Rivers twist and turn as they make their way to the sea. Why does this happen and how can this be explained mathematically? In this module we look at the geometry of meandering rivers. In the process we'll discover some fascinating numerical relationships.

Students will learn some basic concepts about the geophysics of how rivers form, but they will focus their analysis on what is called the sinuousity ratio. This is the ratio of the straight-line distance of the river and its meandering distance. This ratio reveals important characteristics of the river. Then, students will develop and examine geometric models involving circular arcs and segments to get a better understanding of the ratio. These models will first involve using a compass and straight edge to model a river. This is followed by an algebraic analysis.

This module is an excellent way of tying real world concepts to geometry and algebra. The real-world application is easy to understand and yet it reveals a wealth of math concepts to be explored.

Turn the Halloween season into an opportunity to do some math activities! In this module, you'll find a clever collection of arithmetic, algebra, and geometry activities.

1. Geometry activity: Watch a video about how spiders build webs and analyze the result geometrically. Students build polygon-based web designs in this hands-on activity.
2. Algebra activity: Going to the pumpkin patch? Use different sized pumpkins on this data-gathering activity, where students measure diameters and circumferences and graph the results. 
3. Arithmetic activity: Two addictive divisibility games based on whack-a-mole.

This interactive crossword puzzle tests knowledge of key terms on the topic of circles. Note: The download is a PDF version of this puzzle.

Circular Area and Circumference: Example 1. Finding the area of a circle, given the radius as a number.

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Circular Area and Circumference: Example 2. Finding the circumference of a circle, given the radius as a number.

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Circular Area and Circumference: Example 3. Finding the area of a circle, given the radius as a variable.

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Circular Area and Circumference: Example 4. Finding the circumference of a circle, given the radius as a variable.

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Circular Area and Circumference: Example 5. Finding the area of a circular region, given the values of the radii as numbers.

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Circular Area and Circumference: Example 6. Finding the area of a circular region, given the values of the radii as numbers and variables.

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Circular Area and Circumference: Example 7. Finding the area of a circular region, given the values of the radii as variables.

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Circular Area and Circumference: Example 8. Finding the area of a sector, given the values of the radius and central angle as numbers.

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Circular Area and Circumference: Example 9. Finding the arc length of a circle, given the values of the radius and central angle as numbers.

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Circular Area and Circumference: Example 10. Finding the area of a sector, given the values of the radius and central angle as variables.

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Circular Area and Circumference: Example 11. Finding the arc length of a circle, given the values of the radius and central angle as variables.

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Circular Area and Circumference: Example 12. Finding the area of a sector, given the values of the radius and central angle as variables and numbers.

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Circular Area and Circumference: Example 13. Finding the arc length of a circle, given the values of the radius and central angle as variables and numbers.

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Circular Area and Circumference: Example 14. Finding the area of a sector, given the values of the radius and central angle as variables and numbers.

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Circular Area and Circumference: Example 15. Finding the arc length of a circle, given the values of the radius and central angle as variables and numbers.

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Circular Area and Circumference: Example 16. Finding the area of a circular region, given the values of the radii and central angle as numbers.

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Circular Area and Circumference: Example 17. Finding the perimeter of a circular region, given the values of the radii and central angle as numbers.

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Circular Area and Circumference: Example 18. Finding the area of a circular region, given the values of the radii and central angle as variables.

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Circular Area and Circumference: Example 19. Finding the perimeter of a circular region, given the values of the radii and central angle as variables.

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Circular Area and Circumference: Example 20. Finding the area of a circular region, given the values of the radii and central angle as variables and numbers.

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Circular Area and Circumference: Example 21. Finding the perimeter of a circular region, given the values of the radii and central angle as variables and numbers.

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Circular Area and Circumference: Example 22. Finding the area of a circular region, given the values of the radii and central angle as variables and numbers.

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