## BP - Integers

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.

*(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 Integer Drills1. Combining integers with no double signs 1.1 Negative plus positive 1.2 Positive minus positive 1.3 Negative minus positive 1.4 Mixed 2. Combining integers with double signs 2.1 Add negative 2.2 Subtract negative 3. Mixed integer sums and differences 3.1 Sums and differences 3.2 Missing number |
4. Integer products 4.1 Products with parentheses 4.2 -1/Opposite 4.3 Squares and square roots of integers 5. Absolute value 5.1 Absolute value and simple expressions inside 5.2 Simple expressions inside and outside 5.3 Mixed absolute value and opposite |