BP - Fractions

I first started thinking about using repetitive practice more often when I got tired of hearing my pre-algebra students, when faced with 3x = 5, (or worse, 5x = 3) tell me “You can’t do that. You can’t divide 5 by 3 (or 3 by 5).”  I knew perfectly well that we had gone over that the year before, because I had taught most of them in 6th grade!  Or when students see (or hear) "What's 4 x 3/5?" or "What's 2/3 of 24?" and want to write out 4/1 x 3/5, or ask "Of means multiply, right?" and THEN write out 2/3 x 24/1...  I am always sensitive to when my students are signalling that they need to do more conceptual work, but more and more I am aware of the difference between understanding and recognizing/remembering.  I think those take place in different parts of the brain, and I am not sure what kind of communication there is between the two parts.  It seems that understanding informs memory and recognition*, but repetition is also an essential nutrient.  These drills are a way to feed the recognizing part.

*(When I say recognition, I mean that sudden knowledge, apparently from nowhere, that to find 2/3 of 24 I divide by 3 first ... I don't have to consciously go through the reasoning behind that, or draw a bar model ... I just know it; I recognize that as familiar territory.  Just like if I woke up on the bus in a familiar part of town, I would know how to get home without consciously thinking about it, but if I woke up in an unfamiliar part, entirely different parts of my brain would be going to work.)

The collection is  a work in progress.  The list of topics is a goal for myself; there are some holes.
Topics for Fraction Drills

1.     Find equivalent forms of fractions
        1.1.  Equivalent fractions given denom or num
        1.2.  Improper to whole and vice verse
        1.3.  Mixed to improper and vice versa

2.     Models
        2.1.  Write the multiplication problem (from a model showing 2/3 x                     15… or make a model from a multiplication problem)
        2.2.  Subdivide divisions - reunitizing

3.     Reciprocals
        3.1.  Simple fractions < 1, > 1
        3.2.  Of mixed numbers

4.     Adding and subtracting
        4.1.  Adding with same denom
        4.2.  Adding diff denom skill sheet, small fractions
        4.3.  Adding, subtracting no borrow mixed numbers
        4.4.  Subtract from one/complete to one (missing part)
        4.5.  Subtract from whole number
        4.6.  Subtract with borrow


5.     Multiply
    5.1.  Simple fractions part (of/* whl)
    5.2.  Simple fractions measurement * whole
    5.3.  Combined meas and part * whole
    5.4.  Simple frac products (incl w/parens)
    5.5.  Mixed numbers (set it up)
    5.6.  Cross cancel
    5.7.  Word problems
    5.8.  Squares of fractions (see Pre-Algebra squares of rational numbers)

6.     Divide
    6.1.  Simple fractions measurement by whole
    6.2.  Whole by whole (include draw the bar model for 27 ÷ 3, and 7 ÷ 5,                 and 4/5; write equivalent forms)
    6.3.  Word problems, long division with fraction answers
    6.4.  Frac/whole by whole
    6.5.  Frac/whole by frac
    6.6.  Frac/whole by frac/whole
    6.7.  Mixed numbers (set it up)
    6.8.  Cross cancel
    6.9.  Word problems

7.     Mixed operations