I reviewed a lesson plan I found at

http://www.cyberlearning.org/middleschoollessonplans/corporatelogo.pdf

This is actually a lesson plan by PBS | Mathline on using symmetry to create corporate logos.

I thought it was a nice lesson plan. Don’t be put off by its 14 pages – it is actually three copies of one five page plan. The objectives are about learning to recognize different types of symmetry and creating figures with those types of symmetry. The target grades are 6 to 8. The main activity is the construction of a symmetric object, similar to a corporate logo.

Students learn about reflection, rotation and translation symmetries. I like the first exercise where the students identify which letters of the alphabet have vertical and horizontal reflective symmetry (or both). I though using very familiar objects was a nice way to get the students minds thinking about this concept.

For rotational symmetry, they could have done more in providing examples. They did not provide an example of an object with rotational symmetry, even though so many exist. They could have used a starfish, sand dollar, hubcap, etc… They also could have made it clear that you may rotate by any angle (though choosing an angle that divides 360 makes things simpler), not just 90 degrees. It also would be nice to have an exercise, as there was for the concept of reflective symmetry. How about showing some common shapes and asking students to identify how many axes of rotational symmetry there are?

For translation, they also could have done much better in providing examples. For instance, a picture of a traditional Asian rug would have been a good example.

One thing that is missing is a method or evaluation. For this activity, a rubric would be a really helpful guide for the students, as well as for the teacher to evaluate their work.

I think this is a good plan in terms of active and authentic learning. Dealing with designing and constructing, it is very active. Using nature and corporate logos makes it feel authentic (real world). It is also interesting to think about the lesson in terms of Bloom’s Taxonomy and the Van Hiele model. It does the first level of Bloom’s well, introducing the three types of symmetry. There is plenty of opportunity to get to all levels of the taxonomy. It could have more exercises to help with transforming that information into understanding. Implicit in the main task is the level of applying and creating. Analyzing is needed for the alphabet exercise, and more exercises would increase the amount of analyzing and/or evaluating in the lesson.

This exercise takes place mainly at the first two stages of the Van Hiele model. It has a lot of visual qualities to it. It also requires students to reflect, rotate and translate geometric shapes, and to join them in various ways with copies of themselves. This activity, I believe, will help develop higher level geometric reasoning. However, it may do this intuitively rather than in the verbal sense of the Van Hiele model. One needs to develop some sense of the properties of geometric objects in order to successfully manipulate them to make constructions.