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.
Activity 1: From Smallest to Largest (Connections Between the Whole and Parts)
Directions
Hand out a random list of simple fractions, such as \(\frac{1}{2}\), \(\frac{1}{4}\) and \(\frac{1}{3}\).
Ask students to put them in ascending order using manipulatives.
Ask them to explain their pattern and justify it.
Note: Represent these fractions with concrete materials using various models (area, set, and length). Refer to B1.7 for more information on these models. It is important that students know what each fraction represents based on the models and that they are able to determine which fraction is larger.
Circulate among the students and ask them questions such as:
- Which fraction is larger? Smaller? How do you know?
- What does each number in a fraction represent?
- What is different between the objects you used to illustrate your fractions and those of others? What is similar?
Source: Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 68-69.
Activity 2: Comparing Unit Fractions
Three friends receive cards to play at the store. They have 10 cards in total. Julian has one fifth of the cards, while Sophie has half of the cards. Loisha has a tenth of the cards. Comparing the fractions, how many cards does each friend get? What do you notice?
Strategy
Use a Model to Compare Unit Fractions
I will use cubes to represent the 10 cards.
Julian has one-fifth of the cards. I take 10 cubes and form 5 groups. The whole is divided into fifths, and each part is a fifth of the whole. A fifth is a unit fraction. In this set, a fifth is represented by the 2 green cubes. So Julian has 2 cards.
Sophie has received half of the cards. I take the same 10 cubes and form 2 groups. The whole is divided into halves, and each part is half of the whole. A half is a unit fraction. In this set, a half is represented by the 5 blue cubes. So, Sophie has 5 cards.
Loisha received a tenth of the cards. I take the 10 cubes and form 10 groups. The whole is divided into tenths, and each part is a tenth of the whole. A tenth is a unit fraction. In this set, a tenth is represented by the yellow cube. So, Loisha has a card.
When I compare the unit fractions one-fifth, one-tenth and one-half, I notice that in this set of 10 cards, one-tenth represents only one card, one-fifth represents 2 cards and one-half represents 5 cards.
So, Sophie has 5 cards, Julian has 2 cards and Loisha has 1 card to play in the store.
I notice that if the whole is divided into many parts, its parts are smaller, and if the whole is divided into fewer parts, its parts are larger.
Source : En avant, les maths! ML, Nombres, p. 3-4.