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’m stumped. I can’t think of any way this student got the answer he did. Rounding doesn’t make sense. 6% sales tax would be $0.039, but that seems above the skill set of a student that would be answering this question.

  • Did the kiddo visualize coins and think s/he got a penny back instead of a nickel? three dimes… but one nickel coin, perhaps?

  • The only thing I can think of is that the student thinks that when you borrow, you make the last column one greater than what you are subtracting since you borrowed a one from the ten. Some review work with place value would need to be done to get the student to move forward.

  • Best guess comes at it from addition not subtraction: You’re at 65 cents. With one coin, you can move to 70 cents, and now the problem is easier (you need 30 cents, a quarter and a nickel). That coin seems to have been interpreted as a penny, not an additional nickel, giving 31 cents. So sort of like Sue said above.

    I think to move forwards you might need to ask the student, or give them a similar problem (like with 69 cents) and see what they do with it. Certainly they seem to know how to make 31 cents using actual coins!

  • louise

    I think the student added the 6 and 5 to make 11.
    Subtract 60 from 100 gives you 40. Then you subtract the ten from 40 and add the plus one.
    I have no idea why the student did this, but I had one once who did, even showed me how, and it had something to do with being taught a “subtract one” method and also an “add one” method for moving tens, without really understanding either one, and combining them both into an art form of amazingness.
    We started from the beginning, going through what base 10 is. “Math Curse” is useful for this.
    I agree, the student knows how to use coins to make values. Hooray! I have a particular bugbear with US coins not having numbers on them. It’s hard on us foreigners.

  • cynthia

    I think Sue is on the right track. Given the answer to part b, it seems that this student has a good sense of coins and money. If he/she counted UP to figure out the change, or thought of a number line, it could simply be that the first “jump” (or coin) going from 65 to 70 was mistakenly considered to be “one” (instead of 5) and then the jump from 70 to 100 was correctly thought of as 30. Of course, 1 plus 30 is 31.

  • cynthia

    Oops – just read Greg T’s explanation more carefully and see that we are basically saying the same thing. The student made a simple slip and mixed up one jump or coin with one penny.

  • Brian Ward

    I think when the student regrouped and the zero in the one cent place value was then turned into ten by putting a one there, the student may have extended the one down too far and made the zero look like a six, then subtracted the five from the new mistaken six.

  • Jasper

    What is the sales tax rate in your jurisdiction? A six percent sales tax would neatly eat up four cents.

    Has the child ever seen a store price that does not end in “9”?