This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
A PDF of the student activity is included.
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order fractions
FIO, Link, Number, Book One, Chocolate Chip Feast, page 22
The way in which each student responds to an activity that requires them to order fractions gives a good indication of their understanding of fractional notation.
Unit fractions (fractions that have a numerator of 1) should be ordered first. The measuring cups in question 1 provide an opportunity to check this ability. Ask the students to order the cups from smallest to largest.
The correct order would be 1/5, 1/4, 1/3, and 1/2. If the students reverse the correct order, it indicates that they do not understand the role of the numeral in the denominator. Explanations such as “the bigger the number in the denominator, the smaller the pieces that make up the unit” would show sound understanding.
Question 2 extends the ordering of fractions to non-unit fractions. Many students find this difficult because they do not understand the role of the numerator. These students need to see the connection between the unit fraction and the non-unit fraction. For example, three-quarters is three lots of one-quarter.
Have the students estimate the order of the fractions in question 2i–v by listing them from smallest to largest. Highlight the fact that the whole (a cup of chocolate chips) is the same for each tray. The students need to understand this in order to be able to compare the fractions for size.
Question the students to check for understanding, for example: “How do you know that 2/5 is smaller than 1/2?” Accept answers such as “A half of five is two and a half, so two-fifths (two out of five) must be less.”
You may wish to explain equivalent fractions based on a common denominator. For example, comparing halves, quarters, and fifths requires a common denominator of 20.
The students could explore the size of each fraction by using small place value blocks to represent chocolate chips and placing 20 of these in a paper cup.
As they order the fractions, they should find that 1/4 = 5/20; 2/5 = 8/20; 1/2 = 10/20; and 3/4 = 15/20 . If you wanted to include 1/3 in this discussion, the students would need to use 60 blocks.
Answers to Activity
1. a.–b. Two possible ways are:
1/2 + 1/4 or 1/4 + 1/4 + 1/4 (or 3 x 1/4)
2. a. The Superchoc sign (3/4)
b. The Nibbler sign (1/4)
c. Superchoc: tray iv
Freckles: tray i
Spotties: tray ii
Nibbler: tray v
Chocaholics: tray iii