Grade 3 Numbers & Operations in Base 10 Place Value

103 > 130 and Other Mistakes

Open thread. Talk about what you find interesting here, or anything. I’ll kick things off in the comments.

Numbers & Operations in Base 10 Place Value

Place Value is Hard



I think that this might be my favorite conversation since I started hanging out (as a math assistant) with 3rd Graders. File this one under “place value.”

The question that this kid was grappling with was to write “8,000 + 500 + 20 + 6” in standard form. I’ve forgotten most of the details of the conversation, but all of the interesting stuff is right there on the page.

First, note how she first writes 25,03 to that first question, at the top of the image. And though it’s harder to see, she’s done that for 60,47 as well. When I came over to her, I thought that she was just confused about the convention, and I offered a correction.

Then she started working on the “8,000 + 500 + 20 + 6” problem. First she wrote 26, and then she tried to figure out how much more it was. She ended up with what you see in the image, at which point I realized that there was something about the way she was thinking that I hadn’t anticipated. She was chunking the number into 26 and everything else.

She really struggled to figure out what to do with 8,000 and 500. The boxes around the numbers are part of my attempt to push her to tell me what each numeral represented (“5 whats? Shouldn’t this just be 8 plus 5 plus 2 plus 6, so 21?”).

But there was no way that was going to work. The fact that she was chunking “26” together means that she doesn’t really get place value for 10s either. Those of you with more experience will hopefully help me out in the comments, but I’d imagine she sees 26 as a single number, not as composed of any parts.

This was confirmed when I asked her what the 2 in the 26 meant. She thought I was nuts. She said that 26 is the number right after 25. I repeated the question, and she thought it was ridiculous.

To me, this really speaks to the value of activities that defamiliarize place value for students. See Anna’s Ba-na-na or Christopher’s Orpda for activities that do this.


Counting Multiplication Numbers & Operations in Base 10 Place Value

“5 is the same as 50, just with a 0.”


The kid also answered the “How do you know?” question:

“Because 5 is half of 10, and 50 is the same number as 5, just with a 0, and 10 is the same number as 100 just with another 0.”

What does this mistake say about the way kids see numbers and multiplicative relationships?

Elementary School Numbers & Operations in Base 10 Place Value Subtraction

Subtraction Algorithms

Let’s have a good old fashioned brawl: is there a mistake here or not?

This submission comes from Chris Hunter, who blogs at Reflections in the Why.

Numbers & Operations in Base 10 Place Value

Place Value, Greatest Value

What would you do next with this student?

(Thanks Sadie for the submission.)

1.NBT.2 Place Value Uncategorized

Mistake Hall of Fame: Cena

Cena, wherever she is these days, deserves a medal. This video is a classic.

Here we get to see how the teacher followed up with the student, so let’s tackle these questions:

  1. What can we say that Cena does know?
  2. What is going through her head as she answers these questions? Where does she go wrong?
  3. What are the teacher’s moves in this clip? What is her strategy for uncovering the student’s errors?