Keep your students engaged with these fun and creative math activities.
It’s the most wonderful time of the year!
Or is it the most chaotic time of the year? You’re ready for winter break, your students are really ready for winter break, and there’s not enough time in the day to get your planning, prepping, and everything else done.
I’ve been there, and if 16 years of excited-for-break high school students taught me anything, it’s that I always need a fun, low-prep activity in my back pocket.
Keep reading for three winter math activities that require little preparation and will keep your students engaged in math exploration while they’re on the edge of their seats for winter break.
Koch Snowflakes: Frozen Fractals All Around (6th–12th Grade)
This creative winter activity engages students in exploring geometry and the creation of fractals.
First studied in 1904 by Swedish mathematician Helge von Koch, the Koch Snowflake is one of the earliest fractals to be described. It’s created by drawing an equilateral triangle, then dividing each side into thirds to create new equilateral triangles in a never-ending pattern.
I like to show this interactive Koch’s Snowflake generator on the whiteboard before asking students to create their own fractal snowflakes so they have a visual support for the process.
To create and explore Koch Snowflakes with your students, follow these steps:
Measure and draw a large equilateral triangle on a big piece of paper (graph paper works nicely). Students can work individually, or if you have access to bulletin board paper, they can work in small groups with a yardstick to draw a huge equilateral triangle.
Divide each side of the triangle into equal thirds. Be sure to measure!
Draw a new equilateral triangle over the middle third of each side.
Erase the base of each new triangle. You should end up with a Star of David shape.
Repeat steps 2-4 until you can’t draw any more triangles. Humans are bound by the materials used, but a computer could continue drawing this fractal for infinity!
To wrap up the activity, ask students to color or decorate their Koch Snowflakes while considering these questions:
What is finite about Koch’s Snowflake?
Define the term “finite” as a class. Then, prompt students to consider the area of the snowflake. Younger students can think of the area as being covered with carpet or paint, while high school students can consider the area of composite figures. They should determine that the area of a Koch’s Snowflake is finite.
What is infinite about Koch’s Snowflake?
Define the term “infinite” as a class. For older students who have studied geometric sequences, work as a group to find the explicit formula for the perimeter of the Koch Snowflake, with a first term of 3 (there are three sides in the first iteration) and a common ratio of 4/3: g_{n} = 3(4/3)^{n-1}.
Then, ask students to consider what it means about the perimeter of the snowflake, comparing the common ratio of the perimeter to 1. They should determine that the perimeter tends towards infinity, because 4/3>1.
What conclusions can you draw about the area and perimeter of Koch’s Snowflake?
This question is a great opportunity for students to describe their observations through written or verbal communication. Support older students in comparing and contrasting the area and perimeter of the Koch Snowflake with a Venn diagram. Modify the question so younger students can discuss the area of the snowflake, or describe the measurement steps they used to create the snowflake.
Winter Temps to Analyze Line of Best Fit (8th–9th Grade)
In many school districts, winter brings the excitement of possible days off from school—sometimes for snow, but also (at least in my area of Ohio!) for below freezing temps. Introduce this activity with a discussion about how different temperatures affect daily activities to get your students excited about graphing and determining the line of best fit for a data set.
Representing data sets in multiple ways is a crucial skill in learning to analyze, interpret, draw conclusions, and make predictions about the data. This low-prep activity from MATHbook, Carnegie Learning’s consumable text, allows students to analyze data in a table and as a scatter plot.
In this activity, students are given a data set for the temperatures in Washington, D.C. since 8 AM on a winter day. From the provided table, they will create a scatter plot of the data; identify increasing, decreasing, and constant associations; determine an equation for the line of best fit for each section of the scatter plot; and identify the domain for which each equation is the trend line.
There’s a grid at the bottom of the downloadable worksheet for graphing. Still, students should be encouraged to select the tool that works best for them: graphing on the worksheet, using technology, or some other creative way to represent the scatter plot. My students always loved creating scatter plots and other data representations on our classroom wall with sticky notes and other materials!
Let It Snow Resort: Linear Combinations (9th–11th Grade)
This fun, low-prep winter activity, also from MATHbook, is great for multiple high school grade levels, from Algebra I students ready for an extension to Algebra II students who will benefit from a review of systems of equations. It also promotes habits of mind such as modeling with mathematics and using appropriate tools strategically.
The Let It Snow Resort has two winter pricing specials. Both specials include meals and overnight accommodations, but is one deal better than the other? Students will create and use a system of equations to compare and draw conclusions about the specials and will end the activity by writing about their discoveries.
Our free worksheets are available for you to download, but also encourage students to choose the graphing tool or problem-solving method that works best for them. Whether they use pencil and paper or graphing technology, they’ll benefit from this exploration activity with real-life applications!
Six More Low-Prep Winter Math Activities
Ready for more? Check out this blog post for three winter math activities for middle school, and this blog post with three interesting winter math activities for multiple grade levels.
Do you have any fun math activities that you use before the holiday break? Join the LONG + LIVE + MATH Facebook community to share your ideas and discover new ones!
Before joining Carnegie Learning's marketing team in 2022, Karen spent 16 years teaching mathematics and social studies in Ohio classrooms. She has a passion for inclusive education and believes that all learners can be meaningfully included in academic settings from day one. As a former math and special education teacher, she is excited to provide educators with the latest in best-practices content so that they can set all students on the path to becoming confident "math people."
Explore more related to this authorIf 16 years of excited-for-break high school students taught me anything, it’s that I always need a fun, low-prep activity in my back pocket!
Karen Sloan, Teacher