Standard #: MAFS.912.S-ID.1.1 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



Represent data with plots on the real number line (dot plots, histograms, and box plots).


Remarks


In grades 6 – 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points.

General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Statistics & Probability: Interpreting Categorical & Quantitative Data
Cluster: 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.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :

    None

    Calculator :

    Neutral

    Clarification :
    Students will represent data using a dot plot, a histogram, or a box
    plot.
    Stimulus Attributes :
    Items should use real-world data and be set in a real-world context
    Response Attributes :
    Items may require the student to apply the basic modeling cycle.

    Items may require the student to choose an appropriate level of
    accuracy.

    Items may require the student to choose and interpret the scale in a
    graph.

    Items may require the student to choose and interpret units.



Sample Test Items (1)

Test Item # Question Difficulty Type
Sample Item 1

Max collected data on the height of each of his 20 classmates. The box plot shown represents his data.

Click above the number line to complete the dot plot that could also represent these data.

N/A GRID: Graphic Response Item Display


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Related Resources

Formative Assessments

Name Description
Winning Seasons

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

Trees in the Park

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

Flowering Trees

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

A Tomato Garden

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

Lesson Plans

Name Description
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.

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.

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.

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.

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.
Can You Walk in My Shoes?

Students use real-life data to create dot-plots and 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.

Exercise Your Brain, Analyze Your Heart Rate

Students will compile the data gathered from measuring their resting heart rates and heart rates after exercising into box plots. Using these displays, they will analyze the data's center, shape, and spread.

Which One: Box plot, Dot Plot, or Histogram?

Students will be asked to obtain data and create a human box plot, which will be analyzed and explained using statistical terms. Students will then understand the differences and advantages to using the box plot, histogram, and dot plot. Students will also practice selecting the most appropriate graphical representation for a set of data.

What's Your Tendency?

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.

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.

How long did you study?

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

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

Students will create different displays, line plots, histograms, and box plots from data collected about types of lollipops. The data will be analyzed and compared. Students will determine "Which lollipop takes the fewest number of licks to get to the center: a Tootsie Pop, a Blow Pop, or a Dum Dum?"

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.

Digging the Plots

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

A Walk Down the Lane

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

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.

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.

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).

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.

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.

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.

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.

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.

Exploring Box plots

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

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.

Burgers to Smoothies.

Students will create double box plots to compare nutritional data about popular food choices.

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.

Advantages and Disadvantages of Dot Plots, Histograms, and Box Plots

Students will compare the advantages and disadvantages of dot plots, histograms, and box plots. During this lesson, students will review the statistical process and learn the characteristics of a statistical question; whether it be numerical or categorical. Students will apply the information learned in a project that involves real-world issues and make an analysis based on the data collected.

Box Plots

An introduction lesson on creating and interpreting box plots.

Where Should I Go to College?

Students will create and use data displays to determine which college is the right fit for him or her / for hypothetical students. They will justify the data displays they selected, present this information to classmates and write an essay justifying their choice.

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.

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.
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.
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.

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.

Original Student Tutorials

Name Description
Movies Part 2: What’s the Spread?

Follow Jake along as he relates box plots with other plots and identifies possible outliers in real-world data from surveys of moviegoers' ages in part 2 in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Movies Part 1: What's the Spread?

Follow Jake as he displays real-world data by creating box plots showing the 5 number summary and compares the spread of the data from surveys of the ages of moviegoers in part 1 of this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Perspectives Video: Expert

Name Description
Histograms Show Trends in Fisheries Data Over Time

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

Perspectives Video: Professional/Enthusiast

Name Description
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.

Problem-Solving Tasks

Name Description
Speed Trap

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Haircut Costs

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Random Walk III

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

Professional Development

Name Description
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.

Teaching Ideas

Name Description
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.

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.

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.

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.

Unit/Lesson Sequence

Name Description
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 an introduction on the CMAP tool, please .

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

Virtual Manipulatives

Name Description
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.

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.
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.

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.

Student Resources

Original Student Tutorials

Name Description
Movies Part 2: What’s the Spread?:

Follow Jake along as he relates box plots with other plots and identifies possible outliers in real-world data from surveys of moviegoers' ages in part 2 in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Movies Part 1: What's the Spread?:

Follow Jake as he displays real-world data by creating box plots showing the 5 number summary and compares the spread of the data from surveys of the ages of moviegoers in part 1 of this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Problem-Solving Tasks

Name Description
Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Random Walk III:

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

Virtual Manipulatives

Name Description
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.

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.



Parent Resources

Problem-Solving Tasks

Name Description
Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Random Walk III:

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



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