Investigating Integers

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The word integer may seem a bit simple, but as I have learned it can actually be tricky to understand. The first thing that one must know about integers is that the number can be either positive or negative. For example, a set of integers looks like this: {…-3, -2, -1, 0, 1, 2, 3…}. This shows that the negative numbers will continue infinitely as well as the positive numbers. Once the idea of integers is understood, adding and subtracting begins.

A simple way to understand the meaning of an integer is to name the number n. So if n=the number, -n=the opposite of the number, and -(-n)=the opposite of the opposite of n. The opposite of the opposite of n would simply mean the number is positive. An example of n+n is 2+2=4. In this example there are two positive numbers which result in a positive answer. An example of -n+n is -2+2=0. This shows that 2 negatives plus 2 positives cancel each other out resulting in zero. An example of -(-n)+n is -(-2)+2=4. In this example the -(-2) is equivalent to 2, so when we add 2+2 it equals 4.

A great hands on activity that helped me to understand integers was using color counters. Color counters are little square shapes; one side of the square is red and the other side is black. The red side stands for the negative integer and the black side stands for the positive integer. For example to show 2+2=4, you would have 4 black color counters. The example -2+2=0 you would have 2 blacks and 2 reds, which cancel each other out. To show -(-2)+2=4 you would simply have 4 black color counters like in the example 2+2=4. The picture provided is a great representation of the examples I have explained.

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