Virginia Department of Education
Logarithmic Modeling
Explore logarithms and logarithmic regression. Young mathematicians first learn about inverse functions and about the logarithm function family. They take their newfound knowledge to use logarithmic functions to model situations and...
Illustrative Mathematics
Modeling London's Population
Looking at London's population from 1801–1961 in 20 year increments, high school mathematicians determine if the data can be modeled by a given logistic growth equation. They explain their thinking and determine the values of each...
Balanced Assessment
A Loud Noise
In a scale measuring noise, an increase in 10 dB is a 10 time increase in power. Mathematicians examine the data graph of a real world exponential growth, with no logarithmic scale, and then create two equations relating the decibels and...
EngageNY
Solving Exponential Equations
Use the resource to teach methods for solving exponential equations. Scholars solve exponential equations using logarithms in the twenty-fifth installment of a 35-part module. Equations of the form ab^(ct) = d and f(x) = g(x) are...
EngageNY
Newton’s Law of Cooling, Revisited
Does Newton's Law of Cooling have anything to do with apples? Scholars apply Newton's Law of Cooling to solve problems in the 29th installment of a 35-part module. Now that they have knowledge of logarithms, they can determine the decay...
EngageNY
Modeling with Exponential Functions
These aren't models made of clay. Young mathematicians model given population data using exponential functions. They consider different models and choose the best one.
EngageNY
The Graph of the Natural Logarithm Function
If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...
EngageNY
Graphing the Logarithmic Function
Teach collaboration and communication skills in addition to graphing logarithmic functions. Scholars in different groups graph different logarithmic functions by hand using provided coordinate points. These graphs provide the basis for...
EngageNY
Why Were Logarithms Developed?
Show your class how people calculated complex math problems in the old days. Scholars take a trip back to the days without calculators in the 15th installment of a 35-part module. They use logarithms to determine products of numbers and...
EngageNY
Changing the Base
I can't calculate a base-2 logarithm since my calculator doesn't have a base-2 log key. Young mathematicians use the change of base formula to extend the properties of logarithms to all bases. Among these bases is the natural log base,...
EngageNY
The Most Important Property of Logarithms
Won't the other properties be sad to learn that they're not the most important? The 11th installment of a 35-part module is essentially a continuation of the previous lesson plan, using logarithm tables to develop properties. Scholars...
EngageNY
Building Logarithmic Tables
Thank goodness we have calculators to compute logarithms. Pupils use calculators to create logarithmic tables to estimate values and use these tables to discover patterns (properties). The second half of the lesson has scholars use given...
EngageNY
Rational and Irrational Numbers
Back to the basics: learning how to add numbers. The 17th installment of a 35-part module first reviews addition techniques for rational numbers, such as graphical methods (number line) and numerical methods (standard algorithm). It goes...
EngageNY
Mid-Module Assessment Task - Algebra 2 (Module 3)
The 15th installment of a 35-part module is a mid-module assessment task. Covering concepts in the first half of the module, the task acts as a formative assessment, providing you with valuable information on how learners are doing.
EngageNY
Solving Logarithmic Equations
Of course you're going to be solving an equation—it's algebra class after all. The 14th installment of a 35-part module first has pupils converting logarithmic equations into equivalent exponential equations. The conversion allows for...
EngageNY
Properties of Logarithms
Log the resource on logarithms for future use. Learners review and explore properties of logarithms and solve base 10 exponential equations in the 12th installment of a 35-part module. An emphasis on theoretical definitions and...
EngageNY
Logarithms—How Many Digits Do You Need?
Forget your ID number? Your pupils learn to use logarithms to determine the number of digits or characters necessary to create individual ID numbers for all members of a group.
EngageNY
The “WhatPower” Function
The Function That Shall Not Be Named? The eighth installment of a 35-part module uses a WhatPower function to introduce scholars to the concept of a logarithmic function without actually naming the function. Once pupils are comfortable...
Mt. San Antonio Collage
Exponential and Logarithmic Functions
High schoolers grow their skills exponentially after completing this thorough activity. Going from simple to difficult, it hits all the major skills regarding exponential and logarithmic functions including simplifying, solving,...
Lane Community College
Review Sheets: Introductory Physical Science
This hybrid worksheet connects mathematics to a science class. Learners practice solving problems that involve making a variety of conversions. An assortment of questions hits all the calculations needed for a middle school or beginning...
NASA
Discovering the Milky Way
What do you call a tiny collection of galaxies? A puny-verse! Young scholars graph data gathered by scientists studying Cepheids. They attempt to identify a relationship between the variables through standard and logarithmical graphing....
Macquarie University
Logarithms and Exponentials
Introduce logarithmic functions and their properties with a straightforward lesson plan. It provides an introduction to new material, examples, and practice problems. The variety of problem types keeps learners engaged while practicing...
Benjamin Franklin High School
Saxon Math: Algebra 2 (Section 9)
Section 9 of the 12 linked Saxon Math sections introduces the young algebrist to graphing periodic functions, creating graphs from quadratic roots, working with inequalities, and rational equations. Common among all the lessons is the...
University of Kansas
Exponential and Logarithm Problems
This worksheet manages to provide both fun and serious work solving exponential and logarithmic application problems in engaging story lines and real-life situations. A strong emphasis on science applications and numbers pulled straight...