Geometry playground

Class 5 geometry lessons are underway! It’s exciting for me to revisit the beauty and symmetry of compass art, Learning about polygons, prisms, pyramids, solids, quadrilaterals, angles, lines and circle language. I enjoy the artistic focus in presenting this work with Lily through the Waldorf curriculum.

On an adventurous day out recently we were happy to find this playground in a small village. (Neustadt near Metzingen) Soon there where exclamations about how this whole place was framed on polygons, prisms and even a quadrilateral pyramid supporting the tree! We are all looking at the world through geometry glasses now!   
    
    
 

I hunted for four leaf clovers (unsuccessfully) and enjoying watching while the two spent half an hour cleaning the sand out of the water play basins and creating waterfalls. I know Lily gets lonely for friends her own size when we travel and I cherish the richness of her relationship with Cedar and their ability to play together despite 6 years age difference. 

They where really engaged with the water pump and this initiated more conversations about living in historical times, continuing on from visiting Lichtenstein Castle earlier in the day. Shall we detour there right now, it’s a lovely late summer day in Southern Germany….

   
    
    
    We took the tour so we could snoop around inside the castle. I was especially enthralled with the detailed paintings on walls and ceilings. Photographing strictly Verboten! So you will have to go there yourself.

Afterwards we sought out the Easter Egg museum, decorated not chocolate !unfortunatley closed but the glimpse in the door was inspiring for our own Easter festival. After studying ancient Egypt lily was taken with the egyptian artwork eggs in the centre. 

  
 Anyway back to geometry!

We have been playing with toothpicks and modelling clay to create a sample board. It began with lines, which naturally flowed into the exploration of what can you make with lines.   

  glimpses from Lily’s main lesson book.

 It is fascinating the different polygons and patterns which are made when you follow the times table…  
  

Draw a dozen intersecting straight lines, then identify and color the various types of triangles.

Mamas exploration.   Lily’s

  Cedar’s

   
  Practicing rays by imagining starlight that shines on forever.The city map practicing all different types of lines. See if you can spot them!  
    
    
  First freehand circle explorations before introducing the compass.  
    
    Cedar watched the above flower of life developing, later he sat quietly and recreated his own very beautiful version. I loved making and colouring this mandala as a child also.

  The hexagon creations are beautiful, followed by a dodecagon.
   The fun side of mathematics for us!

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3,4,5 triangle

       While researching  Ancient Egypt in June for Lily’s studies, I came across the 3,4,5 triangle. Apparently the Ancient Egyptians used a rope of 12 (we used metres) knotted sections. With angles made at 3m and 7m a right angle or Egyptian triangle is made. Fascinating little insight into geometry without a compass or ruler. 

With my father we went out in the hof (courtyard between the house and barns) with string and sticks and measures and markers and  water cans, we created an Egyptian triangle in the dirt. After we marked the triangle we flipped it and made another triangle, for a rectangle, then marked the centre and made circles with 3, 4 and 5 m diameters. Finally we finished with a central post and made a pyramid! A really fun, visual exploration. 

  

  

  

  

  

  

  

  

          While we travel I homeschool Lily. I follow the Waldorf curriculum as closely as I can (with guidance from her teacher in Australia) while not being a trained teacher myself. It usually works really  well and it’s a fantastic opportunity to tutor Lily in areas she has challenges. Getting her motivated is not always easy though and the differentiation from parent to teacher is interesting (read challenging, inspiring,frustrating) for me. I learn so much alongside her and enjoy the intellectual stimulation and discovery in research also. It is difficult to maintain consistency when we are moving a lot so this 6 week interlude with my parents in Germany was a good foundation for studies. We visited the Egyptian museum in Berlin which inspired us with incredibly detailed and beautiful carvings and paintings. It is the home of the famous bust of Nerfetiti which cannot be photographed, so we took our sketchbooks and drew her. The guard commented Lily was the youngest artist he had witnessed sketching her.    

  Her drawing books are full of images of Egypt.