesson Plan

Currents and Temperature:

Students will construct graphs from existing weather data sets establishing statistical relationships between air temperature over land in proximity to large bodies of warm water with continuous currents, and construct a model to visually support causality for those relationships. Students will be able to understand that ocean currents can have an effect on local weather conditions, influencing temperature (and precipitation with extended lesson), and use that understanding to make plausible explanations for the differences in temperature and precipitation between two geographically close Florida cities of a similar latitude.

Type: Lesson Plan

Analyze Data:

This lesson uses statistical analysis to evaluate data. The data used is from the app created by the students in lesson 2 of the Data Set and Statistics Unit. This lesson also guides students in recognizing the different types of data collected and how the distribution's shape can be affected when graphed at different intervals in histograms. This is the final lesson in the unit.

Type: Lesson Plan

Gather Data For Distribution by Programming an App:

This lesson allow students to gather, calculate, and plot data using both computer code and mathematical equations. In this lesson students will create a pedometer app to demonstrate the understanding of algorithms, components (such as buttons, textboxes, sensors, etc.), and If/Then statements. This lesson uses algebraic equations and random data to access the needed components to store data in a spreadsheet.

Type: Lesson Plan

Data Sets Represented in Computers:

This lesson shows how data can be represented by computers, in relation to everyday activities we may not be aware that we use computer. It gives an overview of graphing data by creating a histogram based on population data. Using the data collected, students will get a chance to hand write code to show what structure is needed for computers to collect, analyze and distribute such data. This lesson is lesson 1 of the Data Set and Deviation Statistics Unit and bridges statistical concepts of data collection, graphing and analysis with programming a computer using coding language while reinforcing foundational algebraic skills.

Type: Lesson Plan

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 mean and variation from the mean of sea ice loss.

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

Measurement and Data Collection:

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.

This lesson uses the Hip Sciences Sensor Wand and Temperature Probe. Please refer to the corresponding Hip Science Sensor Guide(s) for information on using the sensor.

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

Measurement and Data Collection:

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.

This lesson uses the Hip Sciences Sensor Wand and Temperature Probe. Please refer to the corresponding Hip Science Sensor Guide(s) for information on using the sensor.

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

Inquiry based challenge to develop a plan to investigate a large tadpole population growth in the town of Belle Pole. Students analyze preexisting data and make conclusions about the data. Student groups compare their approaches and conclusions with other student groups. A whole group discussion leads students to conclude that results often varied based on methods used to conduct the same investigation. The lesson ends with students writing a self reflection from their student group and whole group discussions.

Type: Lesson Plan

May the neutrally buoyant force be with you !:

• This lesson helps students understand that forces affect motion and that some forces can be manipulated to be balanced or unbalanced with respect to motion. In the lesson, students use their knowledge of types of forces and free body diagrams to do an inquiry activity where they attempt to make a film canister neutrally buoyant in a 10 gal tank full of fresh water. (I have also used 2 L bottles with tops cut off and an empty pie pan to collect spillage.) Students need to predict, observe, and explain along the way as well as collect and record data to help quantify their results.
• After the lesson, students apply their new knowledge gained through experiential learning to real life scenarios in an abstract way as a formative assessment.

Type: Lesson Plan

Statistical Question Sort:

In this lesson, students will explore statistical questions. Students will be able to create statistical questions and understand when a question is non-statistical. This lesson incorporates a YouTube video, direct instruction, and a question sort. By the end of the lesson, students will be able to write their own statistical questions for future statistical lessons.

Type: Lesson Plan

Data Detectives:

In this lesson, students will become "Data Detectives" as they investigate that a measure for the center of a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. The students will utilize cooperative learning structures, hands-on learning activities and the Standards for Mathematical Practices as they delve into the world of understanding the concept of "mean" and numerical data sets.

Type: Lesson Plan

Universal GPA:

This lesson incorporates examples that are relevant to students' interests and uses diverse methods of presentation to demonstrate how changes in measures of variation can affect the measure of central tendency. The lesson utilizes the concept of grade point average (GPA) to create a real world example that student can relate to and apply. The lesson also includes a manipulative lab to demonstrate the idea of distribution of data as it relates to changing the value of a data point(s).

Type: Lesson Plan

Survey Says:

This lesson addresses statistical and non-statistical questions. The hook will be getting the students talking about what is exciting about shows like "The Family Feud" and how the questions on these shows are examples of statistical questions because they yield numerical answers that vary from one individual to another. The students will have several attempts to identify statistical or non-statistical questions.

Type: Lesson Plan

What is a Question?:

Students will learn how to recognize and formulate a statistical question. After a statistical question is established, students will engage in collecting data from their classmates. The lesson concludes with student presentations of analyzed data and conclusions about the topic selected.

Type: Lesson Plan

Backpack Weight:

Just how heavy is your backpack? In this lesson students find measures of center in fun and meaningful ways. They will review mean, median, range and outlier, become a number set, and work together gathering and representing data about the weight of their backpacks.

Type: Lesson Plan

Statistical Questions and Variability:

This lesson helps the student identify and write statistical questions and determine the variability based on the collected data.

Type: Lesson Plan

Comparing and Contrasting Data Sets Using Measures of Center and Spread:

This lesson is designed to show students how to apply their understanding of data distribution, center, and spread to compare and contrast data sets. The lesson should be covered over two class periods (or one if on a block schedule). In this lesson, students will be asked to:

• Review important vocabulary and prior knowledge.
• Make observations from dot plots and data sets.
• Calculate measures of central tendency (mean, median, mode).
• Calculate a measure of spread (range).
• Examine how outliers affect data sets.
• Complete a group activity and compare results to other groups.
• Use measures of center and spread to compare/contrast data sets.

Type: Lesson Plan

Calculating the Mean, Median, Mode, and Range from a Frequency Chart:

This lesson lasts a total of two hours: 15-minute pre-lesson, 90-minute lesson, and 15-minute follow up lesson or homework. Students will need the two worksheets, a mini-whiteboard, a pen, and an eraser. Each small group will need both card sets, a large sheet of paper, and a glue stick. Students will generate responses to a question about favorite computer games and use this data for the lesson. Students will then work collaboratively to display different data and discuss various strategy approaches.

Type: Lesson Plan

What's the Question?:

This lesson introduces students to statistical questions with answer variability versus non-statistical questions with singular answers. Students will identify and create questions of both types, as well as those that correlate to a given set of data presented as a bar graph. Students will also create bar graphs to represent a statistical question and a non-statistical question.

Type: Lesson Plan

Flipping the house:

The Gonzalez family is moving to Florida and they need our students' help deciding which neighborhood to live in. To help them, the students will calculate the mean and median of home prices in the neighborhood and trends in price changes.

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

Type: Lesson Plan

Statistically Speaking Part II: An Investigation of Statistical Questions and Data Distribution:

This lesson is Part 2 of 2 and uses an inquiry-based learning method to help students recognize a statistical question as one that anticipates variability in the data. Through cooperative learning activities, the students will develop an understanding of how to analyze the collected data to answer a statistical question. Students will complete a statistical research project in teams. Since this lesson focuses on math concepts related to identifying clusters, gaps, outliers, and the overall shape of a line plot, it will help students build a strong foundation for future concepts in the statistics and probability domain. The corresponding lesson is Statistically Speaking Part I: An Investigation of Statistical Questions and Data Distribution, Resource ID 48649.

Type: Lesson Plan

Play Like you "MEAN" It! - Understanding a Measure of Center:

In this lesson, students will investigate how a measure of center, the mean, summarizes a numerical data set of all the values with a single number. Inquiry-based instruction along with hands-on learning is utilized to build understanding of the concept of "mean." Students will utilize Mathematical Practice Standards, as they build understanding of how the mean is used to describe a numerical data set.

Type: Lesson Plan

Statistical Question?:

The lesson will start by assessing prior knowledge about asking varied questions. To hook the students, the teacher will ask students questions to which they must decide if they are statistical or non-statistical. Finally, the teacher will ask students to volunteer questions so the class can discuss why or why not the question is statistical.

Type: Lesson Plan

Statistically Speaking Part I: An Investigation of Statistical Questions and Data Distribution:

This lesson is Part 1 of 2 and uses the inquiry-based learning method to help students recognize a statistical question as one that anticipates variability in the data. Through cooperative learning activities, students will learn how to analyze the data collected to answer a statistical question. Since this lesson focuses on math concepts related to identifying clusters, gaps, outliers, and the overall shape of a line plot, it will help students build a strong foundation for future concepts in the statistics and probability domain. Part 2 of this lesson is Resource ID #49091.

Type: Lesson Plan

Heartbeat in a Box:

This lesson teaches how to make a box plot paying attention to what the quartiles mean. Students find resting heartbeat and active heartbeat. They make observations of this data displayed in box plots on the same number line. Students will interpret and make sense of this data, as well. Outliers are introduced, but not calculated, as is the intent of the standards, at this grade level.

Type: Lesson Plan

Data Doctors:

Have your students become "Data Doctors" by examining and analyzing means of central tendency. This lesson is a great introduction to mean, median, mode and range. Students will be sets of data, get to work in small groups examining the sets, view a poem that will help them remember each term, and take surveys to get real data sets.

Type: Lesson Plan

## Original Student Tutorials

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

Castles, Catapults and Data: Histograms Part 2:

Learn how to interpret histograms to analyze data, and help an inventor predict the range of a catapult in part 2 of this interactive tutorial series. More specifically, you'll learn to describe the shape and spread of data distributions.

Type: Original Student Tutorial

Learn how to calculate and interpret the Mean Absolute Deviation (MAD) of data sets in this travel-themed, interactive statistics tutorial.

Type: Original Student Tutorial

It Can Be a Zoo of Data!:

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

Type: Original Student Tutorial

## 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

## Perspectives Video: Professional/Enthusiast

Determining Remote Locations with Math:

Ecologist, Rebecca Means, describes the process of determining remote locations in the USA and developing quantitative questions that are appropriate.

Type: Perspectives Video: Professional/Enthusiast

How Long is 30 Seconds?:

The purpose of this task is for students to gain a better understanding of the passage of time. Students with the help of their teacher should work to design an investigation to find out how successful the class is at predicting when 30 seconds has passed. Once the data is recorded students should begin to graph their findings to make comparisons.

Electoral College:

Students are given a context and a dotplot and are asked a number of questions regarding shape, center, and spread of the data.

Buttons: Statistical Questions:

Students are given a context and a series of questions and are asked to identify whether each question is statistical and to provide their reasoning. Students are asked to compose an original statistical question for the given context.

Puppy Weights:

Using the information provided, create an appropriate graphical display and answer the questions regarding shape, center and variability.

## Teaching Ideas

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

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

Drops on a Penny (Box-and-Whiskers Graph):

Students collect data, compute measures of central tendency, and create stem-and-leaf plots and box-and-whiskers plots.

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

Whole Lotta Shakin' Goin' On: Busy Stretch for Large Earthquakes:

This article is intended to support reading in the content area. The text investigates whether the number of large magnitude earthquakes has significantly increased. The article explores the challenge of trying to determine why the amount and intensity of earthquakes can vary across time. The text also briefly explores the recent rise in man-made earthquakes.

Type: Text Resource

## Tutorials

Shapes of Distributions:

In this video, you will practice describing the shape of distributions as skewed left, skewed right, or symmetrical.

Type: Tutorial

Statistics Introduction: Mean, Median, and Mode:

The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.

Type: Tutorial

Statistical Questions:

Discover what makes a question a "statistical question."

Type: Tutorial

## Virtual Manipulatives

Box Plotter:

Users select a data set or enter their own data to generate a box plot.

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

## Worksheet

Splash of Math - SeaWorld Classroom Activity:

This resource allows students to assume the role of an ethologist provide 4 activities that challenge students to apply mathematics to solve complex real-life problems:

• Activity A: Watch the Whales - Determine average speed, distance, and percentage of time at the surface of gray whales.
• Activity B: Time Tally - From observations of a dolphin determine total time and percentage of time of certain behaviors.
• Activity C: Deep Divers - Determine average dive depth, diving time, and surface time of an elephant seal.
• Activity D: Breaches of the Humpback - Graph data and make a prediction from the graph. In this activity, the students will practice problem solving skills to solve complex real-life problems.

Type: Worksheet

## Student Resources

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

## Original Student Tutorials

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

Castles, Catapults and Data: Histograms Part 2:

Learn how to interpret histograms to analyze data, and help an inventor predict the range of a catapult in part 2 of this interactive tutorial series. More specifically, you'll learn to describe the shape and spread of data distributions.

Type: Original Student Tutorial

Learn how to calculate and interpret the Mean Absolute Deviation (MAD) of data sets in this travel-themed, interactive statistics tutorial.

Type: Original Student Tutorial

It Can Be a Zoo of Data!:

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

Type: Original Student Tutorial

Electoral College:

Students are given a context and a dotplot and are asked a number of questions regarding shape, center, and spread of the data.

Buttons: Statistical Questions:

Students are given a context and a series of questions and are asked to identify whether each question is statistical and to provide their reasoning. Students are asked to compose an original statistical question for the given context.

Puppy Weights:

Using the information provided, create an appropriate graphical display and answer the questions regarding shape, center and variability.

## Tutorials

Shapes of Distributions:

In this video, you will practice describing the shape of distributions as skewed left, skewed right, or symmetrical.

Type: Tutorial

Statistics Introduction: Mean, Median, and Mode:

The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.

Type: Tutorial

Statistical Questions:

Discover what makes a question a "statistical question."

Type: Tutorial

## Virtual Manipulatives

Box Plotter:

Users select a data set or enter their own data to generate a box plot.

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

## Parent Resources

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

Electoral College:

Students are given a context and a dotplot and are asked a number of questions regarding shape, center, and spread of the data.