Factoring and Primes - Advanced

This math unit progresses students through a comprehensive understanding of prime factorization, beginning with basic prime factorization tasks and extending into more complex exercises that require a deeper understanding. Initially, students learn to decompose numbers into sets of three prime factors, using tools like factor trees and multiple-choice questions to guide their understanding. As the unit progresses, the complexity increases as students work with four and eventually five prime factors. They practice expressing these factors in exponential form, which is particularly useful for succinctly representing repeated prime factors. Towards the middle and end of the unit, the focus shifts to applying prime factorization in various contexts, such as completing and explaining parts of factor trees, and identifying missing factors. The unit culminates in ensuring students can differentiate between prime and composite numbers, enhancing their foundational understanding of number properties and ultimately strengthening their skills in recognition and categorization of numbers based on their factorization. This progression not only solidifies their comprehension of prime factorization but also enhances their analytical and problem-solving skills in mathematics.