Here are some ideas pupils need to learn about integers:
•A number represents a quantity. An integer is a type of number. An integer represents a quantity.
•Integers are useful in representing quantities and includes opposite sense. For example, going up 5 floors and going down 5 floors can be represented by +5 and -5 respectively. The sign ‘+’ represents up and ‘-’ represents down. The ‘5’ represents the number of floors.
•The integer +5 is read as “positive five” and NOT “plus five”. The integer -5 is read as “negative five” and NOT “minus 5”.
•The words positive and negative are descriptions of the whole number 5 while the words plus and minus describe operation to be done with the numbers. That’s why it doesn’t make sense to read the integer -5 as “minus 5”. From what number are you subtracting it?
•The number 0 is an integer which is neither positive nor negative.
•Integers can be represented in a number line. An integer and its opposite are of the same distance from 0. For example, -4 is 4 units to the left of zero so its opposite must be 4 units to the right of 0. This integer is +4.
Problem: The distance between two integers in the number line is 4 units. If one of the integer is 3 units from zero, what could be these two integers?
•The distance of an integer from zero is called the absolute value of the integer. So the absolute value of -4 is 4 and the absolute value of +4 is also 4.In symbol, /+4/ = 4 and /-4/ = 4.
Of course, merely explaining to students these ideas and giving them lots of exercises will not work. It will never work for many of them. Teachers have to design tasks or activities pupils can work on so that students can construct their own understanding of these ideas. Teachers can help scaffold their learning through problem solving tasks and through the questions and feedback they will provide the students.
Next post on this topic will be about absolute value and operations with integers.