Here’s the mistake we started with:

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.

What do you think?

Update: This post from Andrew seems relevant.

Natasha had \$8.72. She spent \$4.89 on a gift for her mother. How much money does Natasha have left?

• I gave this question to my 4th Grade class. (11 kids, one absent.) It was December, I had seen them do a variety of subtraction work. I knew that a lot of them could handle subtraction using something like the standard algorithm — though certainly not everyone — and I was wondering whether a money context would be easier or harder for them. Would you predict that \$8.72 – \$4.89 would be easier or harder than 872 – 489?
• What approaches would you predict kids to take for this money problem? What mistakes do you expect to see?

Take a look below, and then report back in the comments:

• Which student’s approach surprised you the most?
• Assume that you’ve got time in the curriculum to ask students to work on precisely one question at the beginning of class the next day. What question would you ask to address some of the ideas you see in their work below?

Student 1

Student 2

Student 3

Student 4

Student 5

Student 6

Student 7

Student 8

Student 9

Student 10

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.

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

From the submitter:

Students were presented with the photo of the bowl of lilikoi and the story: Brayden and Caelyn picked lilikoi.  There were 13 lilikoi in the bowl. Caelyn picked 5 lilikoi.  How many lilikoi did Brayden pick? The second photo shows student predictions.  If a student changed their mind, we crossed out their previous prediction and wrote the new one.

Give a theory as to why students answered 13 before answering 5 (or 8).

Thanks to Mitzi Hasegawa for the excellent submission.

I usually try to at least come up with an idea of what the student was thinking before I post these mistakes on the site. Sometimes, though, I’m totally stumped. Here’s one that got me:

How did the kid get that answer? Anybody?

Also, how would you help the student move forward?

I love this mistake.  From their work, what can we infer about what the student knows? Where are they getting confused? How would you help? (Also, if you don’t feel as if you have enough information, feel free to jump in with want information you’d like.)

Elementary teachers? You out there?