Sixth grade homework can sometimes look like this: 5/12 divided by 5/9. I wish fractions problems would use easier numbers so that the student can feel if their answer makes sense. I like to use 12 divided by 1/2 or perhaps the more difficult problem used by Liping Ma and/or Deborah Ball : 1 3/4 divided by 1/2.

Students can build intuition by asking themselves if the answer would be more than 1 or less than 1 by using 3/12 or 12/3 and seeing which of these examples their problem resembles.


These fraction problems are usually also related to attention to detail and reading. One of the other problems was you have 12 yards of fabric and will use 2/3 of a yard for each item -- how many items can you make? The student will often perform the multiplication of12 x 2/3 without asking themselves the question: Can I make more than 12 items or less? Once they have answered that questions, then they have a more clear sense of what to do. 1/2 vs. 2 can be used here.

1/2 x 1/2 is a great example as students often add instead of multiply and do not feel that multiplication should make their answer smaller!!

For division of fractions, why do we invert and multiply? If the student just memorizes the procedure, they will not know which procedure to use. It might (definite maybe) be ok if students were able to memorize these concepts and procedures but they get all jumbled!! Students will better comprehend the material and have the ability to more accurately retrieve it if they rely upon examples rather than memorizing procedures.