# Winter Math

Whether charting cold weather or creating snowflakes, you'll find that math comes alive in wintry explorations.

## SNOWFLAKE MATH

There's something about snow that's irresistibly compelling to kids. Whether you live in an area that sees lots of snow or one that never feels a flake, you and your students can enjoy the fun and fascination of mathematical snowflake explorations.

Capture Snowflakes
It's great to have an educational justification for running outside when the flakes start falling! Here are several ways to capture and preserve the details of real snowflakes for classroom study:

• Chill black construction paper, black or blue foam core, or black felt taped to cardboard by placing it in a freezer, and then take the sheets outside while snow is falling. Snowflakes landing on the cold surfaces will hold their shape long enough for you and your students to examine them with a magnifying glass or take close-up digital photos of them while you are still outside. Back in the classroom, you can display the photos on a computer monitor or print them for study.
• Chill a sheet of glass and a can of aerosol hairspray. (Cover the edges of the glass with masking tape or use old picture frames.) On a snowy day, spray the chilled glass with chilled hairspray and take the glass to capture some snowflakes on the sprayed side of the glass. Back inside, after 15 minutes, you should be able to see residual snowflakes where the real ones landed. Place the glass over black paper and use a magnifying glass to see them more clearly.
• Chill microscope slides, cover slips, and superglue or acrylic spray. The next steps depend on which adhesive youâre using, but this method will enable you and your students to study preserved snowflake "fossils" for examination under a microscope. For details, see SnowCrystals.com.

Analyze Snowflakes
The next best thing to being there -- or maybe even better -- is to plunge into the world of snowflake photographs. (See links at the end of this article.) We've all heard that no two snowflakes are alike, but can students find ways in which two or more snowflakes are similar and different? Can they devise a simple system for categorizing the snowflakes they are studying?

After students have had a chance to consider their own ideas for categorizing snowflakes, see if they can categorize an assortment of snowflake photographs using a snowflake chart. For a printable snowflake chart and descriptions of categories, visit the Guide to Snowflakes at the SnowCrystal site.

Make Snowflakes

• Fold and Cut Paper Snowflakes
Simple directions for folding and cutting paper snowflakes can be found at Paper Snowflakes or Paper Snowflakes for Children, or you can purchase books of paper snowflake templates and ideas. (There are many to choose from if you search "paper snowflakes" at Amazon.com.) Students in grades 4 or 5 and above can measure exact 60 degree angles for their folds; younger students can approximate 60 degree angles by folding paper in half and then into thirds by visual approximation, or by cutting out hexagon patterns.
Extra challenges:
• Try to predict how your snowflake will look before it is unfolded.
• Experiment with cuts to replicate a specific snowflake model as closely as possible.
• Symmetry: What kinds of symmetry does a snowflake have? How many lines of symmetry does it have? Which of the paper snowflakes is most carefully executed and most symmetrical?
• Measure the angles in your snowflake.
• Pipe Cleaner Snowflakes
Create symmetrical snowflakes from white pipe cleaners or chenille stems. Use a protractor to measure the angles. Hang the snowflakes from clear thread in a classroom window.

• Koch Snowflakes
Introduce students of any age to fractals as they study and draw several iterations of a Koch snowflake.

• Simulated snowflakes: Suspend small pipe cleaner snowflakes in a solution of supersaturated borax, sugar, or salt, and watch crystals grow on them. For details, see Grow a Borax Snowflake.
• Grow real snow crystals in supersaturated cold air using dry ice. For details on the set-up and information about the physics involved, see Growing Your Own Snow Crystals.
• Online Snowflakes
• Click repeatedly in one or two cloud layers of this applet to simulate the creation of different types of snowflakes.
• Design digital snowflakes with applets and visit online snowflake galleries. The detail in some of the gallery flakes is impressive; you might print some for students to attempt to replicate or categorize in small groups:
• Click and drag repeatedly in this applet to simulate cuts in a folded paper, and watch the evolution of the resulting snowflake design.
• At Make-a-Flake, click to mark the start and end of simulated scissor cuts; preview periodically, or be surprised when you finish snipping. Download your flakes or gallery flakes as JPG or EPS files if you wish.
• Estimate and check the angles and line lengths used to create randomly-generated online snowflake designs. (Requires a free plug-in.)
• Explore an online Koch snowflake fractal. (Be sure to read the "learner" information accompanying the applet. Students might also like to try drawing a few paper and pencil iterations.)

## WINTER FUN: ESTIMATION, COUNTING, AND MEASURING

For each activity, students first should make a prediction, then count or measure to test their prediction. Older students also might graph the class's findings and/or determine the mean, median, mode, and range of data.

• How many cubes fit in your mitten or glove? Use Unifix cubes or centimeter cubes. After packing each glove as fully as possible, empty it out and count the cubes. Younger students can snap together their Unifix cubes and tape them to a wall to see whose chain is the longest. For a math-literature connection, read Jan Brett's The Mitten.
• How many "snowballs" (large marshmallows) are in the estimation jar?
• Measuring snow:
• How much does a snowball weigh? What is its circumference?
• How much does a cup of snow weigh compared to a cup of water?
• What is the liquid volume of a cup of snow after it melts?
• How long does it take cup of loose snow to melt compared to a packed snowball and/or a cup of ice?
• How do you compare to a penguin or a polar bear? (Compare students to these cold-loving animals in terms of height, weight, leg length, or other measurements.)

## WINTER GLYPHS

Create winter-themed glyphs -- decorating the outlines of snowmen, mittens, or penguins -- to communicate information using categories and legends that you provide or that the class agrees on. For example, on a snowman glyph, the number of buttons could indicate the student's age or number of people in the student's family. The color of the snowman's scarf could indicate birth month. The style of hat could indicate a preference for fiction or non-fiction books.

• sample snowman glyph template and instructions.
• winter glyph ideas and photos. (Look for other great winter math ideas on this page and the comparable pages for 2006 and 2007.)

## WINTER DATA COLLECTION AND ANALYSIS

After collecting data, graph and analyze the results. For survey data, you might compare responses of boys and girls, different grade levels, or adults and children. Here are some possible winter-themed survey ideas:

Winter Clothing

• Do you wear mittens or gloves?
• How many students in the class wore a hat/scarf/mittens/boots/coat today? (Track the data each school day for a week or longer, along with before-school temperatures. What early morning temperature seems to be the trigger for wearing or foregoing a particular item of winter clothing?)

Preferences:

• Do you prefer warm weather or cold weather?
• What's your favorite winter activity? (sledding, making a snowman, snowball fight, ice-skating, skiing, other)

Home Energy Conservation Data

• At what temperature does your family set the heat?
• Do you have storm windows? attic insulation?

Winter Weather Data

• Graph the daily high and low temperature over the course of several weeks or a month. Obtain data from the local newspaper or a weather site (see below).
• Graph the number of cloudy, snowy, rainy days and/or the amount of precipitation reported in the local newspaper or on a weather site.
• Compare the daily local forecast to the actual weather data over a period of days or weeks. (For example, when the forecast gives a 30 percent chance of snow, how often does it actually snow?)
• Compare current local weather data to historical data.
• Over a period of days or weeks, measure and graph the outside temperature at the beginning of the school day, during math class or lunch recess, and at the end of the school day. (Is there a difference between temperatures in the sun and in the shade?)

## BRRRRRING IT ON! MORE WINTER-FRIENDLY ONLINE RESOURCES

Snowflake Photographs

Weather Sites
At weather sites, you can find local forecasts, recent weather data, and weather data for any other location you and your students might like to compare with your own. Just type in a zip code or city name of interest.

Beyond Penguins and Polar Bears
Supported by an NSF grant, this online magazine for K-5 teachers was launched in March 2008. It has kid-friendly articles as well as lesson ideas and other resources for teachers.

Polar Bear

Penguins
The facts, photos, and activities at Penguins were assembled by kids for kids.

Ice and Snow
These Web pages of Ice and Snow information and activities were written by kids for kids.

National Snow and Ice Data Center
This comprehensive National Snow and Ice Data Center Web site, useful for teacher reference or for older students, includes information on snow and ice as indicators of climate change, snow avalanches, blizzards, historical snow data, the climate of the Arctic and Antarctic regions, glaciers, sea ice, ice sheets, ice shelves, and icebergs.

Online Climate Data Directory from the National Climatic Data Center
The Online Climate Data Directory Web site includes historical data.

Snowflake Activity Sheet
Produced by amazon.com to accompany Ken Libbrecht's Field Guide to Snowflakes, this activity sheet includes nice snowflake photos, paper snowflake instructions, a word search puzzle, snowflake Q&A, and more

Wendy Petti is the creator of the award-winning Math Cats Web site, author of Exploring Math with MicroWorlds EX (LCSI, 2005), and a frequent presenter at regional and national math and technology conferences. She teaches grades 4 at Washington International School.

Article by Wendy Petti
Education WorldÂ®