Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

Students apply their knowledge of linear regression and design to solve a real-world challenge to create a better packing solution for shipping cell phones. They use different materials, such as cardboard, fabric, plastic, and rubber bands to create new “composite material” packaging containers. Teams each create four prototypes made of the same materials and constructed in the same way, with the only difference being their weights, so each one is fabricated with a different amount of material. They test the three heavier prototype packages by dropping them from different heights to see how well they protect a piece of glass inside (similar in size to iPhone 6). Then students use linear regression to predict from what height they can drop the fourth/final prototype of known mass without the “phone” breaking. Success is not breaking the glass but not underestimating the height by too much either, which means using math to accurately predict the optimum drop height.

Students are introduced to the "Walk the Line" challenge question. They write journal responses to the question and brainstorm what information they need to answer the question. Ideas are shared with the class (or in pairs and then to the class, if class size is large). Then students read an interview with an engineer to gain a professional perspective on linear data sets and best-fit lines. Students brainstorm for additional ideas and add them to the list. With the teacher's guidance, students organize the ideas into logical categories of needed knowledge.

Living in a big city like New York can be very challenging. City planning is an interdisciplinary enterprise where social scientists, humanists, psychologists, scientists, statisticians, citizens, politicians, etc. come together to offer solutions to improve quality of life in the city. To find such solutions, these people need clear and reliable (qualitative and quantitative) information about specific challenges that residents and visitors face For the variety of stakeholders in the city, many different things might be considered worthy of study, depending on their interests and needs regarding, e.g., employment, financial status, family size, healthcare, mobility, and education.
For example, do you know whether your neighborhood issufficiently protected from a fire? What about other neighborhoods in the city? To what extent does a CUNY degree help a person gain employment in the City? In which ways do race or gender or sexual preference play a role in how people experience city life? Can these be quantified in dollar terms? Once you have identified a problem, write an essay that describes a question
about city life that you believe is worthy of a statistical study.

Students act as engineers contracted by NASA to create water filtration devices that clean visible particulates from teacher-prepared "dirty water." They learn about the worldwide need for potable water and gain appreciation for why water quality is an important issue for people on Earth as well as on the International Space Station. Working in groups, students experience the entire engineering design process, including a read-aloud book about the water cycle; a visiting water engineer presentation; their own online research about filter methods and designs; group brainstorming of designs (using ordinary household materials); filter construction and testing; redesign and retesting; lab book documentation of their notes, research, plans and results; and a summary poster presentation at a mini-engineering fair. Two design planning worksheets, a poster layout suggestion sheet and a grading rubric are provided.

As if they are environmental engineers, student pairs are challenged to use Google Earth Pro (free) GIS software to view and examine past data on hurricanes and tornados in order to (hypothetically) advise their state government on how to proceed with its next-year budget—to answer the question: should we reduce funding for natural disaster relief? To do this, students learn about maps, geographic information systems (GIS) and the global positioning system (GPS), and how they are used to deepen the way maps are used to examine and analyze data. Then they put their knowledge to work by using the GIS software to explore historical severe storm (tornado, hurricane) data in depth. Student pairs confer with other teams, conduct Internet research on specific storms and conclude by presenting their recommendations to the class. Students gain practice and perspective on making evidence-based decisions. A slide presentation as well as a student worksheet with instructions and questions are provided.

Students explore the definition of a function by playing an interactive game called "Club Function." The goal of the game is to be in the club! With students each assigned to be either a zebra or a rhinoceros, they group themselves according to the "rules" of the club function. After two minutes, students freeze in their groups, and if they are not correctly following the rules of the club function, then they are not allowed into the "club." Through this activity students come to understand that one x-coordinate can only have one corresponding y-coordinate while y-coordinates can have many x-coordinates that correspond to it.

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

This course covers relations and functions, specifically, linear, polynomial, exponential, logarithmic, and rational functions. Additionally, sections on conics, systems of equations and matrices and sequences are also available.

It is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Farmers, cattlemen, and tradesmen used tokens, stones, or markers to signify a single quantity—a sheaf of grain, a head of livestock, or a fixed length of cloth, for example. Doing so made commerce possible, leading to improved communications and the spread of civilization.

As a class, students use a low-cost air quality monitor (a rentable “Pod”) to measure the emissions from different vehicles. By applying the knowledge about combustion chemistry that they gain during the pre-activity reading (or lecture presentation, alternatively), students predict how the emissions from various vehicles will differ in terms of pollutants (CO2, VOCs and NO2), and explain why. After data collection, students examine the time series plots as a class—a chance to interpret the results and compare them to their predictions. Short online videos and a current event article help to highlight the real-world necessity of understanding and improving vehicle emissions. Numerous student handouts are provided. The activity content may be presented independently of its unit and without using an air quality monitor by analyzing provided sample data.

This resource provides helpful information as well as sample problems and solutions for common math used in construction programs. 

Students groups create scientific research posters to professionally present the results of their AQ-IQ research projects, which serves as a conclusion to the unit. (This activity is also suitable to be conducted independently from its unit—for students to make posters for any type of project they have completed.) First, students critically examine example posters to gain an understanding of what they contain and how they can be made most effective for viewers. Then they are prompted to analyze and interpret their data, including what statistics and plots to use in their posters. Finally, groups are given a guide that aids them in making their posters by suggesting all the key components one would find in any research paper or presentation. This activity is suitable for presenting final project posters to classmates or to a wider audience in a symposium or expo environment. In addition to the poster-making guide, three worksheets, six example posters, a rubric and a post-unit survey are provided.

Students learn about isometric drawings and practice sketching on triangle-dot paper the shapes they make using multiple simple cubes. They also learn how to use coded plans to envision objects and draw them on triangle-dot paper. A PowerPoint® presentation, worksheet and triangle-dot (isometric) paper printout are provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

Students teams design and build shoe prototypes that convert between high heels and athletic shoes. They apply their knowledge about the mechanics of walking and running as well as shoe design (as learned in the associated lesson) to design a multifunctional shoe that is both fashionable and functional.

Students act as mining engineers and simulate ore mining production by using chocolate chip cookies. They focus on the cost-benefit analysis of the chocolate ore production throughout the simulation, which helps them understand the cost of production. As students “mine” with tools such as paperclips and toothpicks, they keep records of their costs—land (cookie), equipment used, cookie size before and after production, and time spent. While the goal is to make as much profit as possible, other costs and goals are taken into consideration—as in real-world mining engineering. For example, mining engineers also consider the resulting amount of destruction to the lithosphere when deciding the best method to obtain ore. Thus, a line item for land reclamation cost is included from the beginning. A provided worksheet serves as a profit and loss statement.

Students learn and apply concepts in thermodynamics and energy—mainly convection, conduction, and radiation— to solve a challenge. This is accomplished by splitting students into teams and having them follow the engineering design process to design and build a small insulated box, with the goal of keeping an ice cube and a Popsicle from melting. Students are given a short traditional lecture to help familiarize them with the basic rules of thermodynamics and an introduction to materials science while they continue to monitor the ice within their team’s box.

A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.

Students explore the science of microbial fuel cells (MFCs) by using a molecular modeling set to model the processes of photosynthesis and cellular respiration—building on the concept of MFCs that they learned in the associated lesson, “Photosynthesis and Cellular Respiration at the Atomic Level.” Students demonstrate the law of conservation of matter by counting atoms in the molecular modeling set. They also re-engineer a new molecular model from which to further gain an understanding of these concepts.

Students learn about the role engineers and mathematicians play in developing the perfect bungee cord length by simulating and experimenting with bungee jumping using washers and rubber bands. Working as if they are engineers for a (hypothetical) amusement park, students are challenged to develop a show-stopping bungee jumping ride that is safe. To do this, they must find the maximum length of the bungee cord that permits jumpers (such as brave Washy!) to get as close to the ground as possible without going "splat"! This requires them to learn about force and displacement and run an experiment. Student teams collect and plot displacement data and calculate the slope, linear equation of the line of best fit and spring constant using Hooke's law. Students make hypotheses, interpret scatter plots looking for correlations, and consider possible sources of error. An activity worksheet, pre/post quizzes and a PowerPoint® presentation are included.