1. G.5.C Use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations

2. What is a Tessellation? A Tessellation is a collection of shapes that fit together to cover a surface without overlapping or leaving gaps.

3. Tessellations in the World Around Us: Brick WallsFloor TilesCheckerboards HoneycombsTextile Patterns Art Can you think of some more?

4. Are you ready to learn more about Tessellations? Symmetry in Tessellations CLICK on each topic to learn more… Once you’ve explored each of the topics above, CLICK HERE to move on.CLICK HERE Regular Tessellations Semi-Regular Tessellations

5. Regular Tessellations Regular Tessellations consist of only one type of regular polygon. A regular polygon is a shape in which all of the sides and angles are equal. Some examples are shown here: TriangleSquarePentagonHexagonOctagon

6. Does a Triangle Tessellate? Regular Tessellations The shapes fit together without overlapping or leaving gaps, so the answer is YES.

7. Does a Square Tessellate? Regular Tessellations The shapes fit together without overlapping or leaving gaps, so the answer is YES.

8. Does a Pentagon Tessellate? Regular Tessellations Gap The shapes DO NOT fit together because there is a gap. So the answer is NO.

9. Does a Hexagon Tessellate? Regular Tessellations The shapes fit together without overlapping or leaving gaps, so the answer is YES. Hexagon Tessellation in Nature

10. Does an Octagon Tessellate? Regular Tessellations The shapes DO NOT fit together because there are gaps. So the answer is NO. Gaps

11. Regular Tessellations As it turns out, the only regular polygons that tessellate are: TRIANGLES SQUARES HEXAGONS

12. Semi-Regular Tessellations Semi-Regular Tessellations consist of more than one type of regular polygon. (Remember that a regular polygon is a shape in which all of the sides and angles are equal.) Hexagon & Triangle Octagon & Square Square & Triangle Hexagon, Square & Triangle Once you’ve explored each of the semi-regular tessellations, CLICK HERE to move on.CLICK HERE

13. Semi-Regular Tessellations Hexagon & Triangle

14. Semi-Regular Tessellations Octagon & Square Many floor tiles have these tessellating patterns. Look familiar?

15. Semi-Regular Tessellations Square & Triangle

16. Semi-Regular Tessellations Hexagon, Square, & Triangle

17. Translation Reflection Glide Reflection Symmetry in Tessellations The four types of Symmetry in Tessellations are: CLICK on the four types of symmetry above to learn more. Once you’ve explored each of them, CLICK HERE to move on.CLICK HERE Rotation

18. Symmetry in Tessellations Rotation To rotate an object means to turn it around. Every rotation has a center and an angle. A tessellation possesses rotational symmetry if it can be rotated through some angle and remain unchanged. Examples of objects with rotational symmetry include automobile wheels, flowers, and kaleidoscope patterns. CLICK HERECLICK HERE to view some examples of rotational symmetry. Back to Symmetry in Tessellations

19. Rotational Symmetry

21. Back to Rotations

22. Translation To translate an object means to move it without rotating or reflecting it. Every translation has a direction and a distance. A tessellation possesses translational symmetry if it can be translated (moved) by some distance and remain unchanged. A tessellation or pattern with translational symmetry is repeating, like a wallpaper or fabric pattern. Symmetry in Tessellations CLICK HERECLICK HERE to view some examples of translational symmetry. Back to Symmetry in Tessellations

23. Translational Symmetry Back to Translations

24. Reflection To reflect an object means to produce its mirror image. Every reflection has a mirror line. A tessellation possesses reflection symmetry if it can be mirrored about a line and remain unchanged. A reflection of an “R” is a backwards “R”. Symmetry in Tessellations CLICK HERECLICK HERE to view some examples of reflection symmetry. Back to Symmetry in Tessellations

25. Reflection Symmetry

26. Back to Reflections

27. Symmetry in Tessellations Glide Reflection A glide reflection combines a reflection with a translation along the direction of the mirror line. Glide reflections are the only type of symmetry that involve more than one step. A tessellation possesses glide reflection symmetry if it can be translated by some distance and mirrored about a line and remain unchanged. A real world example is footsteps! CLICK HERECLICK HERE to view some examples of glide reflection symmetry. Back to Symmetry in Tessellations

28. Glide Reflection Symmetry

29. Back to Glide Reflections