LESSON PLAN

Name:  Itzel Suárez

Title of lesson:  Tessellations & Floors

Grade level:  10th grade Geometry

Length of Lesson:  1 class period (50 minutes)

Sources of the lesson:                                                                                                         

Interactive:  Geometry in Tessellations http://www.shodor.org/interactivate/lessons/GeometryTessellation/

National Library of Virtual Manipulatives:  Tessellations                                                                      http://nlvm.usu.edu/en/nav/frames_asid_163_g_4_t_3.html?open=activities

Interactive:  Tessellations—Geometry and Symmetry                                                             http://www.shodor.org/interactivate/lessons/Tessellations/

TEKS addressed:

 

I.  Overview:  This lesson allows students to examine tessellations and their geometric properties. The activity and discussion may be used to develop students' understanding of lines, planes, angles, and polygons.

II.   Performance or learner outcomes

Upon completion of this lesson, students will:

III. Resources, materials and supplies needed

 

Five-E Organization

Teacher Does                                                             Student Does

Engage: (10 mins.)

Show students works of art on the projector that involve tessellations (MC Escher, Indian art, etc.) and ask them what all these have in common. 

Has anyone ever heard of M. C. Escher?

Escher was a famous artist who enjoyed twisting perceptions of reality. He was responsible for works such as Reptiles, Horseman and many more that incorporated the use of tessellations.

Question :

How does this relate to your dream home ?  Is there any way you can use these to help you in the building of your home ?

 

 

Students will say that the shapes repeat themselves, that the drawings are colorful, that they are pretty, etc. 

Not many students will have heard of MC Escher. 

Expected student answers:

You can create a floor full of tessellations.  It creates a repeated pattern.

Evaluate:  The teacher should call on various students to say what they see in the art and how they think the art relates to the building of their home.

Teacher Does                                                       Student Does

Explore: (20 mins.)

Open the browser to the Tessellate! (http://www.shodor.org/interactivate/activities/Tessellate/) page in order to demonstrate this activity to the students.

Show students how to select one of the regular polygon shapes and click the "tessellate" button to see it displayed.

Ask students to count the number of sides of the polygon.

Record the number of sides in the data table , and help students complete the rest of the information for the shape the teacher has chosen to demonstrate.

Try another shape, letting the students take the lead in completing the data table for this new shape.

Select the third regular polygon, observe what it looks like in the Tessellate activity, and then complete the data table for this shape.

 

 

Students will explore the Tessellate! applet. 

Students will select one of the regular polygon shapes and click on the “tessellate” button.

Students will count the number of sides of the polygon.

Students will record the number of sides in the data table for both the 3 shapes.

Evaluate:  The teacher should walk around and make sure all students are on task and participating in the activity.

Teacher Does                                                    Student Does

Explain: (10 mins.)

Follow-up by having the students write a concise definition for a regular polygon tessellation. Have them expand this definition to describe a tessellation made from non-regular polygons.

polygon

A closed plane figure formed by three or more line segments that do not cross over each other

regular polygon

A polygon whose side lengths are all the same and whose interior angle measures are all the same

tessellation

A tessellation is a repeated geometric design that covers a plane without gaps or overlaps

Encourage students to determine a pattern among the regular polygons that they work with. Ask the students to predict which regular polygons will and will not tessellate and why.

After the students have determined which regular polygons tessellate, discuss the types of symmetry present in tessellations.

Ask students what the data table would look like for 5, 7 and 8-sided polygons.

Help students analyze the data and draw a conclusion about which shapes will tessellate the plane and why.

 

Students will listen to the definitions of polygon, regular polygon, and tessellation. 

Students will try to determine a pattern among the regular polygons.

Students will predict which regular polygons will and will not tessellate.

Students will work out the pattern to predict as to what a data table for 5, 7, and 8-sided polygons will look like.

 

Evaluate:  The teacher listens attentively to the students ideas for predicting the pattern as to what the table for 5, 7, and 8-sided polygons looks like.  The teacher walks around as the students try to work out the data table.

                        Teacher Does                                                  Student Does

Extend / Elaborate: (10-15 mins.)

Lead a discussion about tessellations in the world. Ask students to identify tessellations that they see in their daily lives and in nature.

Question :

Now can you see how this relates to your house ?  What can you use this concept on ?

Have them play around with the rest of the shapes on the NLVM : Tessellations applet to see what kind of floor tiling they would like for their houses. 

Students will discuss and identify the type of tessellations they see in the real world.

Expected answers:

You can make your floors tessellations.

Students work on ideas for their floor.

Evaluate:  The teacher should make sure that he/she gets enough discussion out of all students by asking probing questions on where students can see tessellations in the real world.  Teacher should listen attentively as students express what they have learned.  Teacher should go around to see what kind of tessellations students are coming up with for the creation of their floors. 

 

 

 

 

 

 

 

Regular Polygon Tessellations Data Table

 

Any point on a polygon where two adjacent sides meet is called a vertex.  The sum of the interior angles of all of the polygons that meet at a vertex is 360 degrees.  How can we use this fact and the interior angle measure of each polygon to determine whether a regular polygon will tessellate a plan?  Which regular polygons will tessellate a plane?  Which will not?

 

Polygon

Number of Sides (n)

Length of a side

Interior Angle Measure (180(n-2)/n)

Triangle

 

 

 

Rectangle

 

 

 

Hexagon

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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