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, joined, or combined quantities. Decomposition implies that a final quantity can be decomposed into different initial, or joined quantities. Grouping, on the other hand, implies that different initial or joined 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 numbers structured in base ten. Students are then able to understand that a number can also be decomposed based on place values. For example, 25 can be decomposed into 2 tens and 5 ones. 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, if one groups the elements of a set into 2 tens and 5 ones, the set contains 25 elements.
Source: translated from Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 47.