Free Sample (PDF):
High School Students: Working with Rates of Change
The Make It Real Learning Calculus I workbook focuses on realworld situations that may be effectively analyzed using derivatives and other rates of change. This book suits best high school or firstyear college calculus courses.
From analyzing the growth of an infant to maximizing the volume of a package, learners get to use mathematics in meaningful ways. Each activity integrates real world information, companies, and issues (e.g. US Postal Service, AIDS, movie ticket prices, rates of change in then number of high school students), not just "realistic" data.
There are multiple ways to use the activities of the book in a teaching environment. The activities are an excellent tool for stimulating mathematical discussions in a small group setting. Due to the challenging nature of each activity, group members are motivated to brainstorm problem solving strategies together. The interesting real world contexts motivate them to want to solve the problems. The activities may also be used for individual projects and classwide discussions.
As a readyresource for teachers, the workbook also includes completely workedout solutions for each activity. To make it easier for teachers to assess student work, the solutions are included on a duplicate copy of each activity.
The mathematical objectives of the activities fall within the standards of the National Council of Teachers of Mathematics.
Activity Title  Mathematical Objectives 

Growing Money: Using Partial Derivatives 
Find and evaluate the first partial derivatives of a multivariable
function Interpret the practical meaning of partial derivatives 
High School Students: Working with Rates of Change 
Find and evaluate the derivative of a polynomial Use technology to determine relative extrema Estimate an inflection point from a graph Calculate and interpret the meaning of rates of change 
Infant Growth Rates: Using Derivatives 
Calculate the derivative of logarithmic and cubic functions Evaluate derivatives and interpret the meaning of the results Recognize the relationship between the slope of a graph and its derivative 
Living with AIDS: Working with Derivatives 
Interpret the practical meaning of the concavity of a graph Determine the sign of the first and second derivatives from a graph Find and evaluate the first and second derivatives of a quadratic function Estimate the derivative at a given value from a table 
Movie Ticket Prices: Using Calculus to Analyze Change 
Find, graph, and interpret the meaning of the derivative Shade the region representing the definite integral Calculate the area of a region represented by a definite integral Interpret the meaning of a definite integral Use an integral to find the average value of a function 
PreK  Grade 8 Students: Working with Rates of Change 
Find and evaluate the derivative of a cubic function Use the derivative to determine the slope of a function Estimate the coordinates of an inflection point from a graph Find the coordinates of an inflection point from an equation 
Shipping Packages: Optimizing Functions with Calculus 
Create a graphical representation of a verbal description Create a volume equation and calculate its derivative Determine the box dimensions that maximize volume 
Shipping Packages #2: Optimizing Functions with Calculus 
Create a graphical representation of a verbal description Create a volume equation and calculate its derivative Determine the box dimensions that minimize a volume function 
Shipping Packages #3: Optimizing Functions with Calculus 
Create a graphical representation of a verbal description Create a volume equation and calculate its derivative Determine the tube dimensions that maximize volume 
Wind Chill Temperature: Using Calculus with Multivariable Functions 
Evaluate a multivariable function at a given point Find and interpret the meaning of the first partial derivatives 
Free samples!
Download these free samples from Make It Real Learning series:
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Samples from Activity Library, Volume II
Sample of States by the Numbers series: North Dakota
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You will be purchasing the download from my authorized reseller Comecero, LLC.
By purchasing any of the Make It Real Learning workbooks, permission IS granted for the teacher (or parent) to reproduce this material to be used with his/her students in a teaching situation; not for commercial resale. However, you are not permitted to share the material with another teacher.
In other words, you are permitted to make copies for the students/children you are teaching, but not for other teachers' usage.
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