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 allows us to compare and order them to better understand their meaning.
A better understanding of numbers is developed when students are able to establish and use relationships between numbers.
For example, by recognizing and understanding the order relationship in the number 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 : , Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 60.
Skill: Comparing Numbers
Comparing 2 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 place of the tens and ones is different in the three numbers, but not for the hundreds, etc.
The ability to compare numbers helps students develop their number sense. In addition, this exploration gives them a foundation for ordering numbers.
Relationships in Ordering and Comparing
The ability to recognize relationships between numbers is acquired by comparing numbers, placing them in ascending and descending order, counting backwards and analyzing the relative proximity of two numbers.
Students should recognize the relationships between numbers by comparing them. They can describe the relationships by stating, for example, that 135 is smaller than 153.
Here are some examples of strategies that can be used to compare numbers.
| Students can recognize that 153 is larger than 135 : | Example
|
|---|---|
| by comparing numbers to a benchmark number; | Discover that 153 is larger than 135, since 153 is larger than 150 and 135 is smaller than 150.
|
| by visualizing or representing important quantities; | Visualize or represent the two numbers using base-10 materials to see that there are, for example, 15 tens
and 3 ones in 153, and 13 tens and 5 ones in 135.
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.
|
| by comparing the numbers in the various place values, starting from the left. |
1 5 3 ↓ ↓
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: adapted with Grade 2 appropriate numbers from Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, p. 46.
Skill: Ordering Numbers
Numbers can be placed in ascending order, from smallest to largest, or descending order, from largest to smallest.
Understanding place value allows for comparison and ordering of numbers.
Source: Ontario Mathematics Curriculum, 2020, Ministry of Education of Ontario.
The ordered numbers can be consecutive, for example 675, 676, 677, 678, 679, 680, or not, for example 39, 209, 399, 501, 998.
It is good for the student to develop the skill of comparing numbers before the skill of ordering in order to have better number sense.