Algebra & Geometry
updated September 3, 2022
Recorded here is my own personal collection of articles, resources, favorite links, teaching ideas, and lesson plans. It encompasses many years, from the very beginning of my experience studying and learning about Waldorf to the present time. People from all around the world visit my site and recommend it to others. Welcome!
This site records my journey. I hope my honesty is encouraging and helps break down some barriers that may prevent people from trying Waldorf methods. Because this is an ongoing site documenting my curriculum planning and ideas, some materials are more Waldorf-y than others. Please feel free to take what you like and leave the rest.
Algebra & Geometry
for Class 7
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Excellent resource! Published Waldorf curriculum books provided here in PDF format for you to download, keep, and read... for free!
(The text link is to OWL, and the image link is to Amazon.)
Essential Resource
Negative Numbers
In the "Publisher's Perspective" by Anita Silvey, part of the introduction to the Curious George anthology, we found out that one year -- in 1945 -- the story of Curious George actually sold -6 copies!
Yes, this is possible. Bookstores returned more copies to the publishers than they bought. If you are teaching Algebra in Seventh Grade, this would be a wonderful way to introduce negative numbers! Jamie York suggests that negative numbers NOT be introduced using a number line, which then either becomes a crutch or becomes a source of confusion (such as why a negative times a negative is a positive). He suggests real life examples, like thinking about a bank account and how you could write a check for more money than you have in the bank and, thus, have a negative balance. I appreciate that idea but I love the Curious George story even more because it is a wonderfully quirky real-life example!
The Complete Adventures of Curious George
by Margret and H.A. Rey
Balancing Equations
In "A Spot of Decorating," chapter 2 of More About Paddington by Michael Bond, we find this hilarious example
of balancing around a central point. In this scene, Paddington is trying to surprise the Brown family by decorating his new
room while they're away, and he's attempting to whitewash the ceiling.
"Paddington set to work quickly. First he tied one end of the rope to the handle of the bucket. Then he climbed up the steps and passed
the other end through the hook in the ceiling. But even so, when he had climbed down again, it still took him a long time
to pull the bucket anywhere near the top of the steps. It was full to the brim with whitewash and
very heavy, so that he had to stop every few seconds and tie the other end of the rope to the steps for safety.
"It was when he undid the rope for the last time that things started to go wrong. As Paddington closed
his eyes and leaned back for the final pull he suddenly felt to his surprise as if he was floating on air. It was
a most strange feeling. He reached out one foot and waved it around. There was definitely nothing there. He opened one eye
and then nearly let go of the rope in astonishment as he saw the bucket of whitewash going past him on its way down.
"Suddenly everything seemed to happen at once. Before he could even reach out a paw or shout for help, his head hit the ceiling
and there was a clang as the bucket hit the floor.
"For a few seconds Paddington clung there, kicking the air and not knowing what to do. Then there was a gurgling
sound from below. Looking down, he saw to his horror that all the whitewash was running out of the bucket. He felt
the rope begin to move again as the bucket got lighter, and then it shot past him again as he descended to land with a bump in
the middle of a sea of whitewash.
"Even then his troubles weren't over. As he tried to regain his balance on the slippery floor, he let go of the rope, and with
a rushing noise the bucket shot downwards again and landed on top of his head, completely covering him."
You can ask the children to think about if there was an amount of whitewash that could be left
in the bucket so that Paddington would be lifted up but then would be stuck in the air across from the bucket, both swinging gently. Lots of fun experimenting
with pan balances could follow!
More About Paddington
by Michael Bond
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