B1.2 Compare and order whole numbers up to and including 200, in various contexts.
Skill: Comparing and Ordering Whole Numbers
Making connections between numbers supports comparing and ordering them and a better understanding of numbers is developed when students see and use relationships between numbers.
For example, by recognizing and understanding the order of numbers in a set, students are able to compare quantities in terms of more than, less than, or equal to. This understanding is a prerequisite to understanding the relationships of one more than and one less than.
The number line is a good tool to help students compare and order numbers because on a number line, the numbers increase as you move to the right and decrease as you move to the left.
Source: translated from Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 61.
Skill: Comparing Numbers
Comparing two or more numbers involves determining which one is "greater than", "less than", or "equal to" another number or numbers.
It is also a matter of highlighting the characteristics of the numbers by observing what is similar or different between them. For the numbers 92, 134 and 176, for example, we notice:
- that two of them are larger than 100 (134 and 176) and that 92 is smaller than 100;
- that they are all smaller than 200;
- that the three numbers are even;
- that the number in tens and ones place are different in the three numbers, but the hundreds are the same.
Being able to compare numbers supports number sense and is foundational for ordering numbers.
Relationships in Ordering and Comparing
Recognizing relationships between numbers involves comparing numbers, placing them in ascending and descending order, counting backwards and analyzing the relative proximity of two numbers.
Students can begin to recognize the relationships between numbers by comparing them. They can describe the relationships by stating, for example, that 135 is smaller than 153.
Examples of strategies that can be used to compare numbers include:
| Students can recognize that 153 is larger than 135: | Example |
|---|---|
| by comparing numbers to a benchmark number; | Students conclude that 153 is larger than 135, since 153 is larger than 150 and 135 is smaller than 150. |
| by visualizing or representing important quantities; | Students represent the two numbers using base ten materials and conclude that there are 15 tens in 153, and 13 tens in 135, so 153 must be larger.
153   135  |
| by placing numbers on a number line or a number chart; |
The number 153 is located to the right of the number 135, so it is larger. |
| by comparing the numbers in the various place values, starting from the left. |
1 5 3 The number 1 represents a quantity of 100 in each number. The number 5 represents a quantity of 50, while the number 3 represents a quantity of only 30. |
Source: translated and adapted with Grade 2 numbers from Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 1, Nombres naturels, p. 46.
Skill: Ordering Numbers
Numbers can be ordered in ascending order - from least to greatest - or they can be ordered in descending order - from greatest to least.
Understanding place value enables any number to be compared and ordered.
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.
The ordered numbers can be consecutive, for example 675, 676, 677, 678, 679, 680, or not, for example 39, 209, 399, 501, 998.
Being able to compare numbers supports ordering them, and both skills are important in developing better number sense.