Exploring Tessellations

Designed by:  Anna Messer, Bradley Elementary

1) CORE CURRICULUM OBJECTIVE:  Explore, scale, perspective and tessellation. (5GS6-3)

GRADE LEVEL: Five      SUBJECT:  Math (Geometry and Spatial Sense)

2) OVERVIEW: Students will use the information they already know about polygons to explore the concept of tessellation (tiling). They will practice creating tessellations (tilings) using pattern blocks or other shape manipulatives. They will search the school grounds, use the library resources, and navigate the internet for examples of tessellations. The final activity will be the construction of a paper quilt, where each individual square is tessellated using one or more of the following polygons: triangle, hexagon, rectangle, rhombus/parallelogram, square, or trapezoid.

3) FOCUS/ESSENTIAL QUESTION(S): Where in the environment can we find examples of different polygons, and what are they used for?  How do polygons fit together to create tessellations?  Where else can we find examples of tessellations in our world?

4) TIME FRAME: three, fifty minute class periods

5) RESOURCES/MATERIALS:

TEACHER = chart paper, various books on tessellations (quilt books, photography books, interior design books, M.C. Escher books..), large cut-outs of various polygons, pattern blocks(or other polygon manipulatives), and markers.

STUDENTS = pattern blocks (or other polygon/shape manipulatives), computer/internet access, construction paper, crayons, markers, pencils, tape, rulers, and notebook paper.

6) CULMINATING ASSESSMENT: Each student will construct a 5”X5” quilt square that is tessellated using one or more of the following polygons: triangle, hexagon, rectangle, rhombus/parallelogram, square, or trapezoid.  There should not be any gaps or overlaps in the tessellation.  After the squares are completed, they will be taped together to form a class quilt. The students will be assessed informally using the following rating scale:

Quilt Square - Tessellation Assessment

Name:  _______________________________________    

Date:  __________________

1. The quilt square measures 5”X5” = needs improvement        satisfactory

2. The quilt square is tessellated using 1 or more of the polygons listed:

triangle, hexagon, rectangle, rhombus/ parallelogram, square, or trapezoid.

= needs improvement         satisfactory

3. The tessellation does not contain any gaps or overlaps in it’s design. 

=  needs improvement     satisfactory

4.      The tessellation is colored neatly.  

=   needs improvement      satisfactory

5.      Overall appearance of the square 

=     needs improvement     satisfactory

7)       INSTRUCTIONAL ACTIVITIES:

A.) Introduce the lesson by displaying the large, construction paper
shapes on the board.  Ask the students what they notice about these shapes.  If they do not come up with the term polygon on their own, review the definition of a polygon (a closed plane figure bounded by straight lines) with them.  Lead in with the first focus question, give them adequate time to discuss it, and write their responses on chart paper.

B.) Form a large circle on the floor with the class.  Take your set of pattern blocks to the circle and introduce the students to the concept of tiling (or tessellation).  Explain that polygons can be used to tile a surface, without any gaps or overlaps showing.  Demonstrate this concept using the square pattern blocks in the center of the circle so everyone can see.  Lead in with the second focus question and discuss. Ask the students to think about all of the shapes they know of and then have them predict which ones will tessellate and which ones will not. (For example, an oval, circle, etc. would not tessellate.)  Write their predictions on chart paper and then test them to see which ones are correct.

C.)   Have the students return to their seats and pass out the pattern blocks, so that every child has several to work with.  On their desks, have them practice tessellating the shapes. Once they get the hang of it, let them try tracing their tessellations on notebook paper.  When they are finished, review what they learned in today’s lesson.  (END OF DAY 1)

D.)   Prior to the beginning of this lesson, display the different books that you collected on tessellations around the room.  Ask the students to recall what we learned in yesterday’s lesson.  Have them look around the room to see if they can find any examples of tessellations (examples may include a tiled floor, bricks that make up a wall, etc.).  Lead in with the third focus question and give them time to discuss it.  Have each child choose a person to work with, and then let the pairs choose a book that you have displayed in the room to look at.  Ask them to list on notebook paper all of the different examples of tessellations that they found within their books.  When they are finished, call on different pairs to discuss with the class the tessellations that they found.

E.)   Break the class up into three large groups and have them begin a search for examples of tessellations using the following three resources: the library, the internet, and the school grounds.  Rotate the groups every 10 minutes so that there is one group using each of the resources at all times.  They will need to record their findings on notebook paper.  When they are finished, bring them back together and make a class list on chart paper of all of the different examples that they found and discuss them.  (END OF DAY 2)

F.)   Prior to the beginning of the lesson, write the names of the following polygons on the board: triangle, hexagon, rectangle, rhombus/ parallelogram, square, and trapezoid. Review all of the things we have learned about tessellations over the past two days with the class.  Explain that today they will apply all of their knowledge on the subject to help in the creation of a class quilt.  Pass out the construction paper, crayons, markers, pencils, and rulers to the students.  Instruct them on the goal of this lesson: to create a 5” x 5” square that is tessellated using one or more of the polygons listed on the board. Pass out an assessment sheet to each student so that they know exactly what is expected from them.  Give them adequate time to construct their squares, and remind them to write their names on the back of their square.

G.)   When they are finished, collect the assessment sheets and the quilt squares.  Work together as a class, and decide how to assemble the quilt.  Once all of the squares are in place, tape them together.  Fill out the assessment sheet on each child’s square and keep it for your records. Hang the quilt in the hallway so that everyone can enjoy it.                  

(END OF DAY 3)