Logarithmic Functions Unit Plan

Introduction to Logarithmic Functions

General Outcome: Develop algebraic and graphical reasoning through the study of relations.

SO4. Demonstrate an understanding of logarithms and the laws of logarithms. [C, CN, ME, R]

4.1 Express a logarithmic equation as an exponential equation and vice versa.
4.2 Determine the value of a logarithmic expression, such as log ₂ 8, without technology.
4.3 Develop the laws of logarithms, using numeric examples and the exponent laws.
4.4 Determine an equivalent expression for a logarithmic expression by applying the laws of logarithms.
4.5 Determine the approximate value of a logarithmic expression, such as log ₂ 9, with technology.

SO5. Solve problems that involve exponential equations. [C, CN, PS, R, T]

5.2 Determine the solution of an exponential equation in which the bases are not powers of one another; e.g., 2^x−1 = 3^x+1 .
5.3 Solve problems that involve the application of exponential equations to loans, mortgages and investments.
5.4 Solve problems that involve logarithmic scales, such as the Richter scale and the pH scale.

SO6. Represent data, using exponential and logarithmic functions, to solve problems. [C, CN, PS, T, V]

6.1 Describe, orally and in written form, the characteristics of a logarithmic function by analyzing its graph.
6.2 Describe, orally and in written form, the characteristics of a logarithmic function by analyzing its equation.
6.3 Match equations in a given set to their corresponding graphs.
6.4 Graph data, and determine the logarithmic function that best approximates the data.
6.5 Interpret the graph of a logarithmic function that models a situation, and explain the reasoning.
6.6 Solve, using technology, a contextual problem that involves data that is best represented by graphs of logarithmic functions, and explain the reasoning.

Mathematical Processes

Connections [CN] Students are expected to make connections among mathematical ideas, other concepts in mathematics, everyday experiences and other disciplines
Problem Solving [PS] Students are expected to develop and apply new mathematical knowledge through problem solving
Reasoning [R] Students are expected to develop mathematical reasoning
Visualization [V] Students are expected to develop visualization skills to assist in processing information, making connections and solving problems
Technology [T] Students are expected to select and use technology as a tool for learning and for solving problems
Mental Estimation [ME] Students are expected to demonstrate fluency with mental mathematics and estimation.