 Mathematics Grade 6

Strand: STATISTICS AND PROBABILITY (6.SP)

Develop understanding of statistical variability of data (Standards 6.SP.1�3). Summarize and describe distributions (Standards 6.SP.4�5).
• Average Number of Siblings
The goal of this task is to compare the mean and median in a context where the data is slightly skewed to the right.
• Box Plot and Five Number Summaries
An understanding of the terms minimum, maximum, median, and quartiles is the focus of this lesson. Students first use the interactive to compare different representations, then learn how to create a visual representation of data. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Box Plots
By completing this lesson students will understand the concept of median, quartiles, and how to build a box plot.
• Buttons: statistical questions
The purpose of this task is to provide questions related to a particular context (a jar of buttons) so that students can identify which are statistical questions. The task also provides students with an opportunity to write a statistical question that pertains to the context.
• Chapter 4 - Mathematical Foundations (UMSMP)
This is Chapter 4 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Fluency.
• Chapter 4 - Student Workbook (UMSMP)
This is Chapter 4 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Statistics.
• Comparative Experimental Design
This Annenberg Learner's Learning Math interactive teaches students the difference between the design of comparative observational studies and comparative experimental studies. Students then design their own study in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Comparing A Stem and Leaf Plot, Histogram, and Frequency Table
This lesson is all about the different ways to represent data. Students then practice creating various representations when given data. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Comparing Test Scores
The goal of this task is to critically compare the center and spread of two data sets.
• Data Analysis Using Mean, Median, Mode, and Range
There are 4 videos in this lesson helping students learn about mean, median, mode and range. The classroom activity consists of a game in which students make attempts to get a pom-pom into a can. They collect the data about attempts. then calculate the mean, median, mode and range. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Data Organization and Representation: Weather Forecasting
In this lesson's video students see how a meteorologist organizes weather data for a presentation on-air. Students are then given sets of recent weather data which they must analyze to find the center and variability. They then predict the next day's temperature based on those statistics. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Describing Distributions
In this task, students are asked to describe data distributions in terms of center, spread and overall shape and to also compare data distributions in terms of center and spread by selecting which of two distributions has a greater center and which has a greater spread.
• Describing Distributions: New Balance
Using the shoe company New Balance, this video takes a look at how the company uses statistical data to plan what to produce and sell. Students then discuss how data can be applied in real world situation. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Electoral College
This task is intended to demonstrate that a graph can summarize a distribution as well as provide useful information about specific observations. With the table provided, the graph and values have context. The purpose of this task is to help students understand that a distribution can be described in terms of shape and center, and also to provide practice in selecting and calculating measures of center.
• Examining California's Prison System: Real-World Ratio
Using an infographic students look at such factors as age, gender and race to examine how the prison population in California compares to the general population. Students then apply an understanding of how they can find the value of a part by using a whole and a percent in order to look at how that can lead to recommendations for how to prevent crime. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Gathering Data for a Line Plot
Two interactives are used in this lesson and both involve counting raisins in boxes and then plotting a graph. Students extend their understanding of mean, median, mode, and range after creating line plots in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Grade 6 Math Module 6: Statistics (EngageNY)
In this module, students move from simply representing data into analysis of data. Students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data. Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in Pre-K-Grade 12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes.
• Grade 6 Unit 6: Statistics (Georgia Standards)
In this unit students will: Analyze data from many different sources such as organized lists, box-plots, bar graphs, histograms and dot plots. Understand that responses to statistical questions may vary. Understand that data can be described by a single number. Determine quantitative measures of center (median and/or mean). Determine quantitative measures of variability (interquartile range and range).
• How Long Is a Minute?
This activity is designed to give students an understanding of arithmetic mean, median, and range of data sets. They practice using a virtual stopwatch in the interactive to estimate how long a minute is. They collect the data from repeat guesses and use that in the activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Identifying Statistical Questions
he purpose of this task is to help students learn to distinguish between statistical questions and questions that are not statistical.
• Is It Center or Is It Variability?
The purpose of this task is to challenge students to think about whether they should be most interested in the center of the data distribution or in the spread of a data distribution in order to answer a given statistical question.
• IXL Game: Statistics
This game is designed to help sixth graders understand how to calculate mean, median, mode, and range.
• Life Expectancy: Finding Ratio Relationships
This lesson using infographics examines how health factors such as obesity and hypertension have changed in the U.S. over the past decades. The classroom activity has students work with the mathematical concept of statistical analysis as they compare the life expectancy of men and women. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Line Plot Representation of Deviation from the Mean
The concepts of means and deviations are the focus of this interactive from Annenberg. Students manipulate dots on a line graph to experiments with deviation. The classroom activity helps them understand positive and negative deviation. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Make a Stem and Leaf Plot
Students use data values to create stem and leaf plots with this interactive. This is further explored in the classroom activity which also asks students to interpret data to answer a question. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Math Homework Problems
The goal of this task is to calculate and interpret the Mean Absolute Deviation in a context. It is intended to be an introductory task but can readily be adapted for a more in depth study.
• Math Task: The Missing Words
Math Task Overview: Students should be able to explain a reasonable strategy for determining the number of missing words. They should accurately compute the mean and range, and select an appropriate graph for displaying the data. Students will explore the concepts of variability and distribution of a data set.
• Mean or Median?
The goal of this task is to examine advantages and disadvantages of the mean and median for summarizing a given data set.
• Measuring Variability Through Tracking Wildfires
Data about wildfires in the U.S. is the basis of this lesson. Students examine the data about active fires as well as historical data and use that data to find changes across decades. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Pie Chart
Students enter values in this applet and create pie charts in which they can vary the number or size of sections and display as fractions or percentages.
• Prison Population: Real World Statistical Variability
Statistical data about changes in state and national prison populations from 1925 is the focus of this lesson. Students examine the data to make observations, find patterns and calculate the median and range. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Puppy Weights
Given the weights of puppies, the student is asked to draw a graph summarizing the varying weights, describe the distribution of the weights, and determine the typical weight of a puppy born in the location.
• Puzzle Times
This is a simple task designed to assess students ability to construct a dot plot and to calculate and compare measures of center.
• Real-World Data Sets: Low- and High-Paying Jobs
Infographics with data about the highest and lowest paying jobs in the U.S. is the basis of this lesson. Students examine the data to find the disparity between the high and low rates and create box plots to represent the data. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Recognize and Represent Proportional Relationships Between Quantities: Ratio, Proportion, Cross Mult
Four videos are included in this lesson explaining ratio, proportion and how to use the shortcut of cross multiply and divide. Students then play the game "Pom-Pom Nose Push" to collect data and determine the ratio of time to distance. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Responses to a Court Verdict: Analyzing Samples to Gain Understanding
The infographic basis of this activity pulls the Trayvon Martin case out of the headlines to examine the data collected from a poll about the case. The students need to analyze the responses to conclude whether the results fall along racial lines. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Spinner
By manipulating a spinner and its pointer students will learn about probability in this activity.
• Statistical Questions
The goal of this task is to promote a discussion of what makes a statistical question.
• Statistics and Probability (6.SP) - 6th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 6 - Statistics and Probability.
In this task, students analyze a survey to decide how many candy bars students typically eat in a week.
In this task, students must help Suzi figure out the annual salary bill for her company and check some statistics about rates of pay.
• Summarize Numerical Data Sets Using Venn Diagrams
The 3 videos in this lesson teach students about Venn diagrams: ones with 2 circles; those with 3 circles; and those with a circle within a circle. Students then apply their understanding to activities where they have to represent certain things, such as students' clothing colors, with a Venn diagram. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• The Bell Curve
This lesson and activity introduces the student to the concept of the Bell Curve and distribution.
• The Hunger Games
By analyzing the lottery system used in the novel Hunger Games students will learn about probability. Students then create their own lottery system based on criteria from the novel in the accompanying classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• The Median: Salary.com
By looking at the data on the website Salary.com students will understand the application of quartiles and percentiles to understand and compare salaries. In the activity students use data set about salaries to create box plots and look at pay differentials. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Using Graphs to Identify Patterns and Trends in US Immigrant Residency
Understanding where immigrants lived and how they moved is the focus of the info graphic used in this lesson. Students interpret the graph to understand the history of immigration in our country and look at patterns, trends and growth. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Variation About the Mean: The Boston Harbor Project
The use and statistical analysis of data in the efforts to improve the water quality in Boston Harbor is the subject of this video. Students then apply an understanding of mean absolute deviation to examine data. They also use data about bacteria found in a river in an analysis of what that data set tells. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort. http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen .

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.