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
Fraction concepts should be introduced gradually. One difficulty in grasping the quantity that is represented by a fraction is that historically, we have not "counted" 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 fractions as numbers, 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 eventually to compose and decompose fractions using models and symbols in later grades.
Some students have difficulty comparing the order of magnitude of two fractions. For example, they might have difficulty grasping the fact that \(\frac{1}{2}\) is larger than \(\frac{1}{3}\) 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. Multiple experiences with these ideas are needed to help students connect to the symbolic representation of fractions to concrete representations, compare fractional quantities, and generate fractions between any two quantities.
Source: translated from Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 74-75.
The size of the whole matters. When comparing fractions as numbers, it is assumed they refer to the same-sized whole. Without a common whole, it is quite possible for one fourth to be larger than one half.
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.
Knowledge: Unit Fractions
A unit fraction is any fraction whose numerator is one (1); for example \(\frac{1}{2}\) and \(\frac{1}{4}\).
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.