- Subject:
- Mathematics
- Material Type:
- Full Course
- Provider:
- Pearson
- Date Added:
- 11/02/2020

# 28 Results

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.

- Subject:
- Mathematics
- Statistics and Probability
- Provider:
- Pearson

Groups begin presentations for their unit project. Students provide constructive feedback on others' presentations.Key ConceptsThe unit project serves as the final assessment. Students should demonstrate their understanding of unit concepts:Measures of center (mean, median, mode) and spread (MAD, range, interquartile range)The five-number summary and its relationship to box plotsRelationship between data sets and line plots, box plots, and histogramsAdvantages and disadvantages of portraying data in line plots, box plots, and histogramsGoals and Learning ObjectivesPresent projects and demonstrate an understanding of the unit concepts.Provide feedback for others' presentations.Review the concepts from the unit.

- Subject:
- Statistics and Probability
- Material Type:
- Lesson Plan
- Author:
- Pearson
- Date Added:
- 11/02/2020

Remaining groups present their unit projects. Students discuss teacher and peer feedback.Key ConceptsThe unit project serves as the final assessment. Students should demonstrate their understanding of unit concepts:Measures of center (mean, median, mode) and spread (MAD, range, interquartile range)The five-number summary and its relationship to box plotsRelationship between data sets and line plots, box plots, and histogramsAdvantages and disadvantages of portraying data in line plots, box plots, and histogramsGoals and Learning ObjectivesPresent projects and demonstrate an understanding of the unit concepts.Provide feedback for others' presentations.Review the concepts from the unit.Review presentation feedback and reflect.

- Subject:
- Statistics and Probability
- Material Type:
- Lesson Plan
- Author:
- Pearson
- Date Added:
- 11/02/2020

In this lesson, students draw a line plot of a set of data and then find the mean of the data. This lesson also informally introduces the concepts of the median, or middle value, and the mode, or most common value. These terms will be formally defined in Lesson 6.Using a sample set of data, students review construction of a line plot. The mean as fair share is introduced as well as the algorithm for mean. Using the sample set of data, students determine the mean and informally describe the set of data, looking at measures of center and the shape of the data. Students also determine the middle 50% of the data.Key ConceptsThe mean is a measure of center and is one of the ways to determine what is typical for a set of data.The mean is often called the average. It is found by adding all values together and then dividing by the number of values.A line plot is a visual representation of the data. It can be used to find the mean by adjusting the data points to one value, such that the sum of the data does not change.Goals and Learning ObjectivesReview construction of a line plot.Introduce the concept of the mean as a measure of center.Use the fair-share method and standard algorithm to find the mean.

- Subject:
- Statistics and Probability
- Material Type:
- Lesson Plan
- Author:
- Pearson
- Date Added:
- 11/02/2020

Students analyze the data they have collected to answer their question for the unit project. They will also complete a short Self Check.Students are given class time to work on their projects. Students should use the time to analyze their data, finding the different measures and/or graphing their data. If necessary, students may choose to use the time to collect data. Students also complete a short pre-assessment (Self Check problem).Key ConceptsStudents will look at all of the tools that they have to analyze data. These include:Graphic representations: line plots, box plots, and histogramsMeasures of center and spread: mean, median, mode, range, and the five-number summaryStudents will use these tools to work on their project and to complete an assessment exercise.Goals and Learning ObjectivesComplete the project, or progress far enough to complete it outside of class.Review measures of center and spread and the three types of graphs explored in the unit.Check knowledge of box plots and measures of center and spread.

- Subject:
- Statistics and Probability
- Material Type:
- Lesson Plan
- Author:
- Pearson
- Date Added:
- 11/02/2020

In this lesson, students are given criteria about measures of center, and they must create line plots for data that meet the criteria. Students also explore the effect on the median and the mean when values are added to a data set.Students use a tool that shows a line plot where measures of center are shown. Students manipulate the graph and observe how the measures are affected. Students explore how well each measure describes the data and discover that the mean is affected more by extreme values than the mode or median. The mathematical definitions for measures of center and spread are formalized.Key ConceptsStudents use the Line Plot with Stats interactive to develop a greater understanding of the measures of center. Here are a few of the things students may discover:The mean and the median do not have to be data points.The mean is affected by extreme values, while the median is not.Adding values above the mean increases the mean. Adding values below the mean decreases the mean.You can add values above and below the mean without changing the mean, as long as those points are “balanced.”Adding values above the median may or may not increase the median. Adding values below the median may or may not decrease the median.Adding equal numbers of points above and below the median does not change the median.The measures of center can be related in any number of ways. For example, the mean can be greater than the median, the median can be greater than the mean, and the mode can be greater than or less than either of these measures.Note: In other courses, students will learn that a set of data may have more than one mode. That will not be the case in this lesson.Goals and Learning ObjectivesExplore how changing the data in a line plot affects the measures of center (mean, median).Understand that the mean is affected by outliers more than the median is.Create line plots that fit criteria for given measures of center.

- Subject:
- Statistics and Probability
- Material Type:
- Lesson Plan
- Author:
- Pearson
- Date Added:
- 11/02/2020

This resource is from Tools 4 NC Teachers. It provides additional resources to support teachers while teaching Grade 4, Cluster 1. This is remixable.

- Subject:
- Mathematics
- Material Type:
- Reading
- Reference Material
- Date Added:
- 07/09/2019

This lesson is from Tools 4 NC Teachers. Students will measure the distance of their feet and make a line plot of the numerical data.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/08/2019

This is from Tools 4 NC Teachers. Students will collect data, complete a table, graph their data, and answer questions about their data. This is remixable.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/08/2019

This lesson is from Tools 4 NC Teachers. Students will collect data, create a table, graph their data, and answer questions about their data. This is remixable.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/09/2019

This lesson is from Tools 4 NC Teachers. In this lesson, students will participate in the long jump to create a class set of data. Students will create a line plot and make discoveries about the data they record. This is remixable.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/09/2019

This lesson is from Tools 4 NC Teachers. In this lesson, students rotate through five measurement stations to collect numerical data. Following the data collection, students create a frequency table and a line plot to organize and display the data. This is remixable.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/09/2019

This lesson involves determining whether data is categorical or numerical. This lesson also addresses mathematical practice #1 and allows students to examine and correct errors.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/09/2019

This lesson is from Tools 4 NC Teachers. Students will collect data, create a table, graph their data, and answer questions about their data. This is remixable.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/09/2019

This lesson is from Tools 4 NC Teachers. Students organize a set of data about their favorite weekend activities and create a representation to display the data. This lesson allows the teacher to assess students’ prior understandings of graphical representations and introduce mathematical practice #4 – Model with mathematics. This is remixable.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/09/2019

This lesson is from Tools 4 NC Teachers. This lesson allows students to pose a question that yields numerical data, collect the data, and then represent the data on a line plot or bar graph. This is remixable.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Lesson Plan
- Date Added:
- 07/09/2019

This resource is from Tools 4 NC Teachers. It includes content and background information for teachers before teaching Grade 4, Cluster 1.

- Subject:
- Mathematics
- Material Type:
- Reference Material
- Date Added:
- 07/09/2019

These parent and family letters are from Tools 4 NC Teachers. They can be sent home at the beginning of Grade 4, Cluster 1. These are remixable.

- Subject:
- Mathematics
- Material Type:
- Reference Material
- Date Added:
- 07/09/2019

This task is from Tools 4 NC Teachers. Students collect data, represent the data in a frequency table and graph, then analyze and interpret the data. This task includes examples of student work to help anticipate student responses and to support teachers with assessment.

- Subject:
- Mathematics
- Material Type:
- Activity/Lab
- Formative Assessment
- Date Added:
- 07/09/2019