Fractal Math Activities

Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

Working on fractals with your students? This lesson includes several step-by-step activities you can do with older students to reinforce concepts related to fractals.

Educate to Last

Math teachers sometimes struggle with how to teach concepts in a way that lets students know how important they are to their real life. Sound familiar? The fact is, we use mathematical principles in our world almost every day. The task for educators like us is to teach students basic skills along with the how to apply them and why they're important.

When teaching students about fractals, we want students to know what they are, why they're learning about them, and how these concepts will translate to them in their lives. The best way to accomplish these three important goals is to use activities to teach and reinforce key vocabulary and ideas. The good news is fractals appeal to a wide audience; they're practical, visual, and (some may even say) fun. With these cross-curricular ideas, you'll have students hooked from the start.

A Fractal Coast

This activity can be introduced and used in conjunction with social studies lessons on geography, particularly coastlines and mapping. Students will need a basic understanding of fractals before starting the lesson. Plan on one 45-60 minute class for this activity.


  • Pencils
  • Paper
  • Rulers
  • Maps


  • Share a map with students and view as a whole class.
  • Zoom in on a coastline (choose one in your area to connect and engage students) and ask:
    • How can we measure this coastline?
  • Allow students to discuss answers in partner-pairs, then lead a conversation about methods.
  • Set aside maps for later and distribute paper and rulers.
  • Have students turn their papers sideways and draw a nine-inch line horizontally on their papers. Ask them to divide the line into three equal parts and erasing the middle section, leaving the two side sections intact.
  • Next, instruct students to connect their two line segments with an upwards 'v' shape taking up the center section. Discuss how the pattern is now broken into four sections.
  • Make more fractals by having students divide each of the four sections into a new upwards 'v' shapes. How many sections are there now?
  • Instruct students to repeat this exercise two more times independently. How many sections do they now have?
  • Ask students to return to the map and set their fractal side-by-side. How are the coastline and fractal similar?
  • Now ask students to measure the coastline using rulers by breaking into sections as they did with the fractal activity.
  • Finish by having students explain to a partner how fractals and coastlines are the same.

Three-Dimensional Fractals

Students love to get busy and to eat. This activity combines these two loves into one fun way to explore fractals. They'll be using their understanding of fractals in cooperative problem-solving and critical-thinking groups. Allow one typical 45-60 minute class period for this activity.


  • Mini-marshmallows (dry out for a day before the lesson)
  • Toothpicks
  • Protractors
  • Colored pencils

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