For the past several weeks, our kindergartners have been playing with 2-digit numbers: they made numbers out of base-10 blocks, wrote them on the board, translated between the two representations, counted by 10’s from different starting points, and more. We also explored 2-digit addition with the base-10 blocks and the students had a great time with it.
Today I decided to spice things up a little and venture into making 3-digit numbers with the base-10 blocks. The students right away predicted that 10 rods would make a flat and 10 flats would equal a cube.
They also had no trouble counting by 10’s to 100 and by 100’s to 1000 (I was actually surprised that no one except for me said 10 hundred. They all knew it was one thousand!). Writing one hundred and one thousand on the board using digits posed no problem as well.
Then I took 2 flats, 5 rods, and 7 little cubes and asked the students what number I just made. With minimal help, they were able to figure out that it was the number two hundred fifty seven. And then came the real challenge of writing that number on the board.
One student volunteered, and wrote:
I asked the students whether they agreed that this was two hundred fifty seven and they all said yes.
So then I wrote another number under it and asked the students what that one was:
Now half the students said that the number that I wrote was two hundred fifty seven and the other half said they didn’t know what my number was, but they thought that two hundred fifty seven was 2057.
I then decided to ask the students how to write the number two hundred. Here they all agreed that it should be 200. However, when I asked them how I should write two hundred one, opinions varied once again. Half the students thought it should be 201 and they other half said 2001.
One student said that they thought that 201 is two hundred one and 2001 is two hundred ten. So of course I had to write 210 on the board and ask them what that would be. They said they didn’t know.
I decided to make one more 3-digit number with the blocks, have someone write the number on the board and see if there’s consistency to their thinking. This time we had four flats, three rods and one little cube.
I asked one student to go up to the board to write down the number and they wrote 40031. A second student raised their hand and asked, “I do not understand, why would you put two zeroes there? It should be 4031!” When I asked the student why one put the one zero there, the student replied, “That’s just the way you write it.”
So in the end we were left with the following three possibilities:
and no consensus as to which one is correct. We left it at that.
My big question now is, how should I start tomorrow’s lesson?