Last week, I wrote a bit about place value after doing a Which One Doesn’t Belong activity with a 3rd grade class. Since then, I have been thinking A LOT about how complicated place value really is. I think you can get a feel for the various ways we handle place value with students in this Twitter thread.

I have been talking about this with my 3rd grade colleagues at school, so one of them did the same WODB activity and ended with the same discussion around the number 146. She asked how many tens were in that number and got a lot of 4’s and 14’s, but this time she also got 40, which I did not hear in the other class. She asked the students to defend their thinking in their journals.

The journal below is the one I anticipate the most, separating the places and naming the number of tens in the tens place. (Although, I am unsure what is going on with the 74, possibly was going to give another example and ran out of time?)

This journal shows a slightly different reasoning because now instead of saying there is 1 hundred, 4 tens, and 6 ones, the student is using the value (or quantity, again not sure what to call this here, its complicated) of the 4 in the tens place as 40 broken into the four 10’s so you can see them.

I want to pair the student above with the student below and have them chat. This student had the same train of thought in the beginning but broke the 100 into ten 10’s to arrive at 14 altogether.

The last one, that surprised us, was the 40 tens. He actually showed 40 ones that make up the 4 tens with his dash marks in the last speech bubble. I may want to pair this student with the second example in this post to have them chat about that 4 tens vs 40 tens.

All of this still leaves me wondering a lot. I know there are times it is helpful to think about the tens only in the tens place while there are times we want to be thinking about how many tens are in the whole number, but….

- When are those times?
- How do we best structure activities to explore these ideas with students?
- What assumptions do we make about student understanding of place value as we teach comparison and computation strategies?

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Cynthia Garland-DoreI look forward learning more about how the students defend their responses and what the overall impact will be for the class. They may want to explore what questions they could ask so 4 and 40 are correct responses.

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mathmindsblogPost authorThat is too funny Cynthia bc that is what I asked the previous class in the earlier post I did! Great minds;)

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CynthiaSorry I am reading backwards in the blog. I am curious still how their discussion will go or has already gone. In what ways did it impact or deepen the classes understanding of PV. Have they had a discussion about the thinking they wrote about? Perhaps it will happen naturally when they discuss PV with in their unit.

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stamp36Hi,

The student that said 40 tens but had tallied up 40 ones. I wonder if he has developed the key understanding of unitizing as it relates to place value. We often look at the key concepts of place value as: each place has a name, the value of the digit depends on the place and zero as a place holder but forget that unitizing is also one of the major key understanding needed for place value. Does that student understand that 10 ones can be a unit of 1 ten etc.Just as unitizing is so important in early multiplication and fractions it is sometimes over looked in place value. Interested to hear what you think? Thanks for sharing this is a informative post and something I see in all the classrooms I work in.

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mjerrellmathA lot of our students have a positional place value understanding and not a “multi-unit” place value understanding. It’s been driving me crazy lately when I’ve walked into 4th and 5th grade classrooms trying to teach “place value” by having students identify the number in the “ten thousands place” or determining the value of the underlined digit. At no point are they able to generalize and understand the place value system, but instead look at the digits in a multi-digit whole number as exclusive.

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