B1.2 Compose and decompose whole numbers up to and including 50, using a variety of tools and strategies, in various contexts.
Skill: Composing and Decomposing Whole Numbers
Decomposition and grouping are reciprocal notions related to the concepts of final, initial, added, or united quantities. Decomposition implies that a final quantity can be decomposed into different initial, added, joined, or compared quantities. Grouping, on the other hand, implies that different initial, joined, or added quantities can be grouped together to form a final quantity.
A quantity of objects can be distributed in different ways; for example, a quantity of seven fish can be distributed in different ways in two aquariums: one fish and six fish, two fish and five fish, three fish and four fish, and so on. In this case, we speak of a distribution of objects. When this distribution is represented by numbers, it is called decomposition; for example, the number 7 can be decomposed in different ways: 1 and 6, 2 and 5, 3 and 4, and so on.
Over time, students develop an understanding of the concepts of quantity and number structure in base 10. Students are then able to understand that a number can also be decomposed based on positional values, for example, 25 can be decomposed into 2 tens and 5 ones, and that, conversely, it is possible to group the elements of a set into tens or ones in order to determine the number of elements, for example, group the elements of a set into 2 tens and 5 ones, and conclude that the set contains 25 elements.
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 47.