“Necklaces”: A Didactic Sequence for Missing-Value Proportionality Problems

Abstract
This research presents a sequence of didactic situations involving a proportionality relationship in which every value in a set (a number of necklaces) is mapped to a pair, a triad, or a quartet of values (numbers of blue beads, red beads, green beads, etc., required to make that number of necklaces) from another set. The sequence includes relatively simple multiplication and division problems, as well as more complex “missing-value” problems. This paper also presents the results of applying the sequence with a group of 4th grade students in a Mexican primary school (9 and 10 years old).