Categories
Addition Division Multiplication Numbers & Operations in Base 10 Subtraction

Some Numbers and Operations in Base 10

IMG_0043

 

Explanations? What lessons are there about the way kids think in this work?

Categories
Multiplication Numbers & Operations in Base 10

Multiplication Shortcut Fail

fawn mult

 

  1. What exactly is the shortcut?
  2. Why does this shortcut seem reasonable?
  3. We’d all agree, I think, that 2 x 6 = 26 is not a result of this kid not understanding what multiplication is. I’ve made that mistake before, and I bet that you have too. So, why is it a  common mistake? What does this say about how a mind works while working on math?

[Any advice on how to tag this, CCSS-wise?]

Categories
Multiplication Numbers & Operations in Base 10

Lattice versus Partial Products

triangleman1

 

I’d love to hear anything that you’re thinking about this in the comments.

I wonder: should we be giving kids explicit guides for these sorts of algorithms at all? Algorithms ought to be patterns in thought. Does a mistake like this begin to make a case against these sort of printed aids?

Thanks to Professor Triangleman for the submission.

Categories
Numbers & Operations in Base 10 Rounding

Significant Figures

TheCommonMistake WhatsGoingOnHere

From the submitter: “I came across these answers to sig fig questions when marking a pre-algebra numeracy test last night. I’ve attached two answers, one is a very common mistake where students just can’t believe that they are asked to round up that much. The second… well I don’t have any idea what the student was thinking, so I thought your readers might be able to help.”

Readers?

Categories
Multiplication Numbers & Operations in Base 10

Multiplication Algorithm

multiplicationmistake

 

How did this kid come to believe in this algorithm?

Thanks to Amy Burk for the submission.