Standard #: MAFS.6.SP.1.3 (Archived Standard)


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Recognize that a measure of center for 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.


General Information

Subject Area: Mathematics
Grade: 6
Domain-Subdomain: Statistics & Probability
Cluster: Develop understanding of statistical variability. (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
Content Complexity Rating: Level 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :
    Data sets in items must be numerical data sets.
    Calculator :

    No

    Context :

    Allowable



Sample Test Items (3)

Test Item # Question Difficulty Type
Sample Item 1 Tim drives the Grand Avenue bus route. The total number of people who ride the bus each week for 5 weeks is shown in the data table.

 

How many more people need to ride the bus in week 6 to increase the mean number of riders per week by 10?

N/A EE: Equation Editor
Sample Item 2 Linda recorded the number of minutes she practiced playing her violin for 10 days. The table shown represents the data she collected.

 

A. According to the data, what is the average amount of time Linda spent practicing per day?

B. What is Linda’s variation among all 10 days?

N/A EE: Equation Editor
Sample Item 3 Tim drives the Grand Avenue bus route. He records the total number of passengers each week for 4 weeks. The mean and mean absolute deviation of the data are shown.
  • Mean: 17,123
  • Mean absolute deviation: 611 
Select all the possible numbers of riders for week 5 that are within the mean absolute deviation.

 

N/A MS: Multiselect


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Related Resources

Formative Assessments

Name Description
Explain Measures of Variability

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

Explain Measures of Center

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

Compare Measures of Center and Variability

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

Lesson Plans

Name Description
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.

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 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.

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.

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.

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).

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.

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.
Flipping the house

After reading the market report for the real estate sales in Miami during the first quarter, students will decide which type of property they want to consider for investment that can be sold during the next year and still make a profit from the sale. In addition, students will determine the best location to make the investment. Luxury homes are selling faster this year, while there is not inventory for single families houses. The median prices for condos and apartments are lower, but the number of sales is going up. Students also consider price fluctuation between different locations.

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.

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.

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, learn a poem that will help them remember each term and take surveys to get real data sets.

Original Student Tutorials

Name Description
Moving MADness

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

Perspectives Video: Expert

Name Description
Mathematically Modeling Hurricanes

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

Problem-Solving Task

Name Description
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.

Teaching Ideas

Name Description
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.

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.
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.

Tutorial

Name Description
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.

Virtual Manipulative

Name Description
Box Plotter

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

Worksheet

Name Description
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.

Student Resources

Original Student Tutorials

Name Description
Moving MADness:

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

Tutorial

Name Description
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.

Virtual Manipulative

Name Description
Box Plotter:

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



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