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Math, Grade 6, Unit 8, Lesson 15
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Gallery Create A Data Set: Students will create data sets with a ...

Gallery

Create A Data Set: Students will create data sets with a specified mean, median, range, and number of data values.
Bouncing Ball Experiment How high does the class think a typical ball bounces (compared to its drop height) on its first bounce? Students will conduct an experiment to find out.
Adding New Data to a Data Set Given a data set, students will explore how the mean changes as they add data values.
Bowling Scores Students will create bowling score data sets that meet certain criteria with regard to measures of center.
Mean Number of Fillings Ten people sit in a dentist's waiting room. The mean number of fillings they have in their teeth is 4, yet none of them actually have 4 fillings. Students will explain how this situation is possible.
Forestland Students will examine and interpret box plots that show the percentage of forestland in 20 European countries.
What's My Data? Students will create a data set that fits a given histogram and then adjust the data set to fit additional criteria.
What's My Data 2? Students will create a data set that fits a given box plot and then adjust the data set to fit additional criteria.
Compare Graphs Students will make a box plot and a histogram that are based on a given line plot and then compare the three graphs to decide which one best represents the data.
Random Numbers What would a data set of randomly generated numbers look like when represented on a histogram? Students will find out!
No Telephone? The U.S. Census Bureau provides state-by-state data about the number of households that do not have telephones. Students will examine two box plots that show census data from 1960 and 1990 and compare and analyze the data.
Who is Taller? Who is taller—the boys in the class or the girls in the class? Students will find out by separating the class height data gathered earlier into data for boys and data for girls.

Subject:
Statistics and Probability
Provider:
Pearson
Math, Grade 6, Unit 8, Lesson 16
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Groups begin presentations for their unit project. Students provide constructive feedback on ...

Groups begin presentations for their unit project. Students provide constructive feedback on others' presentations.

Key Concepts

The 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 plots
Relationship between data sets and line plots, box plots, and histograms
Advantages and disadvantages of portraying data in line plots, box plots, and histograms

Goals and Learning Objectives

Present projects and demonstrate an understanding of the unit concepts.
Provide feedback for others' presentations.
Review the concepts from the unit.

Subject:
Statistics and Probability
Provider:
Pearson
Math, Grade 6, Unit 8, Lesson 17
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Remaining groups present their unit projects. Students discuss teacher and peer feedback. ...

Remaining groups present their unit projects. Students discuss teacher and peer feedback.

Key Concepts

The 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 plots
Relationship between data sets and line plots, box plots, and histograms
Advantages and disadvantages of portraying data in line plots, box plots, and histograms

Goals and Learning Objectives

Present 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
Provider:
Pearson
Algebra I Module 2: Descriptive Statistics
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In this module, students reconnect with and deepen their understanding of statistics ...

In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

Subject:
Statistics and Probability
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Statistical Methods in Brain and Cognitive Science, Spring 2004
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Descriptive and inferential statistics for the behavioral and neurological sciences are considered. ...

Descriptive and inferential statistics for the behavioral and neurological sciences are considered. Techniques such as t-tests, factorial analysis of (co)variance, correlation, multiple regression, and nonparametric tests are introduced. Subject provides an introductory overview of some advanced methods such as path analysis, factor analysis, discriminant analysis, and analysis of functional MRI data. Basic issues of research design and methodology intimately associated with data analysis are discussed.

Subject:
Statistics and Probability
Psychology
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Rosenholtz, Ruth
Math, Grade 6, Unit 8, Lesson 4
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In this lesson, students draw a line plot of a set of ...

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 Concepts

The 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 Objectives

Review 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
Provider:
Pearson
Math, Grade 6, Unit 8, Lesson 7
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Students will apply what they have learned in previous lessons to analyze ...

Students will apply what they have learned in previous lessons to analyze and draw conclusions about a set of data. They will also justify their thinking based on what they know about the measures (e.g., I know the mean is a good number to use to describe what is typical because the range is narrow and so the MAD is low.).

Students analyze one of the data sets about the characteristics of sixth grade students that was collected by the class in Lesson 2. Students construct line plots and calculate measures of center and spread in order to further their understanding of the characteristics of a typical sixth grade student.

Key Concepts

No new mathematical ideas are introduced in this lesson. Instead, students apply the skills they have acquired in previous lessons to analyze a data set for one attribute of a sixth grade student. Students make a line plot of the data and find the mean, median, range, MAD, and outliers. They use these results to determine a typical value for their data.

Goals and Learning Objectives

Describe an attribute of a typical sixth grade student using line plots and measures of center (mean and median) and spread (range and MAD).
Justify thinking about which measures are good descriptors of the data set.

Subject:
Statistics and Probability
Provider:
Pearson
Math, Grade 6, Unit 8, Lesson 6
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In this lesson, students are given criteria about measures of center, and ...

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 Concepts

Students 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 Objectives

Explore 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
Provider:
Pearson
Math, Grade 6, Unit 8
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Distributions and Variability Type of Unit: Project Prior Knowledge Students should be ...

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
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Aluminum Cans
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In this data analysis activity students investigate data in connection with recyclable ...

In this data analysis activity students investigate data in connection with recyclable materials and develop plans to help the environment. Students collect data about aluminum can usage and graph that data in a line plot. The lesson includes student worksheet and extension suggestions.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
An Average Autumn
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This lesson will be a review of skills for calculating mean, mode, ...

This lesson will be a review of skills for calculating mean, mode, median, and range of a set of numbers to be created by the students. It will result in a seasonal display for the classroom or school-wide bulletin board.

Material Type:
Lesson Plan
Provider:
University of North Carolina at Chapel Hill School of Education
Provider Set:
LEARN NC Lesson Plans
Author:
Scott Counce
Bears in a Boat
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In this math activity, learners are challenged to create aluminum foil boats ...

In this math activity, learners are challenged to create aluminum foil boats that will hold plastic bears until the boats sink. The lesson serves as a fun, hands-on way to collect data. Data from two attempts is collected and used to make two class box-and-whisker plots with some surprising results. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

Subject:
Mathematics
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Jim Rubillo
NCTM Illuminations
Thinkfinity/Verizon Foundation
Bubbling Plants
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Students learn a simple technique for quantifying the amount of photosynthesis that ...

Students learn a simple technique for quantifying the amount of photosynthesis that occurs in a given period of time, using a common water plant (Elodea). They can use this technique to compare the amounts of photosynthesis that occur under conditions of low and high light levels. Before they begin the experiment, however, students must come up with a well-worded hypothesis to be tested. After running the experiment, students pool their data to get a large sample size, determine the measures of central tendency of the class data, and then graph and interpret the results.

Subject:
Engineering
Material Type:
Activity/Lab
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering NGSS Aligned Resources
Author:
Mary R. Hebrank
Building Height
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Working in pairs, students create a clinometer and use isosceles right triangles ...

Working in pairs, students create a clinometer and use isosceles right triangles to find the height of a building. The class will compare measurements, discuss their results, and select the best measure of central tendency to report the most accurate height. All handouts and excellent class discussion questions are provided.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
The Celebrated Jumping Frog
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Using the story "The Celebrated Jumping Frog of Calaveras County" by Mark ...

Using the story "The Celebrated Jumping Frog of Calaveras County" by Mark Twain, learners simulate a jumping-frog contest and determine the distances "jumped." Learners record the distance of individual jumps in centimeters and determine the total distance jumped (the sum of the three separate jumps) and the official distance (the straight-line distance from the starting line to the end of the frog's third jump). Learners compare the range and median of the total distances with those of the official distances of the group.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
National Council of Teachers of Mathematics
NCTM Illuminations
Thinkfinity/Verizon Foundation
Collaborative Statistics: Custom Version modified by R. Bloom
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Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members ...

Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. This custom textbook collection has been modified by R. Bloom for her classes at De Anza College; the homework content for the custom collection is now contained in a separate homework collection.

Subject:
Statistics and Probability
Material Type:
Full Course
Reading
Provider:
Rice University
Provider Set:
Connexions
Author:
Roberta Bloom