Created on: September 11, 2011

Website Address: https://library.curriki.org/oer/Hands-on-and-real-world-application-problems-by-Professor-James-Sandefur-Georgetown-University-and-R

TABLE OF CONTENTS

- Hands on and real world application problems by Professor James Sandefur (Georgetown University) and Rosalie Dance (University of the Virgin Islands)
- Down to Business - Rewriting Formulas
- Factoring Research - Projectile Motion
- Trapping Lab - Linking Equations and Graphs
- Paying the Price - Rational Equations
- Introduction to Functions - Basics and Applications
- Working Together - Rational Equations
- Linear Modeling - Barbie Bungee Jump
- Packaging Lab - Volume and Surface Area
- Motion - Toy Train Collision
- Real World Exponential Equation (Car Loan)
- The Coffee Shop - Linear Inequalities
- Logs and Exponents: Population, Earthquakes, and Sound
- Quadratic Equations: From Factored to Standard Form
- Repeating Decimals and Geometric Series

- Genetic Factors: Effects on Medication (inverse proportionality, asymptotes, percents)
- Computing Speed
- Stacking Cups (slope, y-intercept)
- Trivial Pursuits and Algebraic Models (writing equations)
- Money Investigation 1 (solving linear equations, formulas)
- Money Investigation 2 (solving linear equations, formulas)
- Money Investigation 3 (graphing, slope, y-intercept)
- A Study of Malaria and Sickle Cell Anemia
- Alcohol in Your Body (Rational functions)
- Reading This Could Help You Sleep: Caffeine in Your Body
- Get the Lead Out (exponential, logarithmic functions)
- So Much Coffee, So Little Time (systems of equations, exponential functions)
- Light's Speed in Water (radical functions, modeling)
- Prescribing Medications: Complicating Factors (systems: 2 and 3 equations)

Each unit contains a complete package for students. In most cases, there is a reading assignment to be completed beforehand, in-class investigations, and homework to follow. You will find a Teacher's Guide for each unit discussing the mathematical content of the activities and pedagogical suggestions for optimal use of the lesson. Each teacher's guide provides a complete set of answers for the questions in the student materials.

Many of the units are mathematical investigations set in contexts that will usually provide new information of interest to students in the context itself, such as studying the problem of lead poisoning or the relationship between sickle cell anemia and malaria. This is intended to help students see that the mathematics they are learning now can be used to help solve significant real problems. It is expected that investigations in context will also help students whose learning style is holistic relate to the analytic methods of mathematics. Units in a context with real significance will be marked with (Real).

For more info: http://www9.georgetown.edu/faculty/sandefur/handsonmath/index.html

Studies y=k/x and the meaning of asymptote. Uses fact that elimination rate for some drugs varies by population.

This lesson should take one day of class time. The purpose of this lesson is to develop an understanding of quadratic functions. We use the linear relation between distance, constant speed and time and the quadratic relation between the vertical distance of a falling object and time. From these, students will develop two new quadratic functions. The graph of one of these provides a picture of the physical phenomenon they have viewed.

Students learn to develop the equation for a line. The emphasis is on the significance of the slope and the y-intercept

Hands-on activity. The purpose is to help students learn to use variables and to write equations to model a problem situation. Helps students learn how to work simple "word problems" by actually doing what is said.

A hands-on activity to help students understand four basic binary operations in algebraic expressions, solving linear equations in 1 variable, and solving a formula for an indicated variable, using value of collections of coins.

The second part of the Money Investigation activities. A hands-on activity to help students understand four basic binary operations in algebraic expressions, solving linear equations in 1 variable, and solving a formula for an indicated variable, using value of collections of coins.

Hands-on activity. Plotting points, writing linear functions algebraically, relating slope and y-intercept to context. Compares value of coins in different piles.

This investigation of the genetics of the Sickle Cell trait via a mathematical model uses probability and teaches properties of quadratic functions and the concept of optimization of a function. The properties of quadratic functions brought out by this investigation are -the relationship between the zeros of the function and its factors, -the relationship between the zeros and the location of its vertex, -the symmetry of its graph, and the location of its extreme point, -factors of quadratics of the form ax^2 + bx

The functions that model the process of the elimination of alcohol from the body serve as an introduction to a study of rational functions at an intermediate algebra level. The lesson focuses on graphs of the functions with an emphasis on interpretation of the horizontal and vertical asymptotes in the context of elimination of alcohol from the body. Other mathematics involved is algebraic manipulation of the rational functions, solution of equations with rational expressions, realistic domain of a function, inverse functions, and equilibrium state of a dynamic process.

"Reading This Could Help You Sleep: Caffeine in Your Body" is an introduction to exponential functions of the form ab^t at the Intermediate Algebra level, with emphasis on the meaning of these functions and their graphs. The concept of half-life is introduced. A conditional function (a piecewise-defined function) is used. "Get the Lead Out" extends the study of exponential functions and can be used to introduce the use of logarithms to "un-do" exponential expressions in solving equations. "So Much Coffee, So Little Time" can be used at the Intermediate Algebra level to help students see the value of "solving systems of linear equations". It shows connections between solving linear equations and exponential functions, and continues the study of exponential functions, this time of the form ab^t + c. End behavior of these functions with horizontal asymptotes is included.

"Get the Lead Out" extends the study of exponential functions and can be used to introduce the use of logarithms to "un-do" exponential expressions in solving equations.

"So Much Coffee, So Little Time" can be used at the Intermediate Algebra level to help students see the value of "solving systems of linear equations". It shows connections between solving linear equations and exponential functions, and continues the study of exponential functions, this time of the form ab^t + c. End behavior of these functions with horizontal asymptotes is included.

2 days. Hands-on activity using the actual path of light through your container of water. Students compute the speed of light in water and develop an understanding of why light reflects back if below a critical angle. It provides an opportunity to build a fairly complicated function from simpler ones in a physical setting, and then investigate the function to learn something about the real world. It involves investigation of function with a parameter. This unit is appropriate for a precalculus course in a unit on functions or or in a unit on functions involving radicals. It has also been used in elementary calculus courses as a conceptual introduction to optimization.

2 days. Hands-on simulation activity. Used to introduce solving linear systems of 2 equations in two unknowns, with follow-up involving 3 equations and 3 unkowns. This unit studies interconversion of two drugs in the blood, that is, the case where the body metabolizes each of two drugs into the other, which is what happens for vitamin K and another chemical. This requires one day, with homework given. On the following day, you discuss solving systems of equations and can use a second set of homework that comes with this unit. The second set of homework studies drugs which are absorbed into different compartments of the body, such as vitamin A which is in the blood and in the liver. Intermediate algebra or precalculus.