jennifer.jasensky.com

Students will use translations, reflections, and rotations to move a shape across the plane.
Students will, by hand, create a Spanish tile pattern.
Students will use the mathematical language of translations to explain how they have made their tile pattern.

Prerequisite Knowledge:

Students will need to be able to perform translations, reflections, and rotations to squares, parallelograms, trapezoids, triangles, and hexagons. To get this knowledge, please see the “Information About Transformations” list of links on the page of my website called “Other Helpful Links.” Also, NCTM has a complete online tutorial on the subject at this link: http://www.illuminations.nctm.org/imath/912/sy_begin/index.html

Materials Needed:

The use of a computer lab or an Internet enabled computer projector and screen
A class set of worksheet 1 (or you can just ask the students to take out a piece of scratch paper)
A transparency of worksheet 1
An example pattern guide sheet
A class set of scissors
A class set of worksheet 2, made on card stock (not necessary, but it makes the shapes easier to trace around)
A class set (or more, for mistakes) of blank printer paper or construction paper
(Optional) A third-of-the-class set of worksheet 3

The Lesson:

Before class begins, make sure that your computer projector is ready to go, open up your Internet browser, and go to jennifer.jasensky.com and click on whichever pattern links you like best. (If you decide to take students to the computer lab to view the links individually, the projector is not necessary. Just have the students find jennifer.jasensky.com and view the pictures on their own to get an idea of what they will be creating and to get ideas for their own creations. This can be done prior to the rest of the lesson.)

First, explain to the students what they will be creating that day. Then show them examples of the pictures from the website. Show them as many or as few as you would like. As you show them pictures of the patterns, remind them of the work they have previously done with translations, reflections, and rotations so that they will connect that information to what they will work with today. Then pass out a copy of worksheet 2 to each student, along with a pair of scissors. Have the students cut out the numbered shapes, throw the scraps away, and return the pair of scissors.

Then pass out a copy of worksheet 1 to each student. Give the students an overview of what they will be doing that day, as far as using various shapes to create their own patterns. Then explain to them that on worksheet 1 they will be copying what you do on the overhead to experience the process of creating a pattern like the ones they saw from the computer. Let them know that their homework assignment will be to color the pattern neatly in any way that they choose and bring it back on the assigned due date.

Using your transparency and your example pattern guide sheet, recreate the design, explaining along the way the different geometric transformations you are using to create it. Emphasize the importance of tracing neatly, with pencil (they can later go over the design with a marker if they choose). Each time you switch shapes, tell the students which shape you are using by its number. When you have finished, have each student take out a scrap piece of paper, or just have them turn over worksheet 1. Explain to them that they will be using that piece of paper to practice making their own design. Ask them to spend a few minutes figuring out which shapes they will use, and encourage them to try to use at least 2 different shapes. Have them trace out at least 3 or 4 repetitions of the design that they want to use.

When they have finished with their “trial” design, have the students show it to you. After you have made sure that there are no problems with their design, give them a piece of plain printer or construction paper. Tell them that they will start over again on the new piece of paper to make their final and complete copy of their design. Walk around the classroom and help those who are having difficulty creating a design. If you want to, offer extra credit for a job done especially well on the project. It is optional if you want the students to list the numbers of the shapes they used on the back of their projects. Have them write their names and any additional information on the back of the project. These projects make great decorations for classrooms.

As an optional extension to the project, you can assign worksheet 3, which is a small writing assignment which asks them to explain each step of their process.