This is a snapshot of a book by Robert Ashlock, Error Patterns in Computation.

Penny for your thoughts in the comments. How does a book like that relate to a blog like this?

Also, jump in if you have anything interesting to say about this sort of fractions error.

  • To me, the book and this blog are one and the same, with the blog obviously much more accessible to social PLNs. I think this is a perfect snapshot of a common error in fraction computation. Ironically, I just had a conversation with a 4th grade teacher who insists on having students 1)write the problems vertically and 2) add with common denominators by “multiplying the top and bottom by the same number.” This same teacher has students who cannot compare 3/4 and 4/3 without going to 12ths….major problem…..but I digress….

    What does Robin understand? The student obviously can find the least common denominator but is not adjusting the numerator to create an equivalent fraction. This seems like the adding fraction algorithm gone bad because there is no conceptual understanding of equivalent fractions. If teachers are telling students to “multiply the top and bottom by 2 to get an equivalent fraction” with no concrete connection or understanding that you are truly multiplying by 2/2 = 1, then we have failed the students.

    Fraction strips, fraction strips, fraction strips….use them and love them!