Escher envy
This is a level 4 geometry activity from the Figure It Out series. It is focused on exploring transformations through tessellations. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Explore transformations through tessellations.
Escher envy
Achievement objectives
GM4-8: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
Required materials
- Figure It Out, Level 4+, Geometry, Book Two, "Escher envy", page 2
- computer drawing program
See Materials that come with this resource to download:
- Escher envy activity (.pdf)
Activity
Although it is possible to create Escher-style tessellations without a computer (as Escher did), this activity assumes that your students will use one. A computer makes it possible for them to create attractive and complex patterns without the lengthy repetition that would otherwise be involved. If they are not sure how to use a drawing program, these two activities give them a suitable context in which to learn. The main functions they will need to use are drawing, copying, pasting, and grouping.
Activity 1
If they wish, the students can make very simple changes to the sides of their parallelogram and still create an attractive tessellation. The next example shows how two triangular translations (shaded) can create a tile that looks nothing like the original parallelogram.
Alternatively, the students could make a less obviously geometrical tessellation by using the freehand drawing tool, as in this example:
Activity 2
This time, the students base their tessellations on a hexagon. They use the same computer functions as in the first activity, with the addition of reflection and rotation. As they work, you should find them using the language of transformations to describe what they are doing.
Question 2 challenges the students to create a more complex design. They will find that it is surprisingly difficult to create a tessellation featuring a recognisable creature or object. If, however, they add eyes or a mouth, their shapes will start to look alive. Using a computer for this activity makes it easy to go back and add to or change the outline of the original tile to get a slightly different tessellation.
There are a number of websites devoted to tessellations and other sites that feature Escher's work, such as the official Escher website, M.C. Escher.
Activity 1
Practical activity.
Activity 2
1.-2.
Practical activities.
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