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
"The development of understanding of the quantity represented by a fraction relies on the student's experience with concrete materials and on instruction that focuses more on the meaning of the fraction than on procedures." (Free translation, Bezuk & Cramer, 1989, p. 157)
In the primary grades, students have the opportunity to explore fractions by sharing sets of objects; for example, if 3 friends want to share 18 apples equally, each person will receive one-third of the apples. Sharing can then be used as a springboard for the study of fractions in upper primary and in junior grades. Note that the Grade 1 curriculum limits the study of fractions to halves and quarters.
By continuing to build on the principle of division, students create connections between the action of a division, the whole, and the parts of the whole. They are able to better understand fractionation and develop a sense of fractions. They understand that the fraction is also used to illustrate a 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 : Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, 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 : Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, p. 58.