Grade 5 Freehand Waldorf Geometry: Ellipse Exercise

We’ve been working on our freehand Waldorf Geometry block the last couple of weeks. Check my Geometry highlights on Instagram  for more.  We are using pushpins as string to first draw a circle from the center, and then moving the focus outward from the circle to see the changes in the circle. 

It’s a cool exercise just by itself, but like much of our homeschool we are doing a lot of ‘notice and wonder.’ There are definitely some things that we noticed that I hadn’t before.  I’ll let you to try it, and you can come back in here and tell me what you all noticed and/or wondered. 

You’ll need 

two large (8.5 x 11) Process of corrugated cardboard

6 pushpins

A piece of string (around 10 to 12 inches)

Colored pencils

  1. Make a loop at the end of your string. When looped around your pushpins you want us your string to be roughly 6-7 inches from end of the tip of loop to loop, such that when you place the loops in the pushpin and the pushpin in the center of your paper, you’ll not quite reach the edge of the paper.
  2. Assemble your stack of cardboard and paper. Two pieces of cardboard on the bottom, paper on top, a pushpin on each corner to hold everything together.
  3. Start at the center: Place both loops of the string on one pushpin, and push the pushpin into the center of the paper and though the cardboard behind it.
  4. Use one color of pencil, place it in the larger loop this creates, applying gentle pressure so that the string stays taunt, draw the outer edge, in this case a circle, that the string will allow. 
  5. Using both pins, place the pins, equal distance, on either side of the center. 
  6. Place the loops on the pins. 
  7. Pull the string to the top/side and using the pencil (of different color) to keep the string taunt draw the outer edge of one side of the ellipse formed.
  8. Lift the pencil, pull the string to the bottom/other side and repeat step 7 for this side. 
  9. Repeat steps 5 through 8, moving the pushpins out along a line, further and further from the center until you have gone as far as the string can reach.
  10. What did you notice? 

We did this exercise twice. The first was practice. It takes a bit to get a feel for how to use the pencil to keep the string taunt.  We discussed a little of what we noticed after the first, which prompted us to be more observant during the second construction.

Leave a comment below and tell me what you noticed.

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