I love all the multiplication that this kid understands. I think they’re totally ready to be able to handle this sort of multiplication.

How would you build on what they know? What problem would you use to help take them to the next step?

From Bedtime Math:

Big kids:The record distance for a thrown boomerang to travel is 1,401 feet. If it traveled exactly 1,401 feet on the return trip too, how many feet did it travel in total?Bonus:Meanwhile, the longest Frisbee throw is 1,333 feet – about a quarter of a mile! How much farther from the thrower did the boomerang travel than the Frisbee?

From the submitter, who sends in the thinking of two of his students:

(1) first student, having doubled the boomerang distance in the earlier question, now doubles the frisbee distance and calculates (2801 – 2666) feet.(2) Second student gets an 100 board and spends a short time calculating 100 – 33 = 67. Then thinks for a long time during which I’m sure he is going to say 67 + 1 = 68, but never quite does it. I stay silent until he announces: 667. No clue where the extra 600 came from. He wasn’t willing to write down or draw anything to explain his thinking.

Interesting! I’m inclined to put the first student in the “extending the thinking you’d do in one model to a less familiar situation” category and the second student in the associational mistake (same link) category.

A nice mistake with the place value here, where kids are adding “.5” to the “.25.”

This is an awfully common mistake. What are some of the curricular approaches that help kids avoid these sorts of things?

(Thanks to Chris for the submission!)

How did the student get from 0.8 times 1.6 to 8.0?

What tendency is this an example of? (Or is the mistake unique to the context?)

How would you test your theories?

Thanks to Chris Robinson for the work.

5 divided by 0 is 0.

Thoughts?

Related: http://rationalexpressions.blogspot.com/2012/11/how-not-to-teach-it-division-by-zero.html