B1.7 Recognize that one third and two sixths of the same whole are equal, in fair-sharing contexts.
Skill: Recognizing Equivalence
To recognize the equality of two fractions is to recognize that both fractions represent the same quantity.
It is sometimes difficult for students to grasp that a quantity can have several names and be represented by several
numbers (for example, the number \(\frac{1}{3}\) represents the same quantity as the number \( \frac{2}{6}\);
therefore, we can say that \(\frac{1}{3}\ = \frac{2}{6}\)).
Understanding equivalent fractions is part of the proportional reasoning that students will continue to develop over the next several grades.
Determining equivalent fractions means determining fractions that represent the same quantity. We are looking for a number of "small parts" of a whole that correspond to a particular number of "large parts" of the same whole. If, for example, we are looking for the number of sixths that correspond to one-third, we can represent the two fractions using identical area models in order to recognize the equivalence.
The equivalence relation must also be explored with respect to fractions of a set. In the image below, students can easily see that \(\frac{2}{6}\) candies are wrapped in red foil wrappers. However, they may have difficulty determining the equivalent fraction, \(\frac{1}{3}\). It is therefore important to present students with activities that allow them to manipulate the elements of the whole, so they can group them into sets of 2 and determine the equivalent fraction.
\(\frac{2}{6}\) sweets are wrapped in red wrappers.
\(\frac{1}{3}\) sweets are wrapped in red wrappers.
Source: Guide d'enseignement efficace des mathématiques de la 4eà la 6e année, p. 50-52.
Knowledge: Equivalent Fractions
Two fractions are equivalent if they represent the same quantity.
Note: In Grade 2 , it is important to emphasize that these are fractions of the same whole. The same part of a whole can be represented by different fractions (for example, one-third and two-sixths are equivalent fractions).
Source: En avant les maths! 2e année, CM, Nombres, p. 2.