Fraction as division.

Clarke, D.

The following activity looks at the notion of "fraction as division" or "fraction as quotient." Rather than seeing 2/3 for example, as two parts out of three, the activity focuses on the meaning of 2/3 as "2 divided by 3."

You will need: 3 chairs and a number of whole chocolate bars (illustrated here with 10).

1. Place the 3 chairs at the front of the class and distribute the chocolate on the chairs. In this case, 5, 3, and 2 chocolate bars respectively (see Figure 6).

2. Ask individuals one at a time to come up and choose a chair to stand behind, with a view to sharing the chocolate at the end of the activity ("more chocolate is better").

3. As more students are selected and make their choice, ask them to explain their reasoning.

Also, ask other students to suggest where they think others should stand and why. Valuable discussion can occur around the strategies that students use to make their decisions and at the end of the activity, the following questions can extend their thinking further:

* If, at the end, you had the choice to move to a different chair, would you do so?

* Where would you choose to stand in the queue? Is it best to go first or last?

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Removing the chocolate from the packets involves further challenges, and instances where there are more blocks of chocolate than people provides a context for discussing improper fractions.

Finally, have the students behind one of the chairs lift it over their heads, with the chocolate still on it. Figure 7 shows a visual image of the numerator, denominator and vinculum of the fraction. In this instance, five blocks of chocolate on top, chair as vinculum (line dividing the numerator and denominator) and two people underneath, provides a powerful image of five over three, or 5/3.

[adapted from Clarke, D. (2006). Fractions as division. APMC 11(3), 4-9.]