Categories
Multiplication Numbers & Operations in Base 10

9 times 13 is 121

IMG_3017

 

The kid’s handwriting is hard to read, so I want to point you towards 9 times 13, near the top of this page.

I think that this is a great example of a mistake that you can feel fairly good about. Your thoughts, on any of his work?

Categories
Counting Multiplication Numbers & Operations in Base 10 Place Value

“5 is the same as 50, just with a 0.”

pic1

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?

Categories
Multiplication Numbers & Operations in Base 10

More, More Numbers and Operations in Base 10

IMG_0041

 

I’m inclined to say that this is a classic working memory mistake. You’ve got a resources-heavy calculation being done in the student’s head, and you’ve got this 3 floating around in the problem, and it ends up in the ones place.

Agree? Disagree? Thoughts?

Categories
Multiplication Numbers & Operations in Base 10

More Numbers and Operations in Base 10

IMG_0040

 

Any idea what’s going on here? In case fuzziness is an issue, the question is “What is the biggest multiplication that you know without thinking very much about it?”

Also, I anticipate getting some flack for the wording of this question being potentially confusing. I don’t disagree, necessarily, but I want to offer a partial defense of the question. First, I had been reading the TERC curriculum and they make a point of not saying “multiplication facts,” instead always saying “multiplication combinations.” I haven’t wrapped my head around what makes sense to me, so I punted on the question, figuring that I’d be there to help kids figure out what it meant. And I did, and everybody else offered answers that made sense. Most importantly, the question served it’s purpose: some kids wrote “8 x 8” while others wrote “1,000,000,000,000,000,000 x 10.”

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
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.

Categories
Area Decimals Geometry Middle School Multiplication Perimeter and Volume

Area of Walls

What’s the mistake? How can you help the kid?

When you’re done with this post, go check out Mary Dooms’ blog and go follow her on twitter. Thanks for the submission, Mary!

Categories
3.OA.1 Multiplication

Khan Academy: Meaning of Multiplication

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