B1.3 Compare and order whole numbers up to and including 50, 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.
Students develop a better understanding of numbers when they are able to establish and use relationships between numbers.
For example, when students recognize and understand the order relationship in the number set, they are able to compare quantities in terms of more than, less than, or equal to. This understanding is a prerequisite for understanding the relationships of one more than and one less than.
The number line or a number strip are good tools to help students compare and order numbers (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. 61.
Skill: Comparing Numbers
In order to compare two or more numbers, you must determine which one is greater than, less than, or equal to another number or numbers.
It is also a question of bringing out the characteristics of the numbers by observing what is similar or different between them; for example, we notice, for the numbers 12, 34 and 26:
- that they are all bigger than 10;
- that they are all smaller than 35;
- that the numeral 2 is found in the numbers 12 and 26, but that this number is not in the same position in these numbers;
- that the numbers in the tens and ones places are different in the three numbers, etc.
The ability to compare numbers helps students develop their number sense, and this exploration gives them a foundation for ordering.
Examples of number comparison strategies include:
- Benchmark numbers can be used to compare quantities; for example, 21 is less than 25, and 28 is greater than 25, so 21 is less than 28.
- Numbers can be compared using their place values; for example, 31 is larger than 13 because, although both have the same digits, 1 and 3, they are different. The number 31 has 3 tens (or 30) and 13 has only 1 ten (10).
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.
Numbers with the same elements can be compared directly; for example, 5 cents and 20 cents, 12 birds and 16 birds.
The pattern in which numbers are organized is a stable order, and regularities in this pattern help to make predictions about order as well as comparisons.
The pattern from 1 to 9 is repeated with every decade. After 9 begins the next ten.
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.
Skill: Ordering Numbers
Numbers can be put in ascending order, from smallest to largest, or in descending order, from largest to smallest.
Understanding place value helps with comparing and ordering numbers.
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.
The ordered numbers can be consecutive (55, 56, 57, 58, 59, 60…) or not (9, 20, 39, 44, 58…).
It is good to develop the ability to compare numbers with students first before the ability to order in order to have a better sense of numbers.