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Part and wholes
In years 3 and 4, students use two dice, one labelled 1 to 6 (called the wholenumber die) and the other labelled with fractions (called the fraction die). The fraction die has fractions appropriate to the year level (e.g. for year 3 the fractions could be \(\frac{1}{2}\), \(\frac{1}{4}\), \(\frac{1}{8}\), \(\frac{1}{3}\), \(\frac{1}{5}\)).
Pairs of students roll the two dice to generate numbers to insert into the sentence:
(fraction roll) of my collection is (wholenumber roll) so altogether I have ____
Students model the problem, using counters to make a group of five.
They then make more groups of five until there are four equal groups, and calculate the total.
Teachers should:
 encourage the formation of arrays to make the relationship with factors and multiples more obvious
 discuss strategies for working out the total without having to build the array

ask what other fractions can be determined from the array, such as
\(\frac{3}{4}\) of 20 = 15
\(\frac{1}{5}\) of 20 = 4
In year 6, students solve problems to determine fractions of collections and multiples of those fractions. For example:
I lost \(\frac{1}{8}\) of my marbles. I have 42 left. How many did I start with?
Discuss with the class:
 possible strategies for solving the problems
 the effectiveness of various strategies.
For students not confident in factors and multiples, creating arrays on grid paper can provide scaffolding for finding strategies.