Designed by:  Anna Messer, Bradley Elementary  

Grade Level: Five      Subject:  Math (Geometry and Spatial Sense)

1) CORE CURRICULUM OBJECTIVE:  identify and demonstrate transformations of geometric figures that are the results of slides (translations), flips (reflections), turns (rotations), or glide reflections.  (5GS3-2)

2) OVERVIEW: Students will tessellate a ceiling tile using a slide (translation) or a turn (rotation) template that they constructed in class.  They will then visualize and design a picture within the slide (translation) or turn (rotation) and paint it to create a repeating picture or pattern that does not have any gaps or overlaps.  When completed, the ceiling tiles will be hung back up and displayed for the whole school to enjoy.

3) FOCUS/ESSENTIAL QUESTION(S): If we transform the polygons that we use when tiling into new shapes, will they tessellate? 

4) TIME FRAME: five, fifty minute class periods

5) RESOURCES/MATERIALS:

TEACHER = sample templates of slides and turns, overhead projector, 1 ceiling tile for each group or pair of students, 20 (or more) bottles of acrylic craft paint (Apple Barrel, Folk Art, etc.) - in various colors, paint brushes (all sizes), paper towels, newspapers, cups for water, and a set of pattern blocks (or any polygon manipulatives).

STUDENTS = 3 x 3 index cards, heavy duty paper (poster-board, oak-tag, etc.), scissors, tape, rulers, and a pencil.

6) CULMINATING ASSESSMENT: Each pair or group of students will create a template of either a slide (translation) or a turn (rotation) that will be used to tessellate a ceiling tile.  The tile will then be painted with a design of their choice.  The tessellation should not have any gaps or overlaps.  The following rubric will be used to assign a grade to each group's tessellated ceiling tile.  The scale will be based on the total points earned for the whole group.  A copy of the rubric should be passed out and explained to each student prior to the beginning of the final project.

TESSELLATED CEILING TILES
ASSESSMENT SHEET

Name(s) _________________________________________________

Date _________________  

Type of transformation used_________________

100 Points = A 

90 Points = B

80 Points = C

70 Points = D

60 Points or Below = F        

10 Points = The template is constructed by using a slide (translation) or a turn (rotation).

10 Points = The template used successfully tessellates the plane of the ceiling tile.

10 Points = The template is traced onto the tile without leaving any gaps or overlaps.

10 Points = A design is created inside of the slide or turn template.

10 Points = The design is repeated throughout the entire tessellation.

10 Points = The tessellation is painted neatly, using a variety of different colors.

10 Points = The ceiling tile tessellation is completed in the allotted amount of time.

10 Points = The ceiling tile's overall appearance is neat and attractive.

10 Points = All group members contributed equally to the completion of the tessellation.

10 Points = The tessellation is free from any apparent mistakes (tracing of the template, design, painting, etc.).

Total Points Earned_____________  Final Grade______

7) INSTRUCTIONAL ACTIVITIES:

A.) Introduce the lesson by asking the focus/essential question listed above.  Give the students adequate time to discuss how polygons tessellate and how we could transform them to make new shapes.  Display several different transformed polygon templates of slides (translations) and turns (rotations) on the overhead projector.  Ask the students to look at the characteristics of each one, and list their attributes on the board.  Have them predict if they think the templates will tessellate.  Test their predictions on the board by tracing the templates.

B.) Inform the class that there are two different types of transformations that we are going to learn about: slides (translations) and turns (rotations).  Both of these can be done using polygons; however, we are going to create our own shapes by "cutting and pasting".  Post the definitions on the board for each transformation as you begin instruction on how to create them.  Teach them in the order that they are listed below.

Slide (Translation) = the action of sliding a figure in any direction.

-Begin instruction by using the overhead to demonstrate how to tessellate a polygon using a slide.

-Number the corners of the shape that is on the overhead.

-Place another shape of the same polygon over the original one.  Slide the one on top beside the original one and number the corners.  Continue using 3 more shapes.

-Review the steps you took with the class: 1. Line up the edges, 2. Lift the shape, 3. Slide it beside the original one, 4. Write down the corresponding numbers, and 5. Repeat.

-Pass out pattern blocks to each student and let them practice on the planes of their desks. 

-Call on a few students to come up to the overhead and demonstrate how they created a slide with their shape.  See diagram below for an example.

-Once the students grasp the concept of how to create a slide using a polygon, introduce to them how to transform the polygon into a new shape.  Demonstrate this technique while you explain it.

-Pass out 2 index cards to each student, a pair of scissors, a ruler, and a pencil.  Have them color one side of the index card so they will not confuse the front and with the back.

-Draw a simple design from one corner of the index card to an adjacent corner. (Do Not Draw A Diagonal Design)

-Use your scissors to cut on the design line (This will create a "slice" in your index card).  You should end up with two pieces.  Do not make any more cuts and do not trim any edges.

-Slide the design ("slice") you cut out across the sheet to the opposite side (from where you cut) and tape the straight edges together.  Do not attach it to an adjacent edge and do not overlap the edges at all when you tape them  together.  The corners of the cut-out design ("slice") and the original index card should match exactly.  If you want, you may repeat the steps above for the other two sides.  Both sides should either be colored or plain.  If you have 1 colored and 1 plain side taped together, it is wrong.

-Pass out a piece of construction paper and let the students practice tessellating it using their slide template.

 C.) Turn (Rotation) = the action of turning a figure around a point or vertex.

-Begin instruction by using the overhead to demonstrate how to tessellate a polygon using a turn.

-Number the corners of the shape (a triangle is a good one to start with).

-Explain that you are going to rotate the shape around one of its points, so that when you have done this correctly, the sum of the angles around any point will equal 360(.  If it does not equal 360(, the shape will not tessellate.

-Review the steps you took with the class: 1. Place the polygon on the
plane and trace it, 2. Rotate it one time to the right and trace it, 3. Rotate it one more time to the right and trace it, 4. Measure the three angles around any one point and add them up, and 5. If they equal 360(, you have correctly tessellated the plane.

-Pass out pattern blocks to each student and let them practice on the planes of their desks.

-Call on a few students to come up to the overhead and demonstrate how they created a slide with their shape.

-Once the students grasp the concept of how to create a turn using a polygon, introduce how to transform a polygon into a new shape.  Demonstrate this technique while you explain it.

-Pass out 2 index cards, a pair of scissors, a ruler, and a pencil to each student.  Have the students color one side of the index card, so that they will be able to tell the front from the back.

-Cut the index card to create a perfect square. They should use the ruler to measure the square to make sure all four sides are the same.

-Cut a design ("slice") from corner to corner of the square. 

-Instead of sliding the design ("slice"), rotate it at its end point to an adjacent side of the square, not an opposite side.

-Tape the design piece on, and make sure that it matches the straight edge without any gaps or overlaps.  Everything should line up exactly, corners and edges.

-Pass out construction paper and let the students practice tessellating their turn template.

D.) Ask the students if they have any questions on creating a slide (translation) or a turn (rotation). Spend some time reviewing if necessary. If there are no problems, explain the final project to the class (tessellating a ceiling tile).  Pass out the rubrics and go over the criteria that they will be graded on.

E.) Break the students up into pairs or groups of four.  Pass out the ceiling tiles, paint, newspapers (to lay the tiles on), paint brushes, paper towels, cups of water, rulers, oak-tag (heavy paper for the template), scissors, tape, and pencils.

F.) Have each group create a shape template using either a slide or a turn.  Once they have tested the template to make sure it tessellates, they may begin tracing it onto the ceiling tile.  Remind them that there should be no gaps or overlaps in their tessellation. When they finish tessellating the tile, they need to create a design inside of each shape and begin painting.  When all of the painting is complete, allow the tiles to dry.  Spray on a clear sealer or some type of protective coating. Make sure each group member writes their name on the back of the tile.

G.) After you have collected the rubrics and assessed each group, hang the tiles back up for the whole school to enjoy.