All Bottled Up

The capacity context of this activity allows students to explore the concept of the fraction of a set more fully. Use the first diagram in each pair shown in question 1 to help the students to appreciate the capacity of the whole container as an equivalent fraction for 1. Have the students record these fractions for 1 for each part
of the question. They could record these fractions in a table.

Question 1e will trap the unwary if they do not read the caption carefully. Question 1e also focuses the students on the complementary relationship between full and empty. After the students have answered question 1e, you could make this relationship quite explicit for each part of question 1 to reinforce the equivalent fractions for 1. Another table could be useful:

This is a good activity to introduce the double number line as a tool for visualising the relationship between the fraction and the set. For question 1a, the number line could look like this:

Question 2 shows the effect of halving again and again. A ratio table would show this very powerfully:

(The shaded part shows what happens if you continue halving.)

Answers to Activity

1. a. Two cups
b. Four cups
c. Six cups
d. Three and a half (31/2) cups
e. 15 cups
f. 40 cups
2. Four cups