Math Art Corner – circles and polygons - project 3 Discovering math in polygons and pattern
Students’ age:
10,11 years old student, 5th and 6th grade
Subject:
It is an afternoon club, each week 70 min. , Club is called Math and Art – digital and with paper, ruler and compass
Project idea:
Discovering as much geometry in the picture/pattern as possible (depending on the grade and math stuff they know), writing it down, then constructing with GeoGebra (changing it) and colouriing it with an image editing program e.g. Paint.
Aims:
- make students (beginners) more familiar with GeoGebra - interests students in designung wonderful symmetric pattern - discovering mathematical objects like different triangles, forms of quadrilaterals, comparing areas, … - learning what it means to do a dynamic construction
Lesson plan:
Students are explained to analyze first the way of construction of one of these figures on this worksheet, then constructing it with GeoGebra, then coloring it. In the next lesson students worked in pairs , discussing about the math and geometry in both designs and writing all things down. As my students are mostly of grade 5 they have started english only two monthz before. The teacher or an older student of my grade 9 will translate their results in english language.
URL:
Geogebra files are in a GeoGebra Bbook: https://www.geogebra.org/m/wmrhaxzz
Projekt 3 : Discovering math in polygons and pattern, then describing, finally constructing! Here you can see some pattern, which contain different polygons (e.g. triangles, squares, regular and irregular quadrilaterals, pentagons, hexagons, ‌ Chose a pattern or search the internet for one which you like. Then describe the math behind this pattern e.g. which geometric forms and properties you discover. Then construct with GeoGebra and colour it with Paint.
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1: rechtwinkliges, gleichschenkliges Dreieck 2: Quadrat bestehend aus 4 kleinen, gleich groĂ&#x;en Quadraten 3: Drachen 4: Drachen 5: spitzwinkliges Dreieck 6: Drachen mit 2 stumpfwinkligen Dreiecken
Translation: 1. 2. 3. 4. 5. 6.
Right angled, isoceles triangle Square consisting of 4 squares with same area kite kite acute triangle kite with two obtuse triangles
1= rechtwinkliges Dreieck (2 ergeben zusammen ein spitzes, gleichschenkeliges Dreieck) 2= Quadrat
3 = Fünfeck
5= Siebeneck (regelmäßig)
4= regelmäßiges Sechseck
6= Achteck
7=rechtwinkeliges, gleichschenkeliges
Dreieck 8= Quadrat, 2x Nr. 7=2 M= Mittelpunkt von Nr. 6
9= spitzwinkeliges Dreieck 10 = gleichseitiges Dreieck
Translation: 1= triangle with 90°
2 = square
5 = regular polygon with 7 edges
3= regular pentagon
4= hexagon
6= octagon
7=right angled, isosceles triangle
8 = 2 0 square consisting of two triangles no. 7 9 = acute triangle
M = mittpoint of the octagon no. 6
10 = equilateral triangle
Translation: 1) 3D house
2) 4 rhombus
5) 6 acute triangles
3) irregular polygons with 6 edges 6) irregular pentagon
7) polygon with 10 edges consisting of 10 acute triangles (orange in the middle)
4) “narrow rombus
Translation: The form consists of 10 regular hexagons and 54 obtuse triangles. The object gets brighter to the middle. The hexagons get smaller from outside to the middle. The colours start out side with dark red to yellow in the middle.
Translation: Nr. 1. equilateral triangle
Nr. 2: square
Nr.3 : regular pentagon
Nr. 4: regular hexagon
Nr. 5: regular octagon
Nr. 6: regular polygon with 9 edges
Nr. 7: regular polygon with 10 edges
Nr. 8: regular polygon with 12 edges
Translation: The star consists of 8 kites and 16 triangles with an obtuse angle. The tips of the star are connected and form a regular polygon with 8 sides. If you regard the rose part you can see two squares. At each edge of the big square you can see a red kite. The kite consists of 2 obtuse triangles each. In the middle of each side of the big square there are two obtuse triangles.
Some students of grade 5 have seen the work of their classmates who are members of the afternoon club who had worked with GeoGebra. They asked me if they can do circle art with a compass on paper. As they did voluntarily extra-work I have added their drawings here to honour their work.
Sophie
Angelina
Linda
Kimiya