Fractions Number & Operations -- Fractions

Sometimes Kids Add When They’re Trying To Multiply

That’s weird, right? They clearly get the visual model. Now, granted, it’s hard to apply this visual model when multiplying by “one and a half.” Still, there’s a clear attempt to work it out with pies, and then they wrote four. I mean, what’s going on? Maybe the kid was just adding instead of multiplying. […]

Exponents Seeing Structure in Expressions

-3X as 3 Negative X’s

Check out this kid’s explanation for why you end up with “+3x” from “-(-3x)”: “You have -3x, so that’s three negatives, and then you have this other negative and that makes four…” You can find this explanation at around 3:33 in the video below: Exponents strike again! (Or, maybe I misunderstood the kid’s explanation in […]

Multiplication Numbers & Operations in Base 10

6 x __ = 240

  You can’t say that the kid is incapable of understanding what the box means here. Still, in the space of one line, it slipped through her fingers. Is this connected to the way kids inconsistently treat exponents? I’m struggling to articulate a general principle, but it goes something like “Operations defined in terms of […]


Writing About Mistakes From Around the Web

We here at Math Mistakes are always happy to share thoughtful writing about mistakes and student work. First up is Nicora Placa, whose Bridging the Gap is one of my favorite new blogs. She asks, “Is a Careless Error Really Careless?” Here’s the headline news from a 1982 experiment: However, as he continued his analysis of […]


Making up a relationship

In the library today, I tried to run a little experiment on a friend. I told him that there was a relationship between the numbers in the circle and the numbers to the right, and I asked him to try and guess what the relationship was between the numbers at the bottom. The catch was […]

Site Business

Summer Project: More analysis, fewer mistakes

At the one-year anniversary of this site, it’s time to take stock. We’ve got a bunch of mistakes — a couple hundred, at this point. A ton of Trigonometry mistakes. A bunch of Algebra material. Not much from middle school or elementary school, though maybe that’ll change next year. (I’d like it to.) I’ve had […]

My Mistakes Number Theory Uncategorized

Problem Solving Strategy: Have hammer, seeking nails.

In yesterday’s post, I shared some mistakes that I made while working on this problem: There were some good questions and thoughts in the comments. A few people wanted to know why I added 15 and 333 to get 348 in my second solution to the problem: I’m also really curious about is “1+2+3+4+5=15″. – […]

exponents Expressions and Equations Multiplying Polynomials

Another pre-instruction survey, this time about polynomial multiplication

Noteworthy: The kids have a ton of confidence, even in the stuff that they haven’t formally studied in class yet.  (For this survey, Questions 1-3 had been covered formally, and Questions 4-5 had not.) To my mind, this continues to reaffirm that the most annoying mistakes aren’t the distortion of instruction; they’re the failure of […]

exponents Rational Expressions Seeing Structure in Expressions


What’s going on in this (reconstructed) student work? Tell a story in the comments. And then go thank Christopher Danielson for sharing this stuff.