A matemática do 6° ano

This app provides a platform for students to learn from the ideas of negative numbers, including addition and subtraction. The primary assumption is that for any positive number such as 1, there is an inverse, -1, with respect to addition, so 1 + (-1) = 0. Zero is often called an additive identity; the inverses are called additive inverses.

In the app, a blue ball represents a positive; a red ball represents a negative. A blue ball plus a red ball equals zero, that is, they cancel each other out as they approach each other. This is a useful strategy for learning and teaching the big ideas behind negative numbers. This strategy is based on inverse relationships in mathematics. It is particularly useful for explaining problems like 2 - (-3). While it's easy to say that negative negative three is the same as plus three, it's not so easy to explain why. Using inverses, we could still use the idea of ​​“subtraction as taking away”. To subtract three negatives from two positives, we need to add three zeros in the form of inverse blue and red pairs. In this case, we need to add three pairs of blue and red balls. So, we take out the three red balls, which means “subtract minus three”. We are left with five blue balls, which means the result is a positive five.

Of course, there are other ways to explain subtraction besides negative numbers, each with their own advantages and disadvantages. Ultimately, students must come to the understanding that, given two numbers A and B, A minus B is a number C such that C plus B equals A, whether they are positive or negative.