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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.

Standard 2 : Summarize and describe distributions. (Additional Cluster)Archived
Cluster Standards

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.6.SP.2.4 : Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  • MAFS.6.SP.2.5 : Summarize numerical data sets in relation to their context, such as by:
    1. Reporting the number of observations.
    2. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
    3. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
    4. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Cluster Information
Number:
MAFS.6.SP.2
Title:
Summarize and describe distributions. (Additional Cluster)
Type:
Cluster
Subject:
Mathematics - Archived
Grade:
6
Domain-Subdomain
Statistics & Probability
Cluster Access Points

This cluster includes the following Access Points.

Cluster Resources

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

Original Student Tutorials
  • 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.

    Click HERE to open part 1.

  • Castles, Catapults and Data: Histograms Part 1: Learn how to create a histogram to display continuous data from projectiles launched by a catapult in this interactive tutorial.

    This is part 1 in a 2-part series. Click HERE to open part 2.

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

  • It's Raining....Cats and Dogs: Learn how to make and interpret boxplots in this pet-themed, interactive tutorial.

Formative Assessments
  • Shark Attack Data: Students are asked to construct a box plot corresponding to a given set of data.

  • Quiz Mean and Deviation: Students are asked to calculate measures of center and variability, identify outliers, and interpret the meaning of each in context.

  • Florida Lakes: Students are given a histogram and are asked to describe the variable under investigation and the number of observations.

  • Chores Data: Students are asked to display numerical data on a dot plot.

  • Basketball Histogram: Students are asked to construct a histogram corresponding to a given set of data.

  • Select the Better Measure: Students are asked to select the better measure of center and variability to describe each of two distributions of data.

  • Analyzing Physical Activity: Students are asked to calculate measures of center and variability, identify extreme values, and interpret the meaning of each in context.

Lesson Plans
  • Voter Task Force: Students will help the Supervisor of Elections determine which voter registration locations could be improved to help more citizens get registered to vote. Students will learn about the number of citizens who registered to vote in a general election year compared to the total population of those eligible to vote. They will discuss which voter registration locations will provide the most access to citizens and allocate funds to help address the issue in this modeling eliciting activity.

    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 to learn more about MEAs and how they can transform your classroom.

     

  • 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.

  • 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.

  • 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.

  • 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.

  • Sea Ice Analysis Grade 6: 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.

  • 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.

  • 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.

  • Cool Special Effects: In this MEA, students will apply the concepts of heat transfer, especially convection. Students will analyze factors such as temperature that affect the behavior of fluids as they form convection currents.

    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 to learn more about MEAs and how they can transform your classroom.

  • 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.

  • 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.

  • Preventing Lake Erosion: How can you save your house on the lake? This is a three-day activity that will reinforce science skills, math skills, and technology skills by taking the students through the design process to create a solution to the real-world problem of lake erosion.

  • Crash Test Dummies: Students will investigate inertia and Newton's laws of motion by completing an engineering challenge. Students will first investigate how mass affects the inertia of a person riding in a car that comes to a sudden stop. After analyzing the data and discussing the results, students will be asked to design a seat belt that will keep their clay person in the car without sustaining an "injury."

  • The Penny Lab: Students will design an investigation to collect and analyze data, determine results, write a justification and make a presentation using U.S. pennies.

    Paired student teams will determine the mass of 50 U.S. pennies. Students will also collect other data from each penny such as minted year and observable appearance. Students will be expected to organize/represent their data into tables, histograms and other informational structures appropriate for reporting all data for each penny. Students will be expected to consider the data, determine trends, and research information in order to make a claim that explains trends in data from minted U.S. pennies.

    Hopefully, student data reports will support the knowledge that the metallic composition of the penny has changed over the years. Different compositions can have significantly different masses. A sufficiently random selection of hundreds of pennies across the class should allow the students to discover trends in the data to suggest the years in which the composition changed.

  • 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.

  • 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.

  • 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.

  • Fun with Surveys: An Activity with Number Sets: In this activity, students will circulate around the classroom obtaining data from fellow classmates.  Students will pick their own question that will produce numerical responses.  Students will hypothesize the mean, median, and mode, calculate the measures, and identify which measure most accurately represents the data.

  • Lucky Number Seven: In "Lucky Number Seven", students will have fun generating individual data in this lesson introducing the creation of histograms. Working in pairs, students will roll number cubes, find the sum of each roll, and complete a chart. Through guided practice, students will learn how to organize the charted data and create a histogram. Supplemental independent practice is provided along with suggestions for formative and summative assessment.

  • Hista what, hista who: Students begin by creating a Venn diagram to compare/contrast bar graphs and histograms. Throughout the lesson students will be exploring histograms given real world data. Students will be asked to create and analyze the data by creating a histogram and answering real world context questions.

  • Archery and Box Plots: This is a two day lesson of activities in which students represent data with box plots and then draw conclusions based on the graphical representation. The lesson begins with an interactive activity using archery skill card ratings and organizing themselves based on this information. This lesson includes group work, homework, and a summative assessment

  • Got Homework?: Students will gather data to create dot plots, box plots, and histograms. They will examine each type of graph and compare the different representations.

  • Dot Plots and Histograms: In this lesson students will be exploring numeric displays including dot plots and histogram. Please note that this lesson does not cover box plots which is also part of this standard. Students will sort data into which type of display would be used between dot plots and histograms. Students will fill in guided (skeleton) notes about both types of display. Then students will create a dot plot with stickers and a histogram with painters tape. These hands on activities are used to solidify understanding of the qualities of each display. There is also independent practice and a performance task assessment for students to complete to practice and show mastery of creating numeric displays (dot plots and histograms).

  • My Pet is Better than Yours: Students will work with the number line to create dot plots. Beginning with a simple warm-up worksheet, students activate prior knowledge (apk) regarding data collection, frequency chart and calculating mean, median and mode.

    Students will collect data, create a dot plot, and interpret the results with teacher guidance, peers, and independently. The lesson concludes with a summative assessment.

  • Swish and Spit Box Plots: In this lesson, students are working as researchers for the Swish and Spit Company to create single serve mouthwash containers for travel. Students will create box plots from data sets of lip length and how much liquid can be held comfortably in human mouths. Students will analyze their graphs to answer questions regarding the size of the mouthwash container and how mouthwash it should hold. This activity should be used as a follow-up activity after students have a base knowledge of box plots.

  • What's Your Favorite?: This lesson is designed to provide students with an opportunity to develop three different data displays from the same set of numerical data. A power point is included to help teachers plan the lesson. Enter and Exit tickets are included.

  • Stats Rock: Using Pet Rocks to Find the Mean, Median and Interquartile Range (IQR): Using pet rocks, the students will determine the mean, median and interquartile range (IQR) of the weights of the rocks. A PowerPoint presentation and YouTube videos will introduce and reinforce the concepts of mean, median, and interquartile range (IQR).

  • Dot plot and Box plots: In this lesson the students will construct graphs from a data set. They will find the mean, median, mode, and range from a data set and a graph the have generated. The students also will also use their ages in months to build a box plot using the data from all the students.

  • The Best Things About Quantitative Measures: Given quantitative measures students will be able to find the all the quantitative measures.

  • Basketball All Star Team: In this Model Eliciting Activity, MEA, students will create a procedure for ranking high school basketball players. Students are given statistics for each player and are asked to recommend the best player to play for an all-star team after determining the free throw, three-point, and field goal percentages. Students write about the procedure used to make their decisions. In a twist, students are given additional data to determine the mean points per game.

    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 process. 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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

  • Speedster: In this activity, students will collect data to compare their reaction time for catching a falling object or to an online stimulus to that of their classmates. Students will collect data for their class, construct a graph to represent the data, and then answer the question, "How good are my reactions compared to other students?"
  • 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.
  • Box Plots are Easy!!: This lesson is a hands-on activity that introduces students to the concepts of number summaries, interquartile ranges and box plots. For a given set of data, students will be able to create a two number summary, three number summary, five number summary and box plot. This lesson will span two or three class periods dependant upon the discretion and pacing of the teacher.

  • Analyzing Data with Bell Curves and Measures of Center: In this lesson, students learn about data sets and will be able to tell if a bell curve represents a normal distribution and explain why a distribution might be skewed. Students will form their own bell curve calculate measures of center and variability based on their data and discuss their findings with the class.

  • 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.

  • Plotting Our Scores: In this lesson students will create two box plots on the same number line and interpret the data. Students will also be shown a double box plot and asked to write questions about the data.

  • 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.

  • 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.

  • Be the Statistician: Students will utilize their knowledge of data and statistics to create a question, collect numerical data, and create a display of their data driven by its quantitative measures of center and variability; mean, median, mode, and range.

  • The Survey Says...: Students will work in groups to conduct class surveys, using the results of the survey to calculate various measures of central tendency.

  • Punkin Chunkin - An Engineering Design Challenge: This Engineering Design Challenge is intended to help students apply the concepts of the transfer of potential and kinetic energy. It is not intended as an initial introduction to this benchmark.

  • Exploring Central Tendency: Students will review measures of central tendency and practice selecting the best measure with real-world categorical data. This relatable scenario about ranking the characteristics considered when purchasing a pair of sneakers, is used to finally answer the age-old question of "When will I ever use this?".

  • Closest to the Pin!: Students will create and analyze real world data while representing the data visually and comparing to a larger sample size.

  • Candy Colors: Figuring the Mean, Median & Mode: In this lesson, students will count candy of different colors and use the data to calculate the mean, median, and mode. Groups of students will work together to share their data and calculate the measures of central tendency again. At the end of the lesson, they will apply their learning to another data collection.

  • Hot, Hot, Hot! Earth Heating Up: Students will explore the concept of the uneven heating of Earth's surfaces by the Sun by collecting and analyzing data. Outside the classroom, students from several classes will record data points to be analyzed collectively to explore rates of heating related to time and material properties for air, water, and soil. Students will use mathematical techniques to help answer scientific questions.

Perspectives Video: Expert
Perspectives Video: Professional/Enthusiasts
Problem-Solving Tasks
  • 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.

  • Don’t Spill the Beans!: The purpose of this task is for students to make a hypothesis, and then doing an experiment to test each students hypothesis. Students will collect and record their data, use graphical methods to describe their data, and finally analyze and interpret their results in the context of the activity.

  • 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.

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

Student Center Activity
  • Edcite: Mathematics Grade 6: Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Teaching Ideas
  • 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.
  • 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.
Text Resource
  • Hitting Streaks Spread Success: This informational text resource is intended to support reading in the content area. Although scientists haven't determined a specific reason why one baseball player's hitting streak improves his whole team's performance, they have observed a very real mathematical pattern. There may be many reasons for the phenomenon, but no one has found them out yet.

Tutorials
Video/Audio/Animations
  • Median and Range Puzzle: Try these interesting median and range challenge problems!

  • Soybean growth rate response to touch: A time-lapse video showing differential growth rates for touch-treated seedlings and control seedlings. This would be appropriate for lessons about plant growth responses to environmental stress and graphing growth rate. Plants were grown in a vermiculite soilless medium with calcium-enhanced water. No other minerals or nutrients were used. Plants were grown in a dark room with specially-filtered green light. The plants did not grow by cellular reproduction but only by expansion of existing cells in the hypocotyl region below the 'hook'.
    Video contains three plants in total. The first two plants to emerge from the vermiculite medium are the control (right) and treatment (left) plants. A third plant emerges in front of these two but is removed at the time of treatment and is not relevant except to help indicate when treatment was applied (watch for when it disappears). When that plant disappears, the slowed growth rate of the treatment plant is apparent.
    Treatment included a gentle flexing of the hypocotyl region of the treatment seedling for approximately 5 seconds. A rubber glove was used at this time to avoid an contamination of the plant tissue.
    Some video players allow users to 'scrub' the playback back and forth. This would help teachers or students isolate particular times (as indicated by the watch) and particular measurements (as indicated by the cm scale). A graph could be constructed by first creating a data table and then plotting the data points from the table. Multiple measurements from the video could be taken to create an accurate graph of the plants' growth rates (treatment vs control).
    Instructions for graphing usage:
    The scale in the video is in centimeters (one cm increments). Students could observe the initial time on the watch in the video and use that observation to represent time (t) = 0. For that value, a mark could be made to indicate the height of the seedlings. As they advance and pause the video repeatedly, the students would mark the time (+2.5 hours for example) and mark the related seedling heights. It is not necessary to advance the video at any regular interval but is necessary to mark the time and related heights as accurately as possible. Students may use different time values and would thus have different data sets but should find that their graphs are very similar. (Good opportunity to collect data from real research and create their own data sets) It is advised that the students collect multiple data points around the time where the seedling growth slows in response to touch to more accurately collect information around that growth rate slowing event. The resulting graph should have an initial growth rate slope, a flatter slope after stress treatment, and a return to approximately the same slope as seen pre-treatment. More data points should yield a more thorough view of this. This would be a good point to discuss. Students can use some of their data points to calculate approximate pre-treatment, immediate post-treatment, and late post-treatment slopes for both the control and treatment seedlings.
    This video was created by the submitter and is original content.
    Full screen playback should be an option for most video players. Video quality may appear degraded with a larger image but this may aid viewing the watch and scale for data collection.

Virtual Manipulatives
  • 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.

  • Advanced Data Grapher: This is an online graphing utility that can be used to create box plots, bubble graphs, scatterplots, histograms, and stem-and-leaf plots.

  • Box Plotter: Users select a data set or enter their own data to generate a box plot.

  • 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.

  • 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.

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.