Why do 2 minus make a plus

I've been into a few Grade 7, 8 and 9 classes over the past few weeks and one of the areas of focus has been integers. It's no big secret that integers can be problematic for many students and, I would add, adults too. Chatting with some students, I heard things like "Two minuses make a plus": is this really true?

My concern is that students have developed misconceptions because they have skipped straight to the abstract part of the concrete-diagrammatic-abstract part of that continuum. So here are some activities I used to help them through the concrete and diagrammatic phases to allow them to make sense of the abstract: 1 My first goal is to get students to be able to add integers.

Like many teachers, I use integer tiles to represent integers concretely:. Adding a negative is the same as Main menu Search. Making Sense of Positives and Negatives.

Perhaps you have heard people say "Two minuses make a plus". This isn't the most helpful way to think about positive and negative numbers. Below are some different ways of thinking about adding and subtracting positive and negative numbers. We hope they will help you to understand what's going on when you might be tempted to use a rule like "Two minuses make a plus". There are four possibilities that we need to be able to understand: Adding a positive number Adding a negative number Subtracting a positive number Subtracting a negative number Hot Air Balloon The first model we offer is the hot air balloon, as seen in the game Up, Down, Flying Around.

In this model, we represent positive numbers as 'puffs' of hot air, and negative numbers as sandbags. I add two sandbags down two , subtract five puffs of hot air down five , subtract one sandbag up one , then add seven puffs of hot air up seven. Practice: Signs of expressions. Practice: Multiplying negative numbers. Dividing positive and negative numbers. Practice: Dividing negative numbers. Why a negative times a negative is a positive. Why a negative times a negative makes sense.

Multiplying negative numbers review. Dividing negative numbers review.