Winter Math Topics
Winter weather presents many opportunities to integrate math skills into literature and science lessons. Teachers often find that winter themes, such as snowmen or penguins, motivate students to play games to help master basic facts or skills. Geometry is also a natural winter theme as students examine snowflake symmetry or symmetry in holiday shapes and cookie cutters.
Symmetry: Incorporate a study of symmetry as students create holiday projects. Ellison cutouts and cookie cutters are very often symmetrical figures. Have students trace, cut out and fold the objects to find the line of symmetry. Mrs. Soranno's kindergarten students created lots of symmetric holiday decorations, pictured above as well as the Symmetry Forest, pictured below on the right.
Shapes: Students also used marshmallows and toothpicks to create marshmallow shapes, such as those pictured to the right. This is a great way to reinforce student knowledge of 2-dimensional shapes. Additionally, the marshmallows make it easy to count vertices.
Challenge students to predict and draw what a snowflake will look like when the given pattern is cut out. Then, have students actually cut out the snowflake pattern to check their prediction. Finally, students will identify and draw in lines of symmetry for the snowflake pattern. Train students to think about and visualize the Snowflake Symmetry.
- Students may cut out virtual patterns to Make a Flake. Challenge students to draw what the opened snowflake pattern will look like before previewing the finished product. Repeat several times so that students develop spatial sense and are better able to predict what the cut pattern will create.
- Enrichment: provide copies of the Snowflake Symmetry Student Handout so that students can record their cut design and challenge their classmates to predict what the finished product will look like.
- Bulletin Board: display both the folded designs and the finished products in random order. Label each design with a number and each finished product with a letter. Challenge students to correctly match each pair.
Match the Snowflake Halves: Mount student original snowflake designs on dark blue or black construction paper. Cut student snowflakes in half along a line of symmetry. Challenge students to find the matching snowflakes, based on their analysis of the symmetry of each design.
Symmetric Snowflakes: Check out these sites for snowflake patterns that can be printed for students to fold and cut into symmetric snowflakes. Once students have mastered these patterns, they're ready for their own creations.
- Print out Ben & Jerry's Snowflake Patterns
- See directions for creating Billy Bear's 6-point snowman snowflake or 8-point snowman snowflake. The directions may be modified to create any type of symmetric snowflake.
- Download a one-page pdf handout for Folding and Cutting a Snowflake.
- See pictures and directions for Paper snowflakes
- Enchanted Learning gives directions and illustrations to make a Paper Snowflake
Pattern Block Snowflakes
Use Ellison cutouts of the pattern blocks on white construction paper, if possible. If not, download the Pattern Blocks and provide copies so that students may cut apart the blocks. Students then arrange the blocks in a symmetric snowflake pattern on blue or black paper for the best contrast. When students are pleased with the arrangement, they may glue the pieces in place.
Variation: Provide students with the Symmetric Snowflake made from pattern blocks and challenge them to complete the design so that it is has line symmetry. Have students use the blank symmetric snowflake design handout to create their own symmetric snowflake challenges.
Snowflake Quilt Squares
Visit Mrs. Burns' Quilt Monthly Quilt Squares to download patterns for snowflake quilt squares. Bookmark this site for your math quilting unit. Extend the activity by including an investigation of the symmetry in the patterns.
Teachers and students love snow days and snow men. These math activities capture student enthusiasm for this seasonal theme.
- Snowman Probability Game: students spin to win all of the pieces to create the snowman. Have students use the Snowman Probability Recording Sheet to collect data on how many spins it takes to get all of the pieces, then analyze the class data.
- See Snowman Glyphs for suggestions for making several different snowman glyphs with students.
- See Snowman Problem Solving from the Winter 2005 Math Activities collection.
- Read The Fattest, Tallest, Biggest Snowman Ever and follow up with some math measurement activities, as suggested in the Winter 2005 Math Activities collection.
Math Activities Themes: Snowmen
See more snowman math activities on the new Mathwire.com Snowman Math Activities theme page which is a collection of all things snowmen on the Mathwire.com site. conveniently pulled together for easy browsing. The collection includes new Snowman Math Activities including a new snowman math mat, and a new Last Snowman Standing Game.
View the Snowman Math Activities theme page .
These activities capitalize on student fascination with penguins.
- Play the Penguin Bowling Game to provide mixed basic facts practice. Students toss 4 dice, then use the numbers from the dice throw and any of the four operations (+, -. *, /) to form expressions to knock down penguin pins. They are trying to create expressions that result in answers of each number from 1-10. Students use a Score Sheet to record group scores as one does in real bowling games. Remember to model the scoring process, using an overhead of the scoring sheet, if students are not familiar with scoring regular bowling games. Teachers will especially have to model how to score a strike, as students will be strongly motivated to knock down all ten penguins in each round.
- Have young students create a Penguin Counting Book
- See Penguin Math from the Winter 2006 Math Activities collection for problem solving, games and penguin links
- Check out Penguin Math from the Winter 2005 Math Activities collection for Pascal's Penguins (discrete math), problem solving and links to penguin tangrams and games.
- Be sure to check out the new Penguin Math Theme page in the Mathwire.com Themed Math Activities Series.
Math Activities Themes: Penguins
See more penguin math activities on the new Penguin Math theme page which is a collection of all things penguin on the Mathwire.com site. conveniently pulled together for easy browsing. The collection includes new Penguin Math Activities including a new penguin math mat, math-literature connection for 365 Penguins and a new Free the Penguins Game.
Gingerbread men and gingerbread houses enjoy special popularity around the holidays, but many of these gingerbread activities are timeless and complement literature titles that teachers use at the beginning of school or after the holidays. It's very easy to incorporate mathematics into a study of gingerbread men, and students will enjoy the data collection activities and games while learning math skills and deepening their understanding of important mathematical concepts.
Data Collection Activity: Run, Gingerbread Men, Run! Game
This game was designed to introduce students to the randomness of spinners and dice. Each color gingerbread man starts at the same place and has the same chance of winning by crossing the finish line, but does it work out that way? Students will enjoy playing the game AND use a clothespin graph [see sample on right] to collect some useful data on the winners.
Once students have collected class data from playing many games, they will come together to analyze the clothespin graph results. Students will be asked to discuss whether or not they think the game is fair for all of the gingerbread men and explain their reasoning.
Download the Run, Gingerbread Men, Run! Game so that students can get started playing and collecting data. The pdf file contains the spinner, gameboard, clothespin graph icons, and an optional tally sheet.
Math Activities Themes: Gingerbread Man
See more gingerbread math activities on the new Gingerbread Man Math theme page which is a collection of all things gingerbread on the Mathwire.com site. conveniently pulled together for easy browsing. This new collection also includes a gingerbread person math math and links to more gingerbread math activities on the web.
Each of these glyphs capture data about students in a visual mode.   Students should analyze the class data by creating tally charts, Venn diagrams, bar graphs, etc. Students should talk about and write about what they learned from looking at the glyphs of their classmates. Or, play a guessing game where students try to match a student's answers to the legend by identifying which glyph belongs to that student.
Consider turning some of your favorite winter crafts projects into math glyphs. It's easy to create a legend that fits your students. Older students enjoy working with teachers to create a class legend for the project.
- The Mathwire Elf Glyph, pictured above, comes complete with legend and downloadable patterns.
- Check out Shari Sloane's outstanding Glyphs Resource page for pictures of glyphs, pdf handouts of glyph legends and math-literature book connections for all seasons. The collection includes a mittens glyph, gingerbread man glyph, and Christmas tree glyph.
- See Mitten Glyph Legend for a different version of a mitten glyph.
- Scroll down this Penguin unit to find suggestions for creating a Penguin Glyph
- See Penguin printout to use for glyphs.
- See legend and pictures of Reindeer Glyphs
- Print out a legend for a Reindeer Glyph and adapt it to your own class, if needed.
- Mrs. Arocho's kindergarten students created Snowman glyphs. See the picture on the right to view the legend students used and to see samples of their glyphs which were proudly displayed in the school hallway for all to admire.
- Mrs. Ritenour's Snowman glyph includes a questionaire, legend and pictures of student glyphs.
- Lynn Weber's Snowperson Glyph is a legend for creating glyphs.
- This Snowman Glyph is a simple coloring project
More Winter Glyphs
- See Winter Glyphs from the Mathwire.com Winter 2005 Math Activities collection.
- See Winter Glyphs from the Mathwire.com Winter 2006 Math Activities collection.
Coordinate Graphing Picture:     Holiday Quilt
This activity requires students to use coordinate pairs to correctly color in the squares of the grid to create a picture. Students need only red, yellow, blue and green crayons or markers to color in squares to create this Holiday Quilt of traditional quilt squares.
If students like this activity, try the Quilt Square Challenge. Complete directions are given as are the pdf files for the quilt squares and quilt mats. This activity was designed to help students develop spatial memory and spatial sense.
Coordinate Graphing Game:     Catch the Gingerbread Men
For this game, students toss two dice (one regular and one marked A-B-C-D-E-F), form an ordered pair (e.g. B5), then remove the gingerbread man from that space, if there is one. Play continues until the timer rings or until one player has caught 10 gingerbread men. Students love playing the game and they get to practice their coordinate graphing skills in the process.
Download Catch the Gingerbread Men game mat, game pieces and directions for playing the game.
If students enjoy this game, they will also like the Capture the Penguins Game from the Mathwire Winter 2006 collection. Students especially love the clothespin penguins so they're worth the time and effort to make!
More Winter Coordinate Graphing Activities
- See more Winter Coordinate Graphing Activities from the Winter 2005 collection including a Gingerbread House activity and Grab the Candy game.
- See Winter Coordinate Graphing Games from the Winter 2006 collection to download directions and game mat for the Capture the Penguins game.
- Have students assemble a Snowman Quilt Square, designed by Ms. Burns. Students place colored squares in the correct locations to form a snowman picture.
More Seasonal Coordinate Graphing Resources
Consult these teacher resources for additional coordinate graphing activities, especially for the holidays. Look through closets as these are oldies-but-goodies. These activities introduce young math students to coordinate graphing and allow teachers to plan seasonal math activities that effectively develop math skills and concepts.
- Holiday Graph Art by Erling and Dolores Freeberg, published by Teacher Created Materials, Inc., 1987. This book contains graphing art directions for these winter activities: Santa Claus, Rudolph, Christmas Tree, Candle, Angel, Baby New Year. See Teacher Created Materials Website to view sample pages from this book.
These open-ended assessments require students to apply mathematical concepts and skills to solve problems and explain their thinking using words, pictures and numbers.
- Let students practice fraction skills to solve Winter Fraction Words, then challenge students to make up their own fraction word puzzles.
- Challenge students with a Wrapping Paper problem. Will either sheet of paper completely wrap the birthday present? Students are asked to use numbers, words, pictures or diagrams to explain their best thinking. Or, actually place paper and boxes in a math center and challenge students to figure out the smallest piece of paper that will completely wrap the gift.
- Students will use statistical skills to solve the Weekly Weather problem. Two temperatures are missing but the teacher has supplied some statistical clues to help students figure out the missing data.
- Because sales are a part of holiday shopping, students will practice percentage skills in Shopping for Sales as they figure out where they should buy mom's present to get the cheapest price.
- Motivate students to try their hand at some code-breaking with Crypto-Lists for Winter.
- See Snowman Problem Solving from the Winter 2005 collection which includes Frosty's Estimation Station, Dress the Snowman templates, and links to additional snowman activities on the web.
- Holiday Problem Solving from the Winter 2005 collection includes links to the Twelve Days of Christmas and Pascal's triangle math activities on the web.
- More Winter Problem Solving from the Winter 2006 collection includes Gingerbread and Snowman combination problems as well as several different patterning problems.
Many books may be used as a springboard for mathematical discussions and activities. These are included to integrate winter themes into mathematics:
The Elves and the Shoemaker retold from the Brothers Grimm and illustrated by Jim La Marche. After reading the book, have fun with patterns!
- Download Scholastic's The Elves and The Shoemaker short story and math lesson that uses input-output tables to study the patterns.
- Challenge students to make up their own variations on the elves' patterns.
- Read the book and then do A Shoe In, an extension activity found in NCTM's Amazing Attributes online lesson. Students use a Venn Diagram to sort and classify shoes worn by students in the class.
- Create an Elf Glyph. This Winter 2006 math activity includes legend and patterns to create the elves.
The Mitten by Jan Brett: After reading the book, have students do a math estimation activity:
Download Math-Literature Connections: The Mitten by Jan Brett for a copy of these Mathwire.com lesson plans.
How Big Is the Mitten?: a lesson on volume of a 3-dimensional object
- Student Estimates: Show students a mitten and several linking cubes. Ask students to estimate how many cubes would fit inside the mitten. Record student estimates and ask students to explain how they figured out their estimate and why they believe it is correct.
- Data Collection: Provide mittens and linking cubes for each small group. Ask students to work together to fill the mitten with cubes. Be sure to explain what filled means for your class (e.g. no cubes sticking over the edge, or no cubes falling out when you hold the mitten in the middle).
- Organizing Data: Draw a line plot on the chalkboard or chart paper. Ask student groups to make an X to mark how many cubes they fit into their mitten.
- Analyzing the Data: Lead a discussion about the data, including an informal discussion of both range (everyone in the class was between ____ and ____) and mode (most groups were able to fit about ____ cubes in their mittens) to introduce the mathematical language of statistics.
- Math Vocabulary: Tell students that when mathematicians talk about filling an object, they are talking about the volume of the object. Also model using the terms range and mode in discussing the line plot.
How Many Cubes Will Cover the Mitten?: a lesson on area of a 2-dimensional object
- Student Estimates: Show students a mitten cutout and several linking cubes. Ask students to estimate how many cubes would completely cover the mitten. Record student estimates and ask students to explain how they figured out their estimate and why they believe it is correct.
- Data Collection: Provide mitten cutouts and linking cubes for each student. Ask students to completely cover the mitten with cubes. Be sure to explain that no cubes should hang over the edge of the mitten.
- Organizing Data: Draw a line plot on the chalkboard or chart paper. Ask student groups to make an X to mark how many cubes they fit on their mitten.
- Analyzing the Data: Lead a discussion about the data, including an informal discussion of both range (everyone in the class was between ____ and ____) and mode (most groups were able to fit about ____ cubes on their mittens) to introduce the mathematical language of statistics.
- Math Vocabulary: Tell students that when mathematicians talk about covering an object, they are talking about the area of the object. Also model using the terms range and mode in discussing the line plot.
Graphing Ideas:Do you wear mittens or gloves in the winter?
- Create a clothespin graph
- Create a Venn diagram which allows for the possibility that some students wear both, depending on the day
- Create a pictograph with mitten and glove cutouts
- Create a bar graph using colored index cards with each student's name that can be placed end to end to form bars
Jan Brett activities for The Mitten
- See The Animals of the Mitten coloring page
- Have students Put the Animals in the Mitten
- Design Your Own Mitten
- Print Animal Masks from The Mitten
These math activities are organized by seasons.   Elementary teachers often incorporate seasonal activities as craft projects.   Many of these seasonal craft projects can be mathematical as well with a little forethought.   Browse the activities for projects to add that reinforce mathematical concepts and skills through seasonal and holiday themes.
- Fall Math Activities 2006
- Fall into Math: Fall 2005
- Back-to-School Math Activities
- Winter 2006: Math Activities
- Winter Math Activities: Winter 2005
- February Math Activities
- 100th Day of School Math Activities
- Earth Day Math Activities
- See all Mathwire Seasonal Math Activities
Teachers can find many shared activities on the internet. These activities integrate mathematical ideas using fall materials and themes. The activities address multiple mathematical strands (e.g. measurement, number sense, probability, estimation, money, data collection, etc.), making it possible for teachers to plan effective mathematics instruction that also captures students' seasonal interest. Use or modify the lessons to fit the needs of your students. Build upon the ideas shared by other teachers through internet sites. These are presented in alphabetical order by activity title.
- Math Cats Winter Math Idea Bank includes snowmen, mittens, snowflakes and penguin math activities,
- Christmas Riddles from Kid's Domain