Reading the math textbook or handouts or extended response problems presents built-in challenges. The vocabulary of mathematics can be confusing, with some words meaning one thing in a mathematical context and another in everyday settings. Symbols can look alike, and different symbols can represent the same operation (for example, *, x, and • for multiplication). Graphs vary in format, even when representing the same data. Writing is valued as a way of communication in most school subjects, yet rarely in math. If students can learn to explain their thinking in solving a math problem (using drawings or tables or graphs as well as words), they acquire a means of setting out their work logically and refining their thinking as they communicate their understandings.

Far from expecting teachers to stretch their class time to include yet more content, a new Explore in Depth publication from the Middle School Portal, Reading and Writing Mathematics, offers resources that can enrich math instruction as teachers help their students better understand the content they are already tackling. Each section of the publication contains articles, many by teachers, who share their experiences, rationale, and classroom methods. Each section also offers lesson plans or activities appropriate for middle school students. Enjoy the challenge of opening your students to mathematical communication!

Science, like other disciplines, has a specialized vocabulary, encompassing both terms that represent scientific concepts and those that describe process skills. Although science education focuses on inquiry and hands-on experiences, current research shows that teachers must also help students develop vocabulary to be successful in both the content and methods of science.

However, this is often easier said than done. Many textbooks introduce 10-30 words per chapter - more than many introductory foreign language texts! In addition, students may struggle with “academic vocabulary” - words such as compare, distinguish, observe, and conclusion. Without guidance (or even formal training), a middle school science teacher may struggle to determine the best way to help students develop crucial vocabulary skills.

A new Explore in Depth publication from the Middle School Portal, Developing Science Vocabulary, can help teachers improve their vocabulary instruction. In this publication, you’ll find background information, best practices, tips for differentiating instruction and assessment, and resources for further reading. We hope you’ll check out Developing Science Vocabulary today!

Do you find that your middle school students still become confused with decimals? Not unusual! The resources here offer support in explaining the concepts underpinning addition and subtraction of decimals, in particular, place value. They also include demonstrations of addition and subtraction and opportunities for practice. The goal for students, as stated in NCTM’s Focal Points, is to develop fluency with computing, solving problems, and making reasonable estimates. I hope these resources will visually and interactively engage your students, helping them toward that goal. 

If you have found other digital resources that have helped your own teaching of this topic, please take a moment to share with your colleagues. Just leave a comment below! 

Builder Ted
This interactive game deals with place value in decimals, necessary to understanding addition and subtraction. In the game scenario, students help Builder Ted by placing numbered bricks on a ladder in numerical order. At the first level of difficulty, all numbers are positive, but the two higher levels include negative numbers as well. If a number is placed incorrectly, all the bricks immediately fall and the player begins again.  

Place Value
The user can type in any number, such as 3601.076, or let the computer choose a number. As the student passes the mouse over each digit in the number, its place value is shown. Also, how to say the number is given, plus a short exercise asking the student to identify the digit in, say, the thousandth position.

Fractions, Decimals, and Percentages
Especially appropriate for tutoring or even review, the site introduces decimals (reading, writing, and comparing) and then offers examples and practice in operating with decimals.

Base Block Decimals
With this virtual manipulative, students can explore the meaning of place value and grouping as they add and subtract decimals. The base blocks can represent negative as well as positive numbers with one to four decimal places. Students exchange and group the blocks as needed to solve the problems created by either the student or the computer. All material is available in Spanish and French as well as English, including instructions for using the manipulative, information about bases and place value, and suggested questions for classroom use.

Decimals
This site offers bare-bones explanations of decimal topics and interactive practice. In the long list of topics are adding and subtracting decimals as well as adding and subtracting money. The computer sets the problem and gives immediate feedback to the student’s response. The bottom of each lesson page contains timed exercises.

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.

The Noon Day Project: Measuring the Circumference of the Earth
Here is a real-world project that will engage your class in measuring the circumference of the Earth! You will find all information you need to enable students to recreate the measurement as done by the Greek librarian Eratosthenes over 2000 years ago. The procedure is based on measurements of shadows taken at high noon local time on a designated day; results from several schools are posted online and used to calculate the circumference. Included are detailed explanations and illustrations of the mathematics involved, including a video of Carl Sagan explaining Eratosthenes’ calculation.

This article was written by Stephanie Chasteen and originally published in the May 2009 Integrating Technology column of Beyond Penguins and Polar Bears, an online magazine for elementary teachers. All versions of this article are licensed under a Creative Commons License. Stephanie is a science teaching fellow at the University of Colorado at Boulder. She is one of the creators of the Beyond Penguins and Polar Bears podcast series. Read her blog at http://expertvoices.nsdl.org/sciencegeekgirl.

Podcasts, audio recordings published on the Internet and played on computers and portable devices, are becoming popular among all types of audiences, including K-12 teachers and students. Classrooms are both consumers and producers of this technology. As consumers, you’ll find a growing amount of high-quality free educational content for you and your students in podcasts, right at your fingertips! We’ve identified some sources in the resources at the end of this article.

Now it’s easier than ever to make podcasts in the classroom, to become producers. You don’t need a media player, such as the Apple iPod, or specialized software to make or listen to a podcast - just your computer and an Internet connection will do. Though podcasts can be audio and video, audio podcasts will be featured in this article.

LISTENING TO PODCASTS
Podcasts are handy ways to get information - captured on your computer or media player, they are available to you when and where you want to listen. (I catch up on the latest science and education news every day while I bike to work.) And you don’t have to spend time checking the web sites of podcast creators for new episodes. By subscribing to an RSS feed at the web sites of your choice, you will receive new podcasts automatically.

You might listen to podcasts of personal interest, use them as an informal source of professional development, or have your students listen to them (as part of class research on a topic, for example). Of course, not all podcasts are appropriate for students. If you are using iTunes, you can use the Parental Control feature (in Preferences) to prevent students from previewing or downloading podcasts marked with the “explicit” label. But don’t assume that iTunes will do all the work for you! Be sure to listen to the entire podcast before assigning it or using it in class.

SUBSCRIBING TO PODCASTS
There are a number of free programs for automatically downloading podcasts to a computer. iTunes and Juice are two such programs.

In iTunes you can find and subscribe to podcasts in several ways:

1. Through the iTunesstore. Click on “podcasts” in the left column of the iTunes store, and then “podcast directory” on the lower right-hand corner. You can then “browse” or “power search” to find podcasts.
2. Drag the podcast’s RSS icon into iTunes. Most podcast pages display the RSS icon. You can drag that icon into the podcast window in iTunes and the program will subscribe you.
3. Type in the URL. In the “Advanced” tab in iTunes menu bar, choose “subscribe to podcast.” Put in the URL for the RSS feed for that particular podcast.
4. Click on a “subscribe” link on the podcast’s web site. Many podcasts will have a “subscribe via iTunes” link that will open up iTunes on your computer.

MAKE A CLASS PODCAST
Creating a podcast in the classroom can be a great way to incorporate writing across the curriculum. Narratives like personal stories, drama, history, and music all lend themselves well to audio presentations. Plus, students can be more motivated to create a podcast that could be heard across the world, rather than just within the classroom.

Classroom podcasts will take some time. Start small. Consider divisions of labor for student-created podcasts (writer, editor, voice actor). You will likely have to do the final production of the podcast and help with the equipment. Your students should use stage names and never give any personal information about themselves. Podcasts on web sites are publicly available.

You can find many examples of elementary class podcasts on the Education Podcast Network or on Podcast for Teachers. You can find information about using and creating podcasts in KidCast: Podcasting in the Classroom. The creator of the KidCast site, Dan Schmit, is the author of books on the subject as well. He gives an overview of classroom podcasting in this podcast: http://edcommunity.apple.com/ali/item.php?itemID=9973.

Briefly, here are the main steps in recording and broadcasting a podcast:

1. Record the audio using recording software such as Audacity (free!) or Apple Computer’s GarageBand for a Mac. Students can also record via telephone for free at Gcast.com and Gabcast.com.
2. Edit using the recording software (Audacity or Garageband) to cut out anything you don’t want.
3. Add music and sound effects, make volume fades, and so forth. Free sound effects and samples are available at FindSounds and Sounddogs.
4. Compress the audio to an MP3 file. This makes your audio file smaller
5. Upload your file to a class web site or other host sites such as Podomatic or Podbean.com. The host will make your web page automatically!

When using sound effects and music in your podcasts, it is important to consider copyright and terms of use. Most podsafe music is licensed under Creative Commons, which allows educators and others to use music as long as they give attribution.

Some ideas for class-produced podcasts are:

1. Interviews: Students can talk to people who use science in their jobs.
2. History:”This day in science history.”
3. Podcast drama: A recorded version of a classroom skit.
4. Pet podcast: Give kids a chance to talk about biology and nutrition using observations of their pets
5. Outdoor observations: Use cell phones or a portable recorder to note observations during urban science walks.
6. Where in the World: Submit a podcast to this worldwide geography quiz show - http://www.intelligenic.com/where/.

In the resources below we’ve included links to web sites that will be helpful sources as you create classroom podcasts and to other sites that provide science news and information in podcast format.

RESOURCES ABOUT PODCASTING

KidCast
A community of educators who are podcasting in K-12 schools. Books and workshops are available.

Education Podcast Network
Directory of podcasts produced by educators.

Listening to Themselves: Podcasting Takes Lessons Beyond the Classroom
An article from Edutopia.org describes podcasting in a fifth-grade classroom.

Tips for Podcast Fans
Apple’s iTunes site gives helpful tips on creating and subscribing to podcasts.

Podcast for Teachers
Articles, blogs and podcasts about podcasting.

PodSafe Music Network and PodSafe Audio
Find music that is license-free and legal to put in a podcast in these two directories.

LINKS TO SCIENCE NEWS PODCASTS

Beyond Penguins and Polar Bears Podcasts
Each month Robert Payo and Stephanie Chasteen trek across the poles to find ways to help you teach science in your classroom. They tackle common misconceptions your students might have about science using stories, teaching activities, and the latest news related to the poles.

Teaching Tips
A podcast series by the author and produced by the Exploratorium Teacher Institute.

60-Second Science
Daily (Monday-Friday) one-minute episodes from the staff of Scientific American, who also produce the weekly Science Talk podcasts.

WNYC Radiolab
One-hour shows about science produced by New York public radio stations.

NOVA Science NOW
Brief audio stories from the NOVA series.

Krulwich on Science
Podcasts from a correspondent for NPR’s Science Desk series.

The Naked Scientists: Science Radio and Science Podcasts
Science podcasts from the British Broadcasting Corporation. Check out the kitchen science portion for ideas on classroom activities.

Slacker Astronomy
Podcasts and blogs about astronomy.

Science Update Podcasts
Daily and weekly podcasts from the Science Update radio program, produced by AAAS.

These resources offer practice in operating on decimals and, moreover, opportunities to think about the processes of multiplication and division. As stated in the NCTM Focal Points, students should make sense of these procedures, become fluent in performing them, and be able to apply them in solving problems. I believe these sites, as a whole, offer practice in both understanding and problem solving.

If you have ideas to offer, please share them with your colleagues.  Just add your comments below.

Learning about Multiplication Using Dynamic Sketches of an Area Model
In this applet, a rectangle represents the familiar area model of multiplication. By changing the height of the rectangle, students can explore the effect of multiplying a fixed positive number, in this case 3, by decimal numbers greater than 1 and less than 1. The visual is powerful!

Too Big or Too Small?
Scroll down to Activity 3: Exploring the Effect of Operations on Decimals. Through playing the cleverly crafted game presented here, students explore the effect of operations on decimal numbers. They begin with the number 100 as they enter a maze. For each segment chosen on the maze, the student calculates the assigned operation and number; for example, “+ 1.2” or “x 0.8.” The goal is to choose a path through the maze that results in the largest value at the finish.

Decimals
This site has explanatory lessons and interactive practice on most aspects of decimals, including multiplying decimals and dividing them. A good set of materials for self-tutoring or review. 

Find the Cost of Meat per Week at a Zoo
In a multi-step, NAEP assessment item, students must determine how much a zoo spends each week on meat to feed the animals. The site links to the scoring guide, sample student responses, and data on how well grade 8 students did on this multiplication/division problem. Only 13% solved it correctly!

Where’s the (Decimal) Point? asks students to explain clearly how they know where to put the decimal point in multiplication and in division of decimals. Students must think beyond the “rules” to the “whys.” I suggest these problems as challenges for older middle school students who are ready to stretch their thinking to the level of generalizing arithmetic.

You probably already incorporate games in your teaching. We even highlighted math games in an earlier post - Let’s Talk Teaching: Math Games. Games are a great way to focus students’ attention as few other teaching strategies can. The ones selected here deal directly with the math content covered in the middle grades. Each has a learning objective; each could be embedded in a lesson plan. Here are a few more games that you can add to your store of games that teach.

Fraction Game
For work on fractions, this applet is a winner! It allows students to individually practice working with relationships among fractions and ways of combining fractions. It helps them visualize what is meant by equivalence of fractions. A link to an applet for two-person play is also given here.

Polygon Capture
This excellent lesson uses a game to review and stimulate conversation about properties of polygons. A player draws two cards, one about the sides of a polygon, such as “All sides are equal,” and one about the angles, such as “Two angles are acute.” The player then captures all the polygons on the table that fit both of the properties. Provided here are handouts of the game cards, the polygons, and the rules of the game.

The Factor Game
A two-player game that immerses students in factors! To play, one person circles a number from 1 to 30 on a gameboard. The second person circles (in a different color) all the proper factors of that number. The roles are switched and play continues until there are no numbers remaining with uncircled factors. The person with the largest total wins. A lesson plan outlines how to help students analyze the best first move in the game, which leads to class discussion of primes and squares as well as abundant and deficient numbers.

Planet Hop
In this online one-person computer game, four planets are shown on a coordinate grid. A player must pass through each on a journey through space. The player must find the coordinates of the four planets and, finally, the equation of the line connecting them. Three levels of difficulty are available. This is one of 12 interactive games created by the Maths File Games Show.

Towers of Hanoi: Algebra (Grades 6-8)
This online version of the Towers of Hanoi puzzle features three spindles and a graduated stack of two to eight discs, a number decided by the player, with the largest disc on the bottom. The player must move all discs from the original spindle to a new spindle in the smallest number of moves possible, while never placing a larger disc on a smaller one. The algebra learning occurs as the player observes the pattern of number of discs to number of moves needed. Generalizing from this pattern, students can answer the question: What if you had 100 discs? The final step is expressing the pattern as a function.

Traffic Jam Activity
Why the jam? There are seven stepping stones and six people. Three stand on the left-hand stones and three on the right-hand; all face center. Everyone must move so that the people on the right and the people on the left pass each other, eventually standing on the side opposite from where they started. But no two people may stand on the same stone at the same time! This problem requires reasoning, but its solution also reveals a pattern that leads to an algebraic expression. A lesson plan is provided.

Many people think that germs are what make us sick but scientifically speaking, germs are microbes that can be both harmful or helpful and come in four varieties - bacteria, viruses, fungi, and protozoa. We’ll leave the discussion of fungi and protozoa for another post and focus on bacteria and viruses in this one. Microbeworld says that viruses are as different from bacteria as goldfish are from giraffes. That is REALLY different! So what are the differences between the two microorganisms? With people still concerned with the H1N1 virus - knowing the differences and similarities might be really helpful!

What’s a Germ?
This page from Science NetLinks provides images of the four types of microbes and a general description of the differences between them.

Virus or Bacterium?
This site gets into more detail in regards to cell structure and reproductive differences.

What’s the Life Span of a Virus?
This podcast and background information tells the differences between the cold virus and flu virus - both life span and how they are transmitted.

Bacteria: More Than Pathogens
This article, written by molecular biologist Trudy Wassenaar, helps clear up the misconceptions associated with bacteria.

Structure Of ‘Beneficial’ Virus That Can Infect Cancer Cells Solved
There are lots of bacteria that are beneficial - not so much for viruses. Here is a Science Daily article that describes a virus that “attacks” cancer cells.

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! 

Down the Drain: How Much Water Do You Use?  

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.

RoadKill 

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.

The Noon Day Project: Measuring the Circumference of the Earth 

 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.

Join Jessica Fries-Gaither and Kim Lightle for a free webinar Tuesday, April 28, 2009 at 3:30pm EST as we discuss global warming and the polar regions. We’re going to highlight resources from the Middle School Portal 2: Math & Science Pathways project, Beyond Penguins and Polar Bears online magazine, and the National Science Digital Library (NSDL). The webinar is being sponsored by the National Middle School Association (NSMA).

We’ll discuss Earth’s energy budget and climate change, how the polar regions are defined, albedo, and regional temperature and sea ice changes. We’ll highlight the National Science Education Standards and misconceptions associated with these concepts, provide resources that will enhance your content knowledge, and recommend middle school science lessons and activities.

For registration information, go to the NMSA Upcoming Free Events page. The presentation will be archived and available one week after the presentation. The slides can be found at the SlideShare website under Global Warming and the Polar Regions. We also have a Diigo list of all the resources we talk about.

Hope you can join us!