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Geometric Patterns and Graphs Exploration at Ehime University - Math Lesson Example

Explore geometric patterns and graph interpretation in a math lesson at Ehime University's Fuzoku Junior High School. Sunada Sensei teaches students to count dots, analyze geometric shapes, and understand mathematical equations. Discover how to generalize geometric patterns, compare with numerical patterns, and represent equations visually. Use tables, graphs, and equations to describe the changing areas of triangles as points move in rectangles. Analyze various geometric properties such as perimeter, height, width, and more. Learn through interactive activities and explore mathematical concepts deeply.

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Geometric Patterns and Graphs Exploration at Ehime University - Math Lesson Example

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Presentation Transcript

  1. Patterns and Tables and Graphs: Oh My!!!日本スタイル

  2. Ehime University Fuzoku Junior High School

  3. Me with Student Teachers

  4. Me with Cooperating Teachers

  5. Sunada Sensei teaching a class

  6. How many dots are in the figure below?

  7. How did you count the dots? • Geometrically how did you see the way to count them? • What mathematical sentence would describe how you saw and counted them?

  8. Is there a geometric representation of this equation?

  9. How many dots would there be if there were n dots on a side?

  10. Generalizing a geometric pattern is different from generalizing a numerical pattern (and easier).

  11. All of these generalizations are equivalent.

  12. In rectangle ABCD, point P moves from B to A through C and D at a rate of 1 cm per second. Using a table, graph and equation, describe the area of triangle ABP as it changes over time.

  13. Describe the area of triangle ABP as it changes over time. GSP

  14. Area versus time in a table

  15. Area versus time in a graph.

  16. Area versus time in an equation

  17. In the figures below, as the step changes, ________ also changes.

  18. Perimeter Height Width Size of enclosing rectangle # of “toothpicks” # of interior toothpicks # of intersections # of corners # of convex corners # of squares # of diagonals leftover space # of segments # of parallel lines Length of longest line # of rectangles

  19. Using a table, graph and equation, describe the change.

  20. Left over Space

  21. Change in left over space.

  22. Total Blocks (Area)

  23. Number of inside right angles.

  24. Number of toothpicks

  25. Number of toothpicks II

  26. Number of pairs of parallel lines.

  27. In rectangle ABCD, point P and Q move from B to D through C and A respectively at a rate of 1 cm per second. Using a table, graph and equation, describe the area of triangle BPQ as it changes over time.

  28. Describe the area of triangle BPQ as it changes over time. GSP

  29. Area versus time in a table

  30. Area versus time in a graph.

  31. Area versus time in an equation.

  32. Thank Youどもありがとうございます Powerpoint presentation on http://www.mathed.byu.edu/~peterson

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