1. This lesson plan will review logarithms and exponential equations by applying the mathematical concepts to real world applications in science and engineering. The goal of the lesson is to apply algebra 2 concepts to topics learned in the chemistry classroom. The importance of logarithms and exponential functions will be tied to local companies like P&G and GE Aircraft Engines. The majority of the lesson will be implemented in the Algebra 2 classroom but certain portions involving chemicals and their lab notebooks will be implemented in the chemistry classroom. Tomorrow's lesson will include a brief introduction discussing how a sound level meter works, then getting into brief applications in engineering, and the students will work on an M&M activity that shows exponential decay. They will gather data, plot their data, and find a linear regression equation for their data using a graphing calculator. The lesson will then be continued in the chemistry class, where they will be given mystery pKa's, which they will have to convert to pH using a logarithmic equation, test a few labeled solutions with litmus papers to find their pH's and then match the "mystery pKa" with the corresponding solution. 1.At the end of the 11 th grade unit, students will be able to understand various real world applications for logarithms. 2.At the end of the 11 th grade unit, will be able to perform computations involving logarithms and exponents. 3.At the end of the 11 th grade unit, will be able to solve for variables in real world equations involving exponents and logarithms. STEM Objectives: Exponential population in the Cincinnati area Logarithms are used by researchers every day in academia and industry for modeling and simulation purposes GE aircraft engines Modeling & analysis Materials research P&G pH very important in body care, shampoos, toothpaste UC biomechanics and biomaterials research which impacts people in need of orthopaedic reconstruction High school, college, and pro athletes Elderly Military Patterns, Functions, and Algebra Standard Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. Data and Analysis and Probability Standard Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators. Design and perform a statistical experiment, simulation or study; collect and interpret data; and use descriptive statistics to communicate and support predictions and conclusions. Connect statistical techniques to applications in workplace and consumer situations. Mathematical Processes Standard Apply mathematical knowledge and skills routinely in other content areas and practical situations. Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation. Scientific Inquiry Participate in and apply the processes of scientific investigation to create models and to design, conduct, evaluate and communicate the results of these investigations. Make appropriate choices when designing and participating in scientific investigations by using cognitive and manipulative skills when collecting data and formulating conclusions from the data. Logarithms in Science & Engineering Safa T. Herfat 1, Maria Lee-Alvarez 2, Jeff Dauwey 2 1 Department of Engineering, University of Cincinnati, Cincinnati OH; 2 West High Design Technology High School, Cincinnati, OH Abstract ActivityWorksheets Objectives State Standards Assessment Results Acknowledgments Future Modifications Project STEP is funded through NSF Grant # DGE058532. Activity #1: M&M Exponential Decay (in Algebra 2 classroom) Have students form groups of 3 or 4. Give each team a zip lock bag with 50 M&M’s inside, the procedure handout and the handout on finding a mathematical model for an exponential equation. Students will gather data and be challenged to come up with a formula that models their data results using the TI-83 and the 2 nd handout. Activity #2: Mystery pKA (in Chemistry classroom) Display pKa to pH conversion equation on the board. Place the following solutions in 5 different beakers: Concentrated HCl Vinegar Water Baking Soda Solution Ammonia or NaOH Students are to form groups of 3 or 4. Give each group 5 strips of litmus paper. Students are supposed to figure out how to match each mystery pKa to the proper solution. The same assessment was given before implementing the lesson and after the lesson. Average student scores improved from 37% to 60%. A total of 10 students completed the assessment before and after the lesson was implemented The assessment seemed difficult for most students due to lack of motivation A couple students achieved a score of 90+ on the post assessment Conclusions The lesson plan was successful in reviewing logarithms and exponential equations by applying the mathematical concepts to real world applications in science and engineering. By implementing activities in both the 11 th grade Algebra 2 and Chemistry classes, students seemed to finally grasp the idea that science and math concepts are many times used together to solve real world problems, especially in the field of engineering. With the first activity, students grasped the concept of exponential decay using candy but the concept was then applied to Cincinnati’s population and radioactive decay. Students were also exposed to a sound level meter and we discussed how it determined the sound level using a circuit that translates sound pressure into a logarithmic sound level scale. Biomedical engineering applications such as drug delivery and biomechanical modeling were also discussed. Many of the students needed additional motivation to try the assessment. Although most of the questions were basic and reviewed, many students were afraid to attempt the assessment because there was an overlap between math and chemistry. On the third day of the lesson, there was no activity and several real-world application problems were done as a class on the board. Most of the students actually remained engaged but were not thrilled about the college-like teaching style. Although it may be beneficial for the students to be exposed to this style of teaching, an entire class period may be too much for the secondary level student. Assessment scores greatly improved from the pre to post assessment, which shows that they were able to grasp at least some of the basic concepts. The following modifications would make this lesson more effective: The first activity would be more efficient if the students were exposed to graphing calculators prior to this lesson. Students were apprehensive about using them even though I had given them a handout with the step by step directions to find the exponential model equation. Secondary students need to be exposed to an activity (even if it takes only a few minutes). They have not yet developed the patience to sit through a college-like lecture or problem-session. The application problems should still be reviewed, but incrementally throughout the 3 day lesson. Students were very engaged when discussing sound level meter ranges and the harm caused by the sound level recorded from many of their mp3 players. The sound level from their headphones were actually measured in the class on the first day. Students should be able to explore other loud sounds such as screaming or car stereo systems. Students need additional motivation to complete the assessment.