This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

The students will use ACC basketball statistics to practice the process of converting fractions to decimals then to percents and will learn how to create and edit a spreadsheet. They will then use this spreadsheet to analyze their data. This unit is done during the basketball season which takes approximately 15 weeks from the middle of November to the middle of March. Teachers must have Clarisworks to open the sample spreadsheet in the lesson, but may recreate it in another spreadsheet program.

Students randomly select jelly beans (or other candy) that represent genes for several human traits such as tongue-rolling ability and eye color. Then, working in pairs (preferably of mixed gender), students randomly choose new pairs of jelly beans from those corresponding to their own genotypes. The new pairs are placed on toothpicks to represent the chromosomes of the couple's offspring. Finally, students compare genotypes and phenotypes of parents and offspring for all the "couples" in the class. In particular, they look to see if there are cases where parents and offspring share the exact same genotype and/or phenotype, and consider how the results would differ if they repeated the simulation using more than four traits.

Students collect data to answer questions about a typical sixth grade student. Students collect data about themselves, working in pairs to measure height, arm span, etc. Students discuss characteristics they would like to know about sixth grade students, adding these topics to a preset list. Data are collected and organized such that there is a class data set for each topic for future use. Students are asked to think about how this data could be represented and organized.Key ConceptsFor data to be useful, it must be collected in a consistent and accurate way. For example, for height data, students must agree on whether students should be measured with shoes on or off, and whether heights should be measured to the nearest inch, half inch, or centimeter.Goals and Learning ObjectivesGather data about sixth grade students.Consider how data are collected.

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.  Throughout the module, students see and represent data distributions using dot plots and histograms.  They study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution.  As the module ends, students synthesize what they have learned as they connect the graphical, verbal, and numerical summaries to each other within situational contexts, culminating with a major project.

Statistics is the study of variability. Students who understand statistics need to be able to identify and pose questions that can be answered by data that vary. 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.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Which of the following are statistical questions? (A statistical question is one that can be answered by collecting data and where there will be variab...

Distributions and Variability

Type of Unit: Project

Prior Knowledge

Students should be able to:

Represent and interpret data using a line plot.
Understand other visual representations of data.

Lesson Flow

Students begin the unit by discussing what constitutes a statistical question. In order to answer statistical questions, data must be gathered in a consistent and accurate manner and then analyzed using appropriate tools.

Students learn different tools for analyzing data, including:

Measures of center: mean (average), median, mode
Measures of spread: mean absolute deviation, lower and upper extremes, lower and upper quartile, interquartile range
Visual representations: line plot, box plot, histogram

These tools are compared and contrasted to better understand the benefits and limitations of each. Analyzing different data sets using these tools will develop an understanding for which ones are the most appropriate to interpret the given data.

To demonstrate their understanding of the concepts, students will work on a project for the duration of the unit. The project will involve identifying an appropriate statistical question, collecting data, analyzing data, and presenting the results. It will serve as the final assessment.

Students write statistical questions that can be used to find information about a typical sixth grade student. Then, the class works together to informally plan how to find the typical arm span of a student in their class.Key ConceptsStatistical thinking, in large part, must deal with variability; statistical problem solving and decision making depend on understanding, explaining, and quantifying the variability in the data.“How tall is a sixth grader?” is a statistical question because all sixth graders are not the same height—there is variability.Goals and Learning ObjectivesUnderstand what a statistical question is.Realize there is variability in data and understand why.Describe informally the range, median, and mode of a set of data.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.