Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Quadrilaterals and Polygons

9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 6 from the EXPLORATIONS Book:
Geometric Investigations on the Voyage 200 with Cabri

## Tessellations and Tile Patterns

#### Activity Overview

Students understand that a tessellation is covering of a plane with a pattern of figures so there are no overlaps or gaps. They draw quadrilaterals and triangles and explore monohedral, dihedral, and trihedral tessellating patterns.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print page 25 from the attached PDF file for your class
• #### During the Activity

Distribute the page to the class.

• Draw a regular polygon
• Reflect the polygon across its own sides and observe the pattern
• Observe that triangles, squares, and hexagons tesselate a plane with monhedral pattern
• Note that dihedral tiling patterns are formed by a regular pentagon together with a rhombus, a regular pentagon with a heptagon, a regular octagon with a square, and a dodecagon with a triangle
• Drag the original figure around the screen and note that the pattern remains unchanged
• Use transformational tools to check if isosceles or scalene right triangles always tessellate the plane
• Determine the methods by which a plane can be tessellated by a rectangle
• Experiment with ways to tessellate the plane with a trapezoid
• Understand that any quadrilateral tessellates the plane by a 180° rotation about the midpoint of its sides
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary