Overview:  In this launch, the teacher introduces the idea of frieze patterns, also known as strip patterns.  The teacher shows an example of a frieze pattern and asks students whether they have seen any similar patterns.  The teacher points out that some frieze patterns use reflections, and in the lesson students will work on a problem that requires them to use reflections.

Prior knowledge:  With the example of frieze patterns, the teacher establishes a connection with the mathematical practice of using different symmetries to make patterns.  With examples from different contexts, the teacher illustrates that this practice is not restricted to school mathematics.  In architecture, different frieze patterns become part of the structure and design of buildings.  With the example of the stocking cap, the teacher illustrates that people who design and sew stocking caps use the practice of creating symmetries in their work.  Finally, the teacher suggests to students that they will be using a specific type of symmetry, with reflections.  Students have prior knowledge of reflections in various contexts, including school mathematics but also including out of school experiences.  In the last line of the script, the teacher uses mathematical language to remind students that in geometry, a reflection is a specific “transformation” that uses a “mirror line”.

Other points of interest:  The teacher shows two examples of frieze patterns in this launch – first the architecture and then the stocking cap.  The example of architecture may be somewhat remote for students.  The example of a stocking cap is likely more closely related to patterns that students have seen.  In addition, although the teacher is making a connection with the practice of using symmetry groups, there is no discussion in the launch with the actual process of creating the patterns, for example how the person who sewed the cap may have created the repeating pattern.  The two examples show the finished products that were the result of the mathematical practice.  In the end of the launch, the teacher makes a connection with school mathematics knowledge by using the formal terminology of “transformations” and “mirror line” to remind students what a reflection is.