B1.2 read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines
Skill: Reading Whole Numbers
Each integer has its opposite, both located at equal distance from zero on the number line. For example, -1 and 1 are opposite integers and are at the same distance from zero.
Pairs of opposite integers equal zero. For example, integer pairs like \({(+ 3)}\;{\rm{and}}\;{(- 3)}\; = \;0\).
The zero is defined as being neutral, therefore neither positive nor negative.
Negative integers are "less than zero". Zero is exactly in the center of the number line of integers; the line is symmetrical about zero.
On a horizontal number line, positive integers are displayed to the right of zero and negative integers are displayed to the left of zero.
On a vertical number line, positive integers are displayed above zero and negative integers are displayed below
zero.
Source : The Ontario Curriculum, Mathematics, Grades 1-8, Ontario Ministry of Education, 2020..
The most common use of negative integers is for temperature. For example, -3ºmeans 3º below 0 degrees. Sometimes negative integers are used to describe debts. For example, if one owes $5, one can think of it as having -$5. Negative numbers are sometimes used in field hockey statistics and golf scoring.
Source: Closing the Performance Gap , Grade 9, p. 11.
Skill: Representing Whole Numbers
Negative integers are located to the left of 0 on the number line. They are the opposites of the positive integers,
which means that they are located as far to the left of 0 as the positive integers are to the right of 0. Thus, -5 is
exactly the same distance to the left of 0 as 5 is to its right. Since the numbers are placed in ascending order from
left to right on the right, a negative integer is therefore necessarily smaller than a positive integer.
It is possible to represent the integers on a vertical number line that is similar to a thermometer rather than on a
horizontal number line. In this case, the positive integers are above the negative integers.
It is also possible to use two-coloured tokens to represent whole numbers, one color to represent positive whole
numbers and another to represent negative whole numbers. For example, 5 can be represented by 5 white tokens and -5 by
5 red tokens.
Source: Closing the Achievement Gap, Grade 9, p. 10-11.
Integers can be represented as points on a number line or as vectors (arrows) indicating magnitude and direction. The
integer -5can be represented as a point positioned 5 units to the left of zero or 5 units below zero. The
integer -5 can also be represented as a vector from zero to -5 on the number line to show that it is 5 units long and
moving in the negative direction.
Source : The Ontario Curriculum, Mathematics, Grades 1-8, Ontario Ministry of Education, 2020.
Knowledge: Integers
Set of integers (\(\mathbb{Z}\))
The set of integers is made up of natural numbers (0, 1, 2, 3…) and negative integers (-1, -2, -3…). We can therefore
say that all natural numbers are integers, but not all integers are natural numbers. The relationship between natural
numbers and integers can be represented by the Venn diagram shown below.
Source : Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, p.
41.