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# Make It Real Learning Calculus I workbook 46 pages
(10 activities)

Free Sample (PDF):
High School Students: Working with Rates of Change

# Introduction

The Make It Real Learning Calculus I workbook focuses on real-world situations that may be effectively analyzed using derivatives and other rates of change. This book suits best high school or first-year 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 class-wide discussions.

As a ready-resource for teachers, the workbook also includes completely worked-out 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.

The PDF for this book is enabled for annotation. This means that if you prefer, your student can fill it in on the computer, using the typewriter and drawing tools in Acrobat Reader version 9 or greater.

## Calculus I Activity List

Activity TitleMathematical 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
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

Bundle specials!

Activity Library, Volume I. Price: \$39.99
Includes 11 Make It Real Learning activity workbooks for the price of 8! You get three workbooks for free!

Activity Library, Volume II. Price: \$39.99
Includes 11 Make It Real Learning activity workbooks for the price of 8! You get three workbooks for free!

States by the Numbers Bundle. Price: \$19.99
Inludes all 50 States by the Numbers workbooks at a whopping 87% discount!
(Normal price would be 50 × \$2.99 = \$149.50)

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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