Think Globally and Locally, Mathematically

Student Explorations in Mathematics, formerly known as Student Math Notes, is an official publication of the National Council of Teachers of Mathematics (NCTM) and is intended as a resource for grades 5-10 students, teachers, and teacher educators. Each issue develops a single mathematical theme or concept in such a way that fifth grade students can understand the first one or two pages and high school students will be challenged by the last page. The content and style of the notes are intended to interest students in the power and beauty of mathematics and to introduce teachers to some of the challenging areas of mathematics that are within the reach of their students.

The teacher version includes additional information on world poverty as well as instructional ideas to facilitate classroom discourse. The student guides are available for free download (see below) but the teacher’s guides are only available with NCTM membership.

In the following activities from the May 2011 and September 2011 issues of the magazine, students use histograms and make comparisons between different country groups, then create graphs that compare these differences in many ways and consider how each of these displays might be used. In part 2, students consider important information about world poverty by using measures of central tendency and box plots. Students analyze data and use a hands-on manipulative to interpret and understand box plots, including the connection between percentiles and quartiles.

Part 1: Hunger at Home and Abroad (May 2011)
World Poverty Data can be downloaded here.

Part 2: Poverty at Home and Abroad (September 2011)
World Poverty Data can be downloaded here.


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Linking Math to Real Problems

Why bother with statistics in middle school? One answer: data analysis is one of the NCTM Standards and an 8th grade Focal Point. But even more important, in my experience, is that statistics links math to real problems.

Working Hours: How Much Time Do Teens Spend on the Job?
This activity challenges students to interpret a bar graph, showing only percentages, to determine the mean number of hours teenagers work per week. A more complicated and interesting problem than it may seem at first glance!

Train Race
In this interactive game, students compute the mean, median, and range of the running times of four trains, then select the one train that will get to the destination on time. Their goal is to find the most reliable train for the trip.

The Global Sun Temperature Project
This web site allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students learn to collect, organize, and interpret data. You will find project information, lesson plans, and implementation assistance at the site.

Down the Drain: How Much Water Do You Use?
In this Internet-based collaborative project, your students share information about water usage with other students from around the country and the world. Based on data collected by their household members and their classmates, students will determine the average amount of water used by one person in a day. Students must develop a hypothesis, conduct an experiment, and present their results.

100 People: A World Portrait Detailed Statistics
You’ve heard the idea before: What if the whole world were represented by 100 people? It is mind-boggling, for example, to realize that 61 would be from Asia and only 5 from North America. This page gives a full list of the data collected, links to a lesson plan and to commentary on the statistics. Excellent for an interdisciplinary project!

If you’d like to focus attention on measures of central tendency, these last two sites help explain the mean and the median though interactive online practice.

Plop It!
Users click to easily and quickly build dot plots of data and view how the mean, median, and mode change as numbers are added to the plot. An efficient tool for viewing these statistics visually.

Comparing Properties of the Mean and the Median Through the Use of Technology
This interactive tool allows students to compare measures of central tendency. As students change one or more of the seven data points, the effects on the mean and median are immediately displayed. Questions challenge students to explore further the use of these measures of center; for example, What happens if you pull some of the data values way off to one extreme or the other extreme?

Join your colleagues in discussing these and other middle school issues at the Middle School Portal 2 (MSP2) social network. Hope to “see” you there!


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/29/2011.

What’s the Average?

Students often answer with the formula: “Add all the numbers together and divide, etc.” with no strong idea of what “average” means. Few adults, in fact, distinguish among the measures of central tendency: mean, median, and mode, but tend to lump them into a general idea of “what’s typical” of the data. Not a bad place to start, but insufficient for understanding the wealth of statistics that overwhelm us in today’s world.

The first activities here immerse students in working with mean, median, and mode both visually and interactively. They will be confronted constantly with the differences among the three concepts of average. The second set offers problems to challenge them to use these statistics in problem situations, such as finding how average temperature changes with distance from the equator.

If you have found a favorite way to help your students understand what “average” is, please share your idea by commenting to this blog post. Thanks!

Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how these statistics change (or, in some cases, how they don’t change).

Understanding Averages
Written for the student, this tutorial on mean, median, and mode includes fact sheets on the most basic concepts, plus practice sheets and a quiz. Key ideas are clearly defined at the student level through graphics as well as text.

Plop It!
Users click to easily and quickly build a bar graph and view how the mean, median, and mode change as entries are added to the graph. An efficient tool for viewing these statistics visually.

Comparing Properties of the Mean and the Median Through the Use of Technology
Seven points appear on a number line, 0 to 400. As students move one or more of these points along the line, the effects on the mean and median are immediately displayed. Questions challenge students to explore these measures of center; for example, What happens if you pull some of the data values way off to one extreme or the other?

Working hours: How much time do teens spend on the job?
This activity challenges students to interpret a bar graph (showing only percentages), to determine the mean number of hours teenagers work per week. A more complicated and interesting problem than it may seem at first glance! A full solution sets out the math in detail. Related questions ask students to calculate averages for additional data sets.

The Global Sun Temperature Project
This web site allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students learn to collect, organize, and interpret data. Classrooms can participate in the project each spring and each fall. You will find project information, lesson plans, and implementation assistance at the site.

Train Race
In this interactive game, students compute the mean, median, and range of the running times of four trains, then select the one train that will get to the destination on time. Players extend their basic understanding of these statistics as they try to find the most reliable train for the trip. Students can select one of three levels of difficulty. There are tips for students as well as a full explanation of the key instructional ideas underlying the game.


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/29/2011.