This lesson is designed to guide teachers through helping students recreate the works of the artist M.C. Escher using the computers while they also cover many of the learning requirements for tesselations in Math. Translations and reflections lend themselves really well to computer use as students can easily cut and paste and manipulate shapes without having to worry about paper and scraps.
It is expected that students will:
- C6 perform a combination of translation(s), rotation(s) and/or reﬂection(s) on a single 2-D shape, with and technology, and draw and describe the image
- C7 perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations
1. View the work of M.C Escher at:
INTERNET SITES ON ESCHER:
-http://www.worldofescher.com/gallery/ – This is another great place to view his works with more information about each piece. Also click on Home to learn a bit more about Escher.
–http://www.mathacademy.com/pr/minitext/escher/ – This site has explanations and information about Escher. The reading level may be difficult.
–http://www.nga.gov/collection/gallery/ggescher/ggescher-main1.html – This is a tour of this work and is easy to use.
2. In class discuss the works of M.C. Escher in terms of the use of the elements of principles and design:
-How does Escher use space? What effect does this produce?
-How are these works coloured? What sort of mood does this create?
-What type of materials is he using and how is this different than the other artists that we have been looking at?
-Talk about how Escher is a mathematician and an artist and how this comes out in his work.
3. In Math do some lessons on Tesselations (as you will be covering most of the requirements in the computer lab, you will only need to go over the terms).
4. In the computer lab students can gather information about Escher and tesselations using the following sheets:
5. In the computer lab have students open up Paint or Paintbrush (if you have Tesselmania then you may choose to have students use this program for that, see instructions for the program).
Click for Paint Brush instructions in MSWord or Adobe Acrobat (PDF).
a. Students must first create the shape that they wish to start with. For the first time, have them draw a square.
b. Now have students draw a new line to replace one of the sides:
Students can now erase the old line on that side of the shape.
c. Select a scissors tool at the top of the tools and draw a loop or square around the line that you just created.
d. Press the CTRL button down on your keyboard and hold it down while you click and drag a copy of the new line over to the other side:
Then erase the old line.
Tell students that these are called slides or translations.
e. Repeat this procedure with the top and the bottom. It is really important that students don’t allow any lines to cross or overlap. A shape like this for example:
Will not work.
This shape will work:
f. Students can now decorate the shape if they wish, or they can go on to the next step.
g. Select the scissors tool at the top again and use it to draw a shape around your shape.
h. Press CTRL on the keyboard and click and drag the copy of your shape so that it fits in the other shape:
Students can continue to do this until their whole screen is filled with their pattern. They can decorate the pattern all together now by drawing things on the shapes or by filling them in with alternate colours.
After students have had an opportunity to work with this and print out a few copies, have them attempt flips (reflections).
1. Using Paint or Paintbrush, have students create a triangle in the top right corner of their screen. Then students should colour the shape in using any colour.
2. Click on the Lasso tool (in Paintin Paintbrush).
3. Have students use the lasso tool to draw a wiggly line on the triange starting at the top point and ending at the bottom left point:
4. Now have students click and drag on the selected part to separate it from the rest of the shape and move it to the right side of it:
5. Make sure the new shape is still selected (if not, click on the lasso (star) and draw a shape around it) then go to Image at the top and click on Flip/Rotate, then click on Flip Vertical and OK.
6. Click outside of the shape to desselect it and then select it again (this will make it so the corners don’t erase if you are using Paint). Click and drag to move the new shape to join the other one:
7. Now click on the lasso (star) and make a dotted line shape around the new one. Press Control on the keyboard (Ctrl) and hold it down while you click and drag a copy of this shape to go beside it and repeat this until you have a row of this shape:
8. Select the lasso (star) and click and drag around this whole row to select them all. Press Ctrl and hold it down while you click and drag a copy of this shape below it.
9. Before you click anything else go to Image at the top and click on Flip/Rotate and Flip Vertical again.
10. Now colour your new row of shapes a different colour using the paint bucket:
11. Use the lasso (star) tool to select the bottom row and click and drag to fit it into the top row:
You could have students create slideshows in Kid Pix or PowerPoint to display their work.
Students can colour their printed out tesselations in online essay class to display. Print out and colour 4 and have them laminated for placemats for a gift.