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Warm-Up

Warm-Up. Copy the following table and find N. OBJECTIVE Shapes and Designs 3.3. I will decide which regular polygons will tile by themselves or in combinations using information about interior angles. LAUNCH 3.3.

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Warm-Up

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  1. Warm-Up Copy the following table and find N.

  2. OBJECTIVEShapes and Designs 3.3 I will decide which regular polygons will tile by themselves or in combinations using information about interior angles.

  3. LAUNCH 3.3 Which of the regular polygon shapes (Shapes A-F) did we learn would tile a surface (fit together so that there are no gaps or overlaps) by themselves?

  4. LAUNCH 3.3 How can we tell for sure that a shape, like these hexagons, fits exactly around each point in a tiling? We know the fit looks good, but how can we use mathematics to tell for sure?

  5. EXPLORE 3.3 • In Problem 1.3 you discovered that only equilateral triangles, squares, and regular hexagons could be used to tile a surface. • Using the shapes set, form three separate tilings with Shapes A, B, and D. 1) Explain why copies of the shape fit neatly around a point?

  6. EXPLORE 3.3 • In Problem 1.3 you also discovered that regular pentagons, regular heptagons, and regular octagons could NOT be used to tile a surface. 1) Why do you suppose that copies of the shapes do not fit neatly around a point?

  7. EXPLORE 3.3 • Working with your partner, List as many tilings using combinations of two or more shapes from your shapes sets. Sketch your results. 1) What do you observe about the angles that meet at a point in the tiling? 2) How many degrees are in all of the angles around this vertex point? 3) What would we expect the angle sum around a vertex to be?

  8. SUMMARY 3.3 The sum of the angles that meet at a point in a tiling is ALWAYS 360°

  9. SUMMARY 3.3

  10. ACE PROBLEMS 3.3 Page 64 (11 and 12)

  11. CLOSURE 3.3 Explain why all of the tilings you created with the shapes today were created without gaps or overlaps.

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