[b]Materials:[/b] [br]puzzle-parts (each pupil gets a package à 55 pieces)[br]possibly a beamer for presenting the photos of the puzzles[br][br][b]Learning outcomes:[/b] [br]Recognising repetitions and symmetries, sharpening perception of the environment, recognising that sequences and series are also a way of repetition, learning mathematical descriptions of repetitions through fractals, patterns, enlargements and reductions, ...[br][br][b]Curricula:[/b][br][list][*]primary school (VS, 6-10 years): symmetries, perception, surfaces, shapes, ...[/*][*]lower secondary school (Sek I, 10-14 years): (Self-)similarity, uniform scaling[/*][*]upper secondary school (Sek II, 14-18 years): fractals, sequences and series[br][/*][/list][b]Duration:[/b] [br]2 school lessons à 50 minutes (on different days)[br][br][b]Teaching Methods:[/b][br][list][*]teacher-centered instruction (frontal) [/*][*]individual work[/*][*]plenary[/*][*]group work[/*][/list]

[list][*]teaching method: frontal[/*][*]duration: 10 min + 5 min time buffer[/*][*]materials: photos, pictures, videos, vegetables, pine cones, ... [/*][/list][br]The teacher explains that in nature sometimes things repeat themselves and that this can basically be described mathematically. [br][br]Pictures/videos/... are being viewed. [br][br][b]further ideas for an extended instruction:[/b][br][i]primary school:[/i][br][list][*]consider if you include the video!?[br][/*][*]students should bring objects such as pine cones, ... [br][/*][*]pass objects through, let them discover regularities and repetitions[/*][/list][br][i]lower secondary school[br][/i][list][*]show video, show pictures of objects that contain repetitions[/*][*]show scaling using GeoGebra[/*][/list]     - square & rectangle, composed/decomposed surface[br]     - cutting surfaces into smaller self-similar parts[br][br][i]upper secondary school[br][/i][list][*]show video, show pictures of objects that contain repetition[/*][*]explaining mathematical concepts of sequences and series[/*][*]explaining the meaning of endless repetition, Mandelbrot set, ...[/*][/list]

[list][*]teaching method: individual work[/*][*]duration: 20 min + 10 min[/*][*]material: puzzle[/*][/list][br]Handing out the puzzle. Explaining the task: "Use this puzzle to make a repetition or pattern that you consider beautifully". (Help may only be given "technically" and not "contentwise".)[br][br]After half the time, announce the time. After 20 minutes, give another 10 minutes extra time. If there are specially fast students, the teacher goes there, takes a photo and asks students to find a new solution.

[list][*]teaching methods: plenary discussion[/*][*]duration: 15 Minuten[/*][*]material: finished puzzle-results, beamer (for presenting photos of further puzzle-results)[/*][/list][br]The students present their results to the rest of the class and explain how they solved the puzzle and what they like about their results (and why).

[list][*]teaching method: group work[/*][*]duration: 30 min[/*][*]material: puzzle[/*][/list][br]Students meet in teams or are divided into teams by the teacher. In this unit the students either try to combine their two results or to work out a new solution for the task together. [br]

[i]primary school[br][/i]"Geometric forms arise from different (other) geometric forms", no longer just "the round must go into the round".[br][br][i]lower secondary school[/i][br]students should work with applets of e.g. Diego Lieban: cutting up triangles, ... so that the result is self-similar.[br][br][i]upper secondary school[/i][br]continue with the topics "sequences and series"