Winter Math Activities

Koch Snowflake

The Koch Snowflake is an example of an iterative drawing as each successive stage begins with the previous stage.   The Koch snowflake begins with an equilateral triangle.   The first iteration divides each side of the triangle into thirds, removes the middle third and replaces it with two line segments of the same length.   Students might visualize this as constructing a smaller equilateral triangle on the middle third, then removing the original middle third line segment.   Students can construct the first couple of iterations with pencil, paper and a ruler for measuring and marking each side into thirds.   Once students experience the first two or three iterations of the Koch Snowflake, they will need to see a computer-generated version in order to see how the perimeter of this snowflake increases through many iterations.

  • Koch Snowflake: Cynthia Lanius java applet that allows students to see each successive iteration of the figure [online activity]
  • Koch Snowflake: diagrams of first three iterations in black on white background.
  • Koch's Snowflake at Shodor Interactive
  • Create a Koch Snowflake with this drag-and-drop colorful online applet [online activity]
  • Anti-Snowflake: Cynthia Lanius instructions and Java applet for this variation on the Koch Snowflake iteration [online activity]

Penguin Math

Build on students' natural fascination with penguins by including these math pattern activities:

  • Pascal's Penguins - 1 introduces primary students to a small version of Pascal's Triangle in this simple patterning activity.
  • Pascal's Penguins - 2 introduces a larger version of Pascal's triangle and encourages students to identify the different patterns within the triangle and use these patterns to fill in the missing penguin numbers.
  • Penguin Parade:   pattern problem-solving task that asks students to figure out how many penguins marched in the parade, given the marching pattern.   PDF file contains problem, challenge and solution.
  • Penguin Puzzler:   pattern problem-solving challenge that provides the total number of penguins and requires students to analyze the pattern to discover how many many rows of penguins marched in the parade.   PDF file contains problem and solution.
  • Penguin Tangrams
  • Place the Penguins Game prompts students to place penguins on the correct multiple of 100, 10 and 0 in the number grid to make the given number.

Snowflake Activities

Snowman Problem Solving

Literature Connections

The Fattest, Tallest, Biggest Snowman Ever by Bettina Ling is a Level 2 Hello Math Reader (Gr. 1-2) that introduces students to the concept of measuring objects using nonstandard units and instruments.   When neither child's arms are long enough to measure around the snowmen to see whose snowman is biggest, they decide to use a string of paper clips to measure.

  • The book also provides suggestions for follow-up measurement activities such as the String-a-Long Game in which students look at (but don't touch) ordinary, everyday objects, then cut a piece of string they think is the same length as the object.   Students compare their strings to the object to see whose string is closest to the length.   Consider using the "String-a-Long Game" as a great measurement center activity.
  • Paper-clip chains:   Have students measure classroom objects using paper-clip chains.   Be sure to ask students to estimate first, then measure.   Students will begin to develop an "eye for distances."

What Are Glyphs?

Glyphs are a pictorial form of data collection.   You might be reminded of the term "hieroglyphics" and think about early picture writing.   Different forms of glyphs are used in many medical situations to quickly record data about a patient in pictorial form.   For example, a dentist records cavities on a picture of teeth.   A chiropractor might record injuries or muscle aches on a skeletal picture. In these cases, a "picture is worth a thousand words" and the glyph allows a doctor to more quickly record and analyze the data.

Students in elementary school often create paper art projects for different seasons or holidays. It is easy to transform these traditional projects into mathematical glyphs that allow students to organize and analyze data over several visits.

Winter Data Collection

There are many possibilities for winter math data collection activities.   Look for opportunities to have students create tally charts, clothespin graphs, Venn diagrams, bar and line graphs to organize data and analyze the results of the data collection.   Consider using the Question of the Day to collect data, then ask students to talk about what they can learn from that data.

Gingerbread Math Activities

Many classes make gingerbread houses or gingerbread cookies as a seasonal activity.   Consider emphasizing the mathematical components of these activities:

Winter Coordinate Graphing

Introduce elementary students to coordinate graphing through seasonal coloring activities.   The winter Gingerbread House activity requires students to use the grid code and crayons or markers to create a gingerbread house on a blank 11x11 grid.   The use of letters on the horizontal axis and numbers on the vertical axis introduces young students to coordinate pairs without the confusion of the standard (h,v) format.   Notice that it is important that elementary students become accustomed to listing the horizontal coordinate first as this will transfer to the Cartesian coordinates they will use in later grades.

Winter Coordinate Graphing Game:   Grab the Candy!

Holiday Problem Solving

The Twelve Days of Christmas Song:   Introduce elementary students to the mathematics behind the Twelve Days of Christmas song.   The person received more than 12 gifts.   In fact, students will appreciate this growing pattern as they use a table to track how many of each gift the person receives by the end of the twelfth day.   Older students can retrieve the current estimated costs online, then calculate the total cost of the presents over twelve days.   No matter which of the activities teachers choose, students are bound to hear the song differently after this mathematical investigation.

Internet Links

White Christmas?:   Students use data on the probability of U.S. cities having at least one inch of snow on the ground on Christmas day to create a contour map of the USA.   Students will locate and analyze real-life contour maps on the web.   By constructing their own contour map, students learn to read a contour map and appreciate the information this type of map conveys.   They also see how probability is used in weather prediction.

Math Mountain:   Students may choose one of two problems to solve at this McREL site: .

  • Goldy's Glide for Grades 2-3 extends a magic squares problem.   First students create a traditional magic square placing the numbers 1-9 in a 3x3 grid so that every column and row have the same sum.   Next students are challenged to create the "complete opposite" of a magic square in which none of the columns and rows have the same sum.   A solution is available for students to check their work, if needed.
  • Nabu's Knee Knocker for Grades 4-6 extends the Pascal's triangle problem.   Students must fill in the missing numbers on a number pyramid, following the pattern that each number in a box is the sum of the two numbers directly below it.

Student Work:   Winter Math Activities

Snowman Glyphs

Students in Mrs. Arocho's kindergarten class at Patten School in Perth Amboy, NJ, created snowman glyphs to collect data about each other.   Visitors could use the glyph legend to find out more about the kindergartners in this class.

Kindergarten Glyphs

Students in Mrs. Winkleman's kindergarten class at James J.Flynn School in Perth Amboy, NJ, created gingerbread man glyphs that collected data on whether or not students liked gingerbread, number of brothers and sisters, pets and birthdays.   Students used the legend to find out more about their classmates.

Gingerbread Man Glyphs

Mrs. Ziegler's and Mrs. Campbell's second graders at Port Monmouth Road School in Keansburg, NJ, created gingerbread man glyphs to represent data about birthdays, number of siblings and favorite things to do.

Student Work: Holiday Math Activities

Name-Collection Trees

Students in third grade at Caruso School in Keansburg, NJ, created name-collection trees for the holiday bulletin board.   Each student created an ornament with a different name for the tree number, giving the Everyday Math name-collection boxes a holiday spin.

Learn more about Everyday Math Name-Collection Boxes

Deck the Halls with...Geometry

Mrs. Thal's sixth graders at Sycamore Drive School in Hazlet, NJ, investigated the geometry in holiday symbols. Students made symbols using various shapes, and then added geometric labels.

Holiday Coordinate Graphing

Ms. Collier's and Ms. Rachko's fourth graders at Caruso School in Keansburg, NJ, practiced coordinate graphing to create these reindeer pictures.

See Winter Coordinate Graphing to download activity sheets for a Gingerbread House coordinate graphing activity or directions and game mats for Grab the Candy! game which provides practice in coordinate graphing.