College Algebra provides a comprehensive exploration of algebraic principles and meets scope …
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.
It is often said that mathematics is the language of science. If …
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 quantitya 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.
College Algebra provides a comprehensive exploration of algebraic principles and meets scope …
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.
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The primary purpose of this problem is to rewrite simple rational expressions …
The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car). Indeed, the given form of the combined fuel economy computation is useful for direct calculation, but if asked for an approximation, is not particularly helpful.
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to interpret exponential and linear functions and in particular to identify and help students who have the following difficulties: translating between descriptive, algebraic and tabular data, and graphical representation of the functions; recognizing how, and why, a quantity changes per unit intervale; and to achieve these goals students work on simple and compound interest problems.
The foundation of this lesson is constructing, communicating, and evaluating student-generated tables …
The foundation of this lesson is constructing, communicating, and evaluating student-generated tables while making comparisons between three different financial plans. Students are given three different DVD rental plans and asked to analyze each one to see if they could determine when the 3 different DVD plans cost the same amount of money, if ever. (7th/8th Grade Math)
Students act as mining engineers and simulate ore mining production by using …
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.
A brief refresher on the Cartesian plane includes how points are written …
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.
This task presents a real world application of finite geometric series. The …
This task presents a real world application of finite geometric series. The context can lead into several interesting follow-up questions and projects. Many drugs only become effective after the amount in the body builds up to a certain level. This can be modeled very well with geometric series.
The primary purpose of this task is to illustrate certain aspects of …
The primary purpose of this task is to illustrate certain aspects of the mathematics described in the A.SSE.1. The task has students look for structure in algebraic expressions related to a context, and asks them to relate that structure to the context. In particular, it is worth emphasizing that the task requires no algebraic manipulation from the students.
Students learn about the mathematical characteristics and reflective property of ellipses by …
Students learn about the mathematical characteristics and reflective property of ellipses by building their own elliptical-shaped pool tables. After a slide presentation introduction to ellipses, student “engineering teams” follow the steps of the engineering design process to develop prototypes, which they research, plan, sketch, build, test, refine, and then demonstrate, compare and share with the class. Using these tables as models to explore the geometric shape of ellipses, they experience how particles rebound off the curved ellipse sides and what happens if particles travel through the foci. They learn that if a particle travels through one focal point, then it will travel through the second focal point regardless of what direction the particle travels.
This task does not actually require that the student solve the system …
This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.
This purpose of this task is to help students see two different …
This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.
This lesson unit is intended to help assess how well students are …
This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.
This classroom activity presents College Algebra students with a ConcepTest and a …
This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential function where C>0 and k is an arbitrarily fixed value in f(x)=Ce^(kx).
This classroom activity presents College Algebra students with a ConcepTest and a …
This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k>0 and C is an arbitrarily fixed value in f(x)=Ce^(kx).
It is essential to lay a solid foundation in mathematics if a …
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.
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