This math unit begins by developing students' understanding of solving algebraic expressions involving exponents, starting with simpler structures like monomials set equal to constants and progressing to more complex binomial ratios. Initially, students practice isolating variables within expressions involving monomial and binomial exponents. As their skills advance, they tackle expressions where binomials are both numerators and denominators, challenging their understanding of exponent rules such as negative and fractional powers. The unit then transitions into deepening the students’ proficiency with logarithmic functions. Starting with applications of the logarithmic product, quotient, and power properties, learners simplify expressions and convert them into quadratic equations or isolate variables using logarithmic transformations. This portion enhances algebraic manipulation skills in logarithmic contexts, leading to solving equations where they must determine if functions are inverses or apply logarithmic identities to identify variables in more intricate setups. By the end of the unit, students are equipped to handle a mixture of algebraic and logarithmic equations, converting logarithmic forms to exponential forms, mastering skills in handling complex logarithmic operations, and isolating variables in various algebraic contexts involving both exponents and logarithms. This prepares them for high-level problem solving in mathematics where exponents and logarithms play a critical role.Skills you will learn include:
Topics are small, focused areas which build towards the greater unit's goals.