Number theory is widely applicable to many areas of elementary school mathematics including: finding the least common denominator when adding or subtracting fractions, finding the greatest common factor when simplifying fractions, and testing for divisibility. Studying number theory develops one’s number sense or insights into the properties that numbers share and fail to share. However, number theory is not explicitly taught in the elementary schools. In discussing number theory, this chapter will examine how children find factors and multiples, what divisibility tests children may use in elementary school, what misconceptions preservice teachers may have about prime and composite numbers, and how children find Greatest Common Factors (GCF) and Least Common Multiples (LCM).
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