Elementary School Grade 3 Multiplication Operations and Algebraic Thinking

Counting Fifty Dollar Bills

This yielded a few really interesting mistakes, all pointing me to the same conclusion: my 3rd Graders need to learn how large numbers work. Though, as always, the student thinking itself was interesting.

Sorry that this kid used the “highlighter.” But they got 6000 for those 30 fifty dollar bills.

Their count: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000. Thousands are stupid, we should just eliminate them entirely and count “11 hundred, 12 hundred, etc.” It would solve a lot of problems! We’ll have to wait until I’m King of Math to do that one.

This same student made another mistake while working on this problem. They asked me if 1000 was made of three 50s. I asked, “wait what?” They clarified that since two 50s make 100, maybe three 50s make 1000?


Elementary School Operations and Algebraic Thinking Subtraction

How Many More Minutes? (#elemmathchat)

Here’s the mistake we started with:


On twitter, I asked some elementary school colleagues what they made of this.

Here are some of the ideas we came up with:

I wasn’t able to turn all of the ideas into activities, but here are the follow-up activities I came up with. If I were addressing this error in class I think this could be a progression of activities that help address the thinking in this mistake.

Response to How Much Longer Mistake (8) Response to How Much Longer Mistake (7)

Response to How Much Longer Mistake (9)

What do you think?

Update: This post from Andrew seems relevant.

Elementary School Operations and Algebraic Thinking Patterns

Patterns for Lil’ Guys

What about this table and her knowledge about numbers, lead this kid to put down 39? Tell a story in the comments.

3.OA.1 Multiplication

Khan Academy: Meaning of Multiplication

What’s going on here?  How would you help?

3.OA.1 Multiplication

Multiplication Issues (from Khan Academy)

This student has done a great job articulating their issue. How would you help?