Integer Experiences in Daily Life

Until now we have taken a strictly mathematical route to understand integers and operations with them.

Integers are difficult to understand for people who are not very familiar with mathematics. We give below some daily events & experiences which can be interpreted with the use of integers. We need to recall here that, in integers, the + & - also represent a “direction”.

1. Altitude or Depth

The altitude at sea level is considered by convention to be 0 meters. A point on a mountain can be thought of as being at +10, 000 meters. A point at a depth of the ocean floor can be thought of as -300 meters. Here “direction” indicates whether a location on earth is above or below sea level.

The altitude and depth are measured in a direction which is perpendicular to the surface of the sea or Earth. They are opposite of each other.

1. Temperature

The freezing point of water is considered by convention as 0 C. Boling point of water can be thought of as +100 degrees. Freezing point of Helium can be thought of as -269 C.

1. Cash Surplus & Debt

Having Rs 1,000 in hand can be thought of it as having Rs +1,000. If Rs 500 is owed to someone, it can be thought of as having Rs -500!

Similarly having Rs 1,000 in the bank account can be thought of as +1,000. Owing Rs 500 to the bank can be thought of as -500.

Recall that Bhaskaracharya in the 7thcentury AD used these terms while talking about negative & positive numbers.

1. Comparative Performance

If in a class test, the class average is 45, then someone who scored 40 can be thought of as scoring “below” average. We can even think of his comparative score as -5. Similarly, one who scores 55 can be thought of as scoring +10, comparatively.

This idea of comparative performance can be applied to any situation which studies the variation of a set of date with respect to the average.

1. Historical Time

Events in history are labelled as BCE (Before Common Era) or CE (Common Era). Our current year is 2020, which can be thought of as +2020. Euclid was born in 300 BCE, which can be thought of as -300.

1. Electron & Proton

Electrons are –ve charges & Protons are +ve charges. Both the charges are equal and of opposite character. Hence an electron can be thought of as -1 and a proton can be thought of as +1. A neutron can be thought of as a combination of an electron & proton. Its weight is almost same as the proton and it has no charge I.e a charge with is 0.

1. Double Negatives in Language

Rules similar to those of integer operations can be seen to operate in language also. Consider the two following statements.

Case 1

Ram is taller than Lakshman. This statement is false.

In language this is equivalent to saying “Ram is not taller than Lakshman”. The second statement makes the first statement also false! This can be seen as the equivalent of ‘+ -‘ equivalent to “-‘.

Case 2

Ram is not taller than Lakshman. This statement is false.

In language this is equivalent to saying “Ram is taller than Lakshman”. We see that 2 negatives are making a statement true!

We can also see that “I am not saying that Ram is not taller than Lakshman” means that “Ram is taller than Lakshman”

We will now look at the issue of explaining integers and their operations to students in the classroom