B1.8 Use drawings to compare and order unit fractions representing the individual portions that result when a whole is shared by different numbers of sharers, up to a maximum of 10.
Skill: Comparing and Ordering Unit Fractions
The concept of a fraction should be introduced gradually. The difficulty in grasping the quantity that is represented by a fraction is compounded by the fact that we do not "count" with fractions as we do with positive whole numbers. According to the Focus on Fractions, students should count in unit fractions (starting at 0 and continuing beyond 1) to develop a sense of the fraction as a number, the role of the numerator and denominator, and the relationship between the numerator and denominator. Therefore, multiple activities should be provided to help students use unit fractions to name and count fractional quantities, and then compose and decompose fractions using models and symbols.
Some students have difficulty comparing the order of magnitude of two fractions.
For example, these students have difficulty grasping the fact that a \(\frac{1}{2}\) is larger than a \(\frac{1}{3}\) because they tend to associate the quantity represented by a fraction with the whole number used as the denominator. This leads them to believe that 2 is smaller than 3, so multiple activities such as those suggested in the Fraction Learning Pathway, Cluster 2 - Comparing Fractions, are needed to help students connect the symbolic representation of fractions to concrete representations, compare fractional quantities, and generate fractions between any two quantities.
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 74-75.
The whole is important. To compare fractions as numbers, we assume that they refer to a whole of the same size. If the whole is different, it is quite possible that a fourth is larger than a half.
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.
Knowledge: Unit Fractions
A unit fraction is the fraction whose numerator is one (1), such as \(\frac{1}{2}\) et \(\frac{1}{4}\).
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.