The computer can be a distraction and a frustration, but it can also be a teaching tool. Usually, you hear that you should be using technology in your teaching, but no one gives an example of a site that works for middle school curriculum. Here are a few online resources that actually show the potential of the Internet as a teaching strategy.

The MegaPenny Project

This site shows arrangements of large quantities of U.S. pennies. It begins with only 16 pennies, which measure one inch when stacked and one foot when laid in a row. The visuals build to a thousand pennies and in progressive steps to a million and even a quintillion pennies! All pages have tables at the bottom listing the value of the pennies on the page, size of the pile, weight, and area (if laid flat). The site can be used to launch lessons on large numbers, volume versus area, or multiplication by a factor of 10.

Cynthia Lanius’ Fractal Unit
In this unit developed for middle school students, the lessons begin with a discussion of why we study fractals and then provide step-by-step explanations of how to make fractals, first by hand and then using Java applets—an excellent strategy! But the unit goes further; it actually explains the properties of fractals in terms that make sense to students and teachers alike.

The Pythagorean Theorem
[This site is temporarily unavailable – we are going to leave this link in place and continue to check back in case it revives – 6/26/2010]
This site invites learners to discover for themselves “an important relationship between the three sides of a right triangle.” Five interactive, visual exercises require students to delve deeper into the mystery; each exercise is a hint that motivates and entices. The tutorial ends with information on Pythagoras and problems that rely on the theorem for their solutions.

Fraction Sorter
A visual support to understanding the magnitude of fractions!  Using this applet, the student represents two to four fractions by dividing and shading areas of squares or circles and then ordering the fractions from smallest to largest on a number line. The applet even checks if a fraction is correctly modeled and keeps score. From Project Interactivate Activities.

Algebra Balance Scales — Negatives
This virtual balance scale offers students an experimental way to learn about solving linear equations involving negative numbers. The applet presents an equation for the student to illustrate by balancing the scale using blue blocks for positives and red balloons for negatives. The student then solves the equation while a record of the steps taken, written in algebraic terms, is shown on the screen. The exercise reinforces the idea that what is done to one side of an equation must be done to the other side to maintain balance. From the National Library of Virtual Manipulatives.

Geometric Solids
This tool allows learners to investigate various geometric solids and their properties. They can manipulate and color each shape to explore the number of faces, edges, and vertices, and to answer the following question: For any polyhedron, what is the relationship between the number of faces, vertices, and edges?  From Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics.

# Teaching With Trade Books – Math

As a middle school mathematics teacher, you probably feel like you don’t have enough time to teach all of your content within the course of a school year. Why on earth would you ever want to add more material in the form of trade books when you can’t seem to finish your assigned textbook? Turns out that making time to incorporate children’s literature in your classroom can led to rich results.

One of the most immediate benefits of using trade books is increasing student engagement. High quality trade books are written as to spark interest and create a desire to read. Many contain colorful, interesting illustrations, photographs, and diagrams, all of which draw students into the text and improve comprehension. Contrast this with the reaction that many students have toward the textbook: either a lack of interest or an assumption that the assigned reading will be too difficult.

Incorporating children’s literature also allows you to differentiate instruction and support English Language Learners and struggling readers in a way that textbooks cannot. If you visit the children’s section of your school or local library, you’ll discover a wealth of books for students on every reading level and topic. Using trade books which better match students’ abilities can help them build content knowledge and interact more successfully with the required text.

Of course, successful integration of children’s literature into your middle school mathematics class requires planning and forethought. Here are some tips for using trade books in your classroom. The following resources will guide you in finding exemplary trade books and lessons.

Mathematics and Children’s Literature
In three lessons from NCTM Illuminations, students participate in activities in which they focus on connections between mathematics and children’s literature. Three pieces of literature are used to teach geometry and measurement topics in the mathematics curriculum, from using and describing geometric figures to estimating volume of figures.

Lesson 1: Shapes and Poetry – Students read the poem “Shapes” from A Light in the Attic, by Shel Silverstein, and create their own illustration of the poem. In this lesson, students explore geometric figures and positional words.

Lesson 2: Estimating Volume by Counting on Frank – In this lesson, students read the book Counting on Frank. They use information in the book to make estimates involving volume. In particular, students explore the size of humpback whales.

Lesson 3: How Big Is a Foot? – In this lesson, students read the book How Big Is a Foot?, by Rolf Myller. They then create non-standard units (using their own footprints) and use them to make “beds.” As a result, students explore the need for a standard unit of measure.

One Grain of Rice
In this lesson, also from NCTM Illuminations, students take on the role of a villager in a third-world country trying to feed her village. While listening to the teacher read aloud the book One Grain of Rice by Demi, students work collaboratively to come up with a bargaining plan to trick the raja into feeding the village using algebra, exponential growth, and estimation.

Ohio Resource Center (ORC) Mathematics Bookshelf
The Mathematics Bookshelf features outstanding trade books that support mathematics instruction in K–12 classrooms. Mathematics Review Board members have selected books that will appeal to students and enrich the teaching and learning of mathematics. Each book review includes:

— a brief summary of the story
— the main mathematical ideas
— suggestions for how to use the book
— the value of the book in standards-based instruction
— standards alignment
— a list of related ORC resources

This print book helps teachers build on their students’ natural passion for knowledge as they engage in real-world mathematical problem solving. The lessons in this book use nonfiction as a springboard to explore mathematical concepts key to the middle school curriculum.

This print book by David Whitin and Sandra Wilde acquaints readers with some of the best children’s literature containing a mathematical subtext, including fiction, nonfiction, poetry, books of games and puzzles, books that reflect different cultures. The titles are diverse, but they all address a range of mathematical topics: place value, estimation, large numbers, geometry, measurement, fractions, classification, addition, subtraction, multiplication, and division.

It’s the Story that Counts
This print book, also by David Whitin and Sandra Wilde, explains ways books have been used to explore mathematical concepts, the importance of children’s spontaneous reactions, and the role of mathematical conversation. It also focuses on the books themselves, exploring multicultural themes and images in books, books on the number system, statistics, and probability.

This print book by Jennifer M. Bay-Williams and Sherri L. Martinie brings the joy of children’s literature to the middle-school math classroom. It contains lessons and ideas based on 30 children’s literature titles. Children explore mathematical concepts based on lessons derived from titles such as Harry Potter and the Sorcerer’s Stone and Holes.

Search for Literature
The California Department of Education has created this online literature search for science and mathematics with over 1,400 titles in the search database. The search includes the typical categories found in a search for literature at a library, such as author, title, and keyword. It also contains a customized search for selecting up to three categories that relate more specifically to education. Those categories include grade level, language, genre, classifications (types of books), curriculum connections, awards (by author or illustrator), science subject area, mathmatics subject area, science standards connections, and math standards connections (California state standards). Teachers will find useful a recommended list of literature for science and mathematics.

# 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!

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.

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.

# Around a Circle: Measuring a Geometric Figure

Your textbook has many, many problems on finding the measurements of a circle, so I looked for problems that are off the beaten track. The result is an unusual set of applications to the circle, therefore challenging but intriguing, I think, for middle school classes. Let your colleagues know of your own ideas  and comments on this topic. Just add a note below.

Discovering the Value of Pi
Students measure the diameter and circumference of several circles, using a handy applet, record their data and reach conclusions about the ratio of circumference to diameter. A genuine guided exploration!

Windshield Wipers: It’s Raining! Who Sees More? The Driver of the Car or the Truck?
In this activity, students compare the areas cleaned by different wiper designs. An animation shows the movement of the two windshield wipers, each cleaning off a different geometric shape on the window. Students are encouraged to draw the shape cleaned by each wiper and find its area.

The Great Circle
By clicking on two cities on a world globe, students see two line segments connecting the cities, one showing the great circle route (the shortest) and the other showing the route on a flat map. An interesting  and visual application of real-world math.

Three Piece Circle Puzzle
Students create the puzzle themselves, using compasses, and are challenged to find the area of each of the three pieces. You will need to guide your eighth- and ninth-grade students through the given solution.

# Math Students Collaborating Nationwide, Even Worldwide!

There are middle school projects that gain impact through collaboration with students outside your own classroom, such as estimating the average amount of water used per person per day. This problem takes on deeper relevance when averages are compared to those of classrooms around the country and the world. Other projects, such as finding the circumference of the Earth, require data input by geographically distant schools.

To connect with and collaborate with classrooms interested in the same project, you can make use of online sites, even though you work in an offline classroom. You need Internet access to register for the project (free registration!), to find suggested teaching procedures, and to submit and retrieve data from other schools. But you can be offline while teaching the lessons, collecting and analyzing data, and presenting results.

The Internet-based projects below are excellent samples of what’s available online for the offline classroom. If you know of similar projects, please share via this blog!

In this project, 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 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.

If your school is located among rural roads, you and your students can collect roadkill data in your community for analysis and compare your data to other areas participating in the project. The site provides a detailed protocol for monitoring and reporting roadkill, a method of reporting data through the web, and access to data collected by all participants. The project crosses many disciplines, including environmental science education and data analysis.

The International Boiling Point Project

Students around the world boil water to discover what influences its boiling point. Is it room temperature, elevation, volume of water, or the heating device used? All you have to do is boil a bit of water, record a bit of information, and send it along to the site for inclusion in the database of results.

In the course of the project, students learn about Eratosthenes and his experiment, and then do a similar experiment themselves by collaborating with other schools. They learn the “why” of the measurements they’re taking, collect the data as precisely as possible, and submit their findings to the central site. By collaborating with a classroom in another state or even another country, they actually determine a good estimate of the Earth’s circumference. The site provides detailed instructions, activities, and reference materials.