Equivalence - well actually, it started out with a preliminary lesson on fractions given by a four year old to a small gathering of 6 year olds. As the lesson continued, one of the 6 year old stated that they were starting to get some ideas for extending the lesson and wanted to know if they could when the first lesson concluded. I agreed and then made every effort to over hear what the 6 year old's lesson involved while remaining committed to another child's work.
The 6 year old retrieved the power of 2 cube from the shelf and gave a quick version of a lesson I gave her on equivalence with the material a couple of months ago.
Next, the pink tower caught her attention. She walked back and forth several times between the tower and her rug until she found the pink cube that matched the power of 2 cube. She then made a huge mental leap. Before she did though, I watched her facial expression. She became so still. Her eyes were fixed on a point overhead but really nowhere. She was thinking her thoughts through. She was mentally analyzing and assessing her next move / her next words. I thought, "This is the normalized child."
Her leap. She looked at me and asked if I could come to her rug for a moment. She said, "They look the same. But, when I pick them up I can tell they don't weigh the same. Miss Dyer, can two things look the same but not weigh the same?"
"What material in the room can you use to answer your question?" I answered.
"The scale," she said almost before I finished my sentence.
She got the scale and begin weighing various cubes.
"Miss Dyer, two things can look the same but they may not always weigh the same. I think I want to work on this some more. I have some other things to try," she said. Her eyes were no longer looking at mine. Her hands were moving with great purpose.
At the end of the day, she came to me with a short list of her determinations:
1. Things that look the same may not always weigh the same.
2. Things can be divided into unequal parts. These parts collectively [put all together] weigh the same as the whole[thing].
3. The hundred chain and the hundred square are equal in weight. But, the glass-beaded thousand cube is not equal in weight to ten glass-beaded hundred squares (taken from the bead cabinet). The thousand cube is much heavier. (see photo above)
She asked to continue her work tomorrow. Absolutely!
P.S. The four year did finish his lesson and walked proudly over to the snack table to tell his accomplishments to a couple of other children. These other four year olds were eager to listen and I imagine composing mental notes on lessons they might give. It's all good.
Note: Re-reading this post, I need to note that the Baric tablets all look the same in size but do not weigh the same.
This is the circle of work, of the materials, They recall earlier work via muscular and mental memory. However, if I was to simply say, "You already know that. You did that work when you were three with the Baric tablets," it would have put out the light she lit with her own mind: her inquisitive thinking mind. She is looking at a bigger picture now. She is pondering the cosmic universe.