Factoring, Multiplication, Division, Fractions - Advanced

This math unit begins with the development of prime factorization skills, starting by completing factor trees with up to four factors to recognize and apply prime factors in different contexts. As learners progress, they refine their ability to perform prime factorizations into three factors, focusing on specific numeric examples. The unit then advances into the application of factorization techniques to simplify multiplicative and divisive operations within fractions. Students learn to simplify fraction multiplication and division by cancelling common factors, aiming toward expressing complex fractions in their simplest form. As the students' skills in recognizing and manipulating factors improve, the unit moves toward comparing factored numbers through relational operators, enhancing their understanding of algebraic manipulation, comparison, and exponentiation. Finally, the unit proceeds to factor large numbers where learners identify specific prime factors and associated powers. They practice factoring under constraints with larger composite numbers, enhancing their overall capabilities in factoring, multiplication, division, and deepening their understanding of number decomposition and algebraic flexibility. The focus on large factored numbers expands from two to three factors, with the incorporation of advanced techniques to simplify multiplicative operations involving large and composite numbers.