Adding and Multiplying Integers

Here is a model of the expression we are solving. The expression is 4 - (-3). in math, we are working on integers, so me and my partner, Rahini, decided to to model it like this; a chip model. The black little ovals represent one positive, and the not filled in ovals represent one negative. In step one, there are four ovals, so we start with positive four. In step two, we bring in the negative three, however, there is nothing there to subtract it from. The solution is to create zero pairs by adding one positive underneath it, because one plus negative one would equal 0. This works because the expression is saying take away negative three, and now you have something to take it away from. Then we crossed out three of the white ovals, because we needed to take away negative three. Then you are left with 7 black ovals, so 7 is the difference. 

Here is a another model of an expression- soon to become an equation. The expression was -4 * (-2). This was a little harder, as it was multiplication. So we first tried to understand the equation. The equation is saying to find 2 groups of -4. Actually, it could also be four groups of negative two because of the commutative property where 6*4 equals 4*6, but we chose the first one that came to mind. But the equation has negatives, so you must take away the two groups. From what, though? The answer to that question yet again has zero pairs. We then created the zero pairs and had something to subtract it from. So, we crossed out/ took away the two groups of -4 from the ovals and were left with two groups of +4. So the product was +8.