Getting students to develop a conceptual understanding of the addition or subtraction of negative quantities is one of the toughest tasks as a middle school math teacher.
Adding and Subtracting Negatives. Teaching why a + (-b) = a - b and a - (-b) = a + b
Simply teaching students tricks or rules doesn't work long-term and doesn't build students' conceptual understanding of rational numbers.
This is an amazing lesson that I use with my 7th graders during our Computing with Rational Numbers Unit. Once my students have mastered adding and subtracting with one sign (a - b, -a + b, or -a - b), I use this resource to teach students why adding a negative is actually subtracting and why subtracting a negative i actually adding. I spend two class periods on this concept, and my students walk away with a really deep understanding that sticks with them throughout the year.
The lesson starts by connecting to what they already know about addition and subtraction, and then walks them through a simulation that allows them to draw their own conjectures. This lesson has the most impact when it is done as a class discussion.
Teacher's Key included