Collecting and Analyzing Real Data

Data collection and analysis can be an avenue into meaningful mathematics, science, and problem-solving skills needed by students in the twenty-first century. And an answer to the student question, Why do we have to study math? can be found when teaching mathematics with a real-world statistics approach. Below are digital teaching resources that demonstrate how data and statistics are a vital part of learning mathematics in a meaningful context. The resource activities are often interdisciplinary, which makes them time-consuming to prepare, as additional expertise is often needed. But the payoffs can be huge: student engagement, in-depth learning, and a real-world context for learning mathematics.

One approach is to look at situations in your community or larger world issues and have the students frame questions to investigate. Students may develop a passion for scientific inquiry when a topic can be analyzed with numbers. Requiring quality work and including a component about sharing results with the community will add value to an interdisciplinary contextual learning experience. Teachers may want to enlist a community person to provide additional expertise. Whether thinking small activity or big project, be ready to be surprised at what the data analysis reveals!

Analyzing Numeric and Geometric Patterns of Paper Pool
Look out, pool sharks! Begin the study of data and statistics with this super student exploration where data are collected and analyzed while students apply mathematical topics studied in grades 6 and 7: factors, multiples, rectangles, and the meaning of being relatively prime. In the Paper Pool applet, a ball is hit from the lower left-hand corner of a grid-lined pool table at a 45-degree angle. Students modify the size of the rectangular pool table and observe how the ball always travels on diagonals of the grid squares. After gathering and organizing data, students look for patterns to predict the corner pocket into which a ball will fall and the number of side hits the ball makes as it moves on the table to a corner pocket. The goal is to determine how the number of hits, final pocket, and number of squares crossed depend upon the relative lengths of the sides of the pool table. Sounds like fun, doesn’t it?

Junk Mail (a mini project)
No one is immune from receiving junk mail, but just how much of it is really finding its way to your address? In this simple activity, data collection and analysis are a key part of a project to learn about the importance of recycling. For one week, students count and record the number of pieces of junk mail received in their homes. The display and organization of the data can be modified to address the data and statistics topics the class is working on.

WWW—Wonderful Web Weather
Just how on-target are those weather forecasters we watch and listen to? In this webquest, students work in groups to track online weather reports for several locations over the course of three days and determine the accuracy of forecasts. Students develop an understanding of how weather can be described by measurable quantities, such as temperature, wind, and precipitation as they find and compare weather data found on the Internet, chart and graph data, and present their conclusions about forecasting. This straight-forward activity is suitable for students who are just beginning their work with data and statistics.

The Global Sun Temperature Project
With this free online collaborative project, students measure the temperature and record the minutes of sunlight for one week. Data are collected on the web site, and average daily temperatures and amount of sunlight are compared. Students draw conclusions about how the distance from the equator influences temperature. If you like this collaborative project, be sure to check out Down the Drain: How Much Water Do You Use?, another collaborative data project from the Center for Innovation in Engineering and Science Education (CIESE).

The Gulf Stream Voyage
If ocean travel is your passion, this site offers a way to spend time at sea without ever leaving your classroom. Here is a science project that uses actual data to help students investigate the science and history of the Gulf Stream. Math students can greatly benefit from the opportunity to collect data and draw conclusions based on the data. In the lesson called Current Now, students use real-time data and satellite images to determine how the Gulf Stream moves in the course of a year. In another activity, students use data about water temperature obtained from ships and buoys to determine the course of the Gulf Stream.

Boil, Boil, Toil and Trouble: The International Boiling Point Project
Be part of an annual event: Enroll your class in this free Internet-based collaborative project. Students discover which factors–room temperature, elevation, volume of water, or heating device–have the greatest influence on boiling point. Students boil water, record their data, and send it via email to be included in the site’s database of results. Student activities focus on analyzing the compiled data to find answers to questions about how and why water boils.

Backyard Birding—Research Project
Birds are everywhere, and here are ideas for creating a data collection project. Work with a science teacher and, possibly, an industrial tech teacher to expand this multiweek activity into a cross-curricular project to help students see how data analysis can support an understanding of nature.

Population Growth
These nine online lesson/activities investigate population growth and its impacts. Students use archived census and demographic data from the U.S. Census Bureau to model population growth and examine how population change affects the environment. Teachers will want to carefully review this resource to choose the activities most appropriate for their students’ mathematics background. Linear, quadratic, and exponential functions are used in some lessons.
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 4/07/2012.

Ratios as Seen in Scale Factors

Ratio underpins so much mathematics in our real world that it deserves occasional return visits. These sites deal mainly with making and building and constructing; mathematically, they concentrate on scale factor, a topic chosen by NCTM as a Focal Point for Grade 7. The very last site is just for teachers who may want a refresher at the professional level on basic but essential concepts. Please let us know any of your favorite sites for exploration!

All About Ratios
Designed to introduce the concept of ratio at the most basic level, this activity could open the idea to younger middle school students. Each multiple-choice problem shows sets of colorful elements and asks students to choose the one that matches the given ratio. The activity is from the collection titled Mathematics Lessons that are Fun! Fun! Fun!

Statue of Liberty
This activity asks students to determine if the statue’s nose is out of proportion to her body size. It carefully describes the mathematics involved in determining proportion, then goes on to pose problems on  enlarging a picture, designing HO gauge model train layouts, and analyzing the size of characters in Gulliver’s Travels. The page features links to a solution hint, the solution, related math questions, and model building resources. Other ratio problems in the Figure This! Series include Tern Turn, Capture Re-Capture, Drip Drops, and Which Tastes Juicier?

Understanding Rational Numbers and Proportions
To work well with ratios, learners need a solid basis in the idea of rational number. This complete lesson includes three well-developed activities that investigate fractions, proportion, and unit rates—all through real-world problems students encounter at a bakery.

Scaling Away
For this one-period lesson, students bring to class either a cylinder or a rectangular prism, and their knowledge of how to find surface area and volume. They apply a scale factor to these dimensions and investigate how the scaled-up model has changed from the original. Activity sheets and overheads are included, as well as a complete step-by-step procedure and questions for class discussion.

Size and Scale
A more challenging and thorough activity on the physics of size and scale! The final product is a scale model of the Earth-moon system, but the main objective is understanding the relative sizes of bodies in our solar system and the problem of making a scale model of the entire solar system. The site contains a complete lesson plan, including motivating questions for discussion and extension problems.

Golden Rectangle (grades 6-8)
This virtual manipulative can help students visualize the golden rectangle. It shows how a golden rectangle is generated by using the golden ratio (the ratio of the longer side to the shorter side of a golden rectangle) to create smaller and smaller golden rectangles within an initial rectangle. Instructions for using this online manipulative are included on the site.

Similarity
In this workshop session, elementary and middle school teachers explore scale drawing, similar triangles, and trigonometry in terms of ratios and proportion. Besides explanations and real-world problems, the unit includes video segments that show teachers investigating problems of similarity. To understand the ratios that underlie trigonometry, participants use an interactive activity provided online. This is session 8 of Learning Math: Geometry, a free online course.


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 12/09/2011.

Geoboard Geometry

Sometimes geoboards are left on the shelf because we don’t know what to do with them. They can be powerful tools for students to study, length, area and perimeter. (But remember to be careful with the perimeter part because the length of one unit is only measured on the horizontal or vertical, not the diagonal.) Geoboards can help students experience area so that they can develop area formulas for themselves.

Geoboards in the Classroom
This unit deals with the length and area of two-dimensional geometric figures using the geoboard as a pedagogical device. Five lesson plans are provided.

The Online Geoboard
An applet simulates the use of an actual geoboard without the usual limitations of working with rubber bands. Most materials designed for real geoboards may be used with this online version.

Rectangle: Area, Perimeter, Length, and Width
This applet features an interactive grid for forming rectangles. The student can form a rectangle and then examine the relationships among perimeter, area, and the dimensions of the rectangle as the rectangle dimensions are varied.

Investigating the Concept of Triangle and the Properties of Polygons: Making Triangles
These activities use interactive geoboards to help students identify simple geometric shapes, describe their properties, and develop spatial sense.

National Library of Virtual Manipulatives: Geometry (Grades 6—8)
This site has a number of virtual manipulatives related to the NCTM geometry standards.


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 12/07/2011.