B1.6 Use drawings to represent and solve fair-share problems that involve 2 and 4 sharers, respectively, and have remainders of 1 or 2.
Skill: Representing and Solving Fair Share Problems
In the primary grades, students have the opportunity to explore fractions by sharing sets of objects; for example, if three friends want to share 18 apples equally, each person will receive six apples. If the same three friends wanted to share 19 apples, there would be one left over. The primary grades focus on this remainder, and how it can be equally shared. In Grade 1, this remainder results in fractions that are halves or fourths. Sharing can then be used as a springboard for the study of fractions in junior grades.
By continuing to build on the principle of equal sharing for a wide range of scenarios, students will create connections between different wholes, and parts of the whole. They understand that the fraction represents a quantity and the remainder after sharing; for example, if 4 students want to share 5 cupcakes, each person receives 1 cupcake and one-fourth of a cupcake.
Source: translated from Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 2, Fractions, p. 28.
Exploration of Fractions
Baroody and Coslick (1998, pp. 9-14 and 9-15) emphasize a meaningful approach to learning fractions. They advocate that learning fractions follows a progression that moves students from informal, concrete representations to formal, abstract representations. The first step in this progression is the sharing of quantities.
Sharing: Any activity that engages students in a meaningful experience of sharing, without explicit reference to terminology or symbolism, provides a concrete foundation for understanding the concept of fractions. By starting with a common everyday task (sharing markers or crayons for an art project, for example), students can develop the ability to divide a set of elements into equivalent parts. Later, they may have experiences that involve more sophisticated thinking in which they need to split a single element (for example, dividing a piece of cardboard into three equivalent parts to make a craft) (Grade 2).
Source: translated from Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 2, Fractions, p. 58.