This is a follow-up post to this one, about introducing 3-digit numbers to kindergartners.

I start this lesson by asking the students to come up to the board one by one and write down consecutive numbers starting with 100. There are 4 students and they each have a chance to go up 4 times. This is what we end up with:

Here are the numbers written by each student:

- Student 1: 100, 1004, 1008, and 10012
- Student 2: 101, 105, 109, and 1013
- Student 3: 1002, 1006, 10010, 1014
- Student 4: 103, 107, 1011, 1015

It was interesting that the students did not really pay attention to what others wrote, but each one had his/her own internal reasoning that she/he stuck to.

Next comes the most interesting part, in my opinion. I ask whether anyone thinks that there are mistakes in the chart. They all unanimously say that all the numbers are written correctly and *there are no mistakes*!

Okay, lets suppose that is true and make some comparisons. What’s bigger, 1000 or 1002? According to the chart, 1002 is one hundred and two, and they all right away recognized that 1000 is one thousand. So without any hesitation, the students tell me that 1000 > 1002.

I then ask them to compare a few more pairs of numbers and we end up with the following:

Notice that everything is consistent with the original chart of numbers. However, other than that, I had a hard time finding any logic to it.

Before fixing their mistakes, I decide to go back to making some 3-digit numbers using base-10 blocks. Each student gets assigned their own number to make.

They then have to go up to the board and write down their number. But this time, I tell them that they have to write down just three digits, one for the number of flats, one for the number of rods, and one for the number of unit cubes.

Then I ask each of them what number they wrote down, and surprisingly they have no trouble at all with this. I point out how all of their numbers have exactly three digits.

We then go back to the original chart that they made with the numbers 100-115 in it. I point to each of the numbers one by one, asking them whether it is correct or not. For the ones that they tell me are incorrect, I ask them how to fix it. They tell me to erase lots of extra zeroes, and at the end we are left with the following:

I confess that I did not expect them to fix all the mistakes just like that and was quite impressed. At the same time, I have no illusions about them internalizing the concept. I am sure that they will make their original mistakes again in the future and I am totally okay with that. They will be solidifying their understanding of place value for many years to come, but I think this was a pretty good first step.

Do you remember your own first experiences with multi-digit numbers? What about those of your students/children?

You have an exceptional group of Kindergarteners. I just wanted to say that this one of the clearest demonstrations I have seen that the base-ten structure of place value and the use of the positional value of the notation system need not develop at the same time for students. Thank you.

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Thanks for the comment. They are pretty special, and it also helps that there are few of them so they get lots of individual attention.

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