Abstract
This study aims to develop a local instruction theory (LIT) based on realistic mathematics education (RME) that is valid, practical, and effective on the topic of multiplication in grade III of elementary school. The research method used is research design type Gravemeijer & Cobb (2013). The research was conducted in three phases, namely preparing for the experiment, experimenting in the classroom, and conducting retrospective analysis. Data was collected using document analysis, observation, interviews, field notes, tests, and questionnaires. The collected data was analyzed qualitatively and quantitatively. Based on the research that has been carried out, LIT is produced which is valid, practical, and effective against students' mathematical problem solving abilities. Students can find a standard multiplication algorithm with a series of activities, namely finding the product of multiplication with repeated additions, ten multiplications, multiples of multiples of ten, and standard multiplication algorithms.
 Keywords: LIT, RME, multiplication
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