Graham Fletcher created a set of Progressions videos for various elementary school themes. J3 and I recently went back to his page and found he had a new(er than we knew) progression on early number and counting. Even for this simple topic, the video highlights some points we hadn't considered explicitly, for example distinguishing producers (of a number) and counters. Also, the cardinality point that smaller natural numbers are nested within larger numbers wasn't something we had talked about, but we soon realized it was part of many examples in how we understand numbers.
With that as inspiration, J3 and I decided to search for a range of examples of a single number, we chose 8, in different forms. There is at least one obvious version we're missing.
Add a comment (with picture, if you can) to show other forms of the number 8!
Marking 8 on the 100 board, an easy place to start:
8 beads on the abacus shows the relationships 3+5 = 8 and 10-2 = 8 (also 100- 92 = 8)
8 can hide in plain sight. Without labeling the three lengths, it would have been hard to recognize the longer one as 8 cm and, for you at home, impossible to know without reference to show the scale.
It happened that, within the precision of our scale, two chocolate wrapped chocolate bars were 8 oz (2x3.5 oz of chocolate + about half an ounce of wrapping for each):
8 cups of water ended up being a lot, so this version unintentionally revealed a relationship 4 + 2 + 2 = 8
Though I'm not sure I can articulate why or show supporting research, I feel it is very valuable to build experience with physical models of numbers to create familiarity and intuition about what they are/mean. In particular, I hope this helped J3 anchor the importance of units of measure and scale in the interpretation of numbers.
Finally, this construction has nothing to do with the number 8 (or does it???)