Picture 1. One example of number conceptualization.
If we want to mix pure math and real world scenarios and objects we are counting, it’s easy! We can just put a small letter beside the number, to keep track what we have counted. Hence, in physics we have 3m + 5m = 8m, for distance, length in meters. Then, also we can put 3 apples + 5 apples = 8 apples in agriculture studies. We essentially do two steps here, during the additions of real objects. When we want to add 3m + 5m, we actually separate pure numbers from the meters counted, we enter with these two numbers the world of pure math, where we do calculation of numbers only, 2 + 3 = 8, and then we go back to real world of meters (because we have those small letters to remind us what we have counted) with the result 8, and associate the name of the object, in this case it’s a physical unit of length, or distance, which is meter, (m), to the number 8. And, voila, we have just used pure math in the real world application!