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Hands-on math activities using Michigan's Great Lakes coastline. Aligned to Michigan Common Core standards for grades 6 and 10.

6th GradeMath / Earth ScienceMeasurement & Geometry

Measuring Michigan's Coastline — Grade 6

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Use rulers, scale, and perimeter concepts to estimate the length of Michigan's Great Lakes coastline. Students apply unit conversion and proportional reasoning to real map data.

45–60 minutes
4 learning objectives
5 questions

Materials Needed

  • Printed Michigan outline map with scale
  • Ruler
  • Calculator
  • Graph paper (optional)

Learning Objectives

  • Use a map scale to convert map measurements to real-world distances
  • Estimate the perimeter of an irregular shape (Michigan coastline)
  • Understand why coastline length depends on the unit of measurement used
  • Compare estimates made with different step sizes

Worksheet Sections

Michigan has the longest freshwater coastline of any state in the United States — over 3,200 miles! It borders four of the five Great Lakes: Lake Superior, Lake Michigan, Lake Huron, and Lake Erie. But here's a puzzle: how do scientists actually measure a coastline? It turns out the answer depends on how you measure it. In this worksheet, you'll explore that question using math.

Teacher Notes

Students should have access to a printed or digital outline map of Michigan with a clear scale bar. Graph paper can help students keep track of segments. Encourage students to compare their estimates with a partner — different step sizes will yield different results, which is the key learning moment.

10th GradeMath / Environmental ScienceGeometry, Statistics & Fractals

Fractal Dimension & Coastline Measurement — Grade 10

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Apply logarithms, power functions, and statistical reasoning to investigate the fractal nature of Michigan's coastline. Students collect measurement data at multiple scales, plot log-log graphs, and calculate the fractal dimension of the coastline.

60–90 minutes
5 learning objectives
6 questions

Materials Needed

  • Michigan coastline map with grid overlays at 3 scales
  • Graphing calculator or Desmos
  • Graph paper
  • Ruler

Learning Objectives

  • Apply the box-counting method to estimate fractal dimension
  • Collect and organize measurement data across multiple scales
  • Plot data on a log-log graph and interpret the slope
  • Connect the mathematical concept of fractals to real-world coastline measurement
  • Evaluate the limitations of mathematical models in environmental science

Worksheet Sections

In 1967, mathematician Benoit Mandelbrot asked: 'How long is the coast of Britain?' His surprising answer: it depends entirely on the length of your measuring stick. As you use smaller and smaller units, the measured length grows without bound — because coastlines are fractal. A fractal is a shape that shows self-similarity at different scales: zoom in and you see the same irregular pattern repeating. Michigan's Great Lakes coastline is a natural fractal. In this worksheet, you'll use logarithms and regression to calculate its fractal dimension — a number that describes how 'rough' or 'complex' the coastline is.

Teacher Notes

Students should be comfortable with logarithms and scatter plots before this activity. Graphing calculators or Desmos are recommended for the log-log plot and regression. The extension question (Q6) is appropriate for pre-calculus students. Published fractal dimensions for Great Lakes coastlines range from approximately 1.15 to 1.35.