Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.

The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively.

The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject.

This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.

Student teams are challenged to navigate a table tennis ball through a timed obstacle course using only the provided unconventional “tools.” Teams act as engineers by working through the steps of the engineering design process to complete the overall task with each group member responsible to accomplish one of the obstacle course challenges. Inspired by the engineers who helped the Apollo 13 astronauts through critical problems in space, students must be innovative with the provided supplies to use them as tools to move the ball through the obstacles as swiftly as possible. Groups are encouraged to communicate with each other to share vital information. The course and tool choices are easily customizable for varied age groups and/or difficulty levels. Pre/post assessment handouts, competition rules and judging rubric are provided.

Under the "The Science Behind Harry Potter" theme, a succession of diverse complex scientific topics are presented to students through direct immersive interaction. Student interest is piqued by the incorporation of popular culture into the classroom via a series of interactive, hands-on Harry Potter/movie-themed lessons and activities. They learn about the basics of acid/base chemistry (invisible ink), genetics and trait prediction (parseltongue trait in families), and force and projectile motion (motion of the thrown remembrall). In each lesson and activity, students are also made aware of the engineering connections to these fields of scientific study.

Students are introduced to the engineering design process within the context of reading Dr. Seuss’s book, Bartholomew and the Oobleck. To do so, students study a sample of aloe vera gel (representing the oobleck) in lab groups. After analyzing the substance, they use the engineering design process to develop and test other substances in order to make it easier for rain to wash away the oobleck. Students must work within a set of constraints outlined within the Seuss book and throughout the activity and use only substances available within the context of the plot. Students also take into consideration the financial and environmental costs associated with each substance.

Students use a recipe to prepare a hydrogel gummy snack, which has a similar consistency to that found in a Haribo® gummy product. They must convert the juice and gelatin-based recipe from US customary units to metric units with dimensional analysis conversion. After unit conversion, teams are given different gelatin quantities and design their gummy snacks. Once the candies have solidified, student groups compare the gummy snacks are for viscosity and taste. After a taste test, teams reflect on their experiment and brainstorm ways to iterate a better gummy recipe.

Explore what it means for a mathematical statement to be balanced or unbalanced by interacting with objects on a balance. Discover the rules for keeping it balanced. Collect stars by playing the game!

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.

Students learn that buoyancy is responsible for making boats, hot air balloons and weather balloons float. They calculate whether or not a boat or balloon will float, and calculate the volume needed to make a balloon or boat of a certain mass float. Conduct the first day of the associated activity before conducting this lesson.

Explore size estimation in one, two and three dimensions! Multiple levels of difficulty allow for progressive skill improvement.

Students apply what they know about light polarization and attenuation (learned in the associated lesson) to design, build, test, refine and then advertise their prototypes for more effective sunglasses. Presented as a hypothetical design scenario, students act as engineers who are challenged to create improved sunglasses that reduce glare and lower light intensity while increasing eye protection from UVA and UVB radiation compared to an existing model of sunglasses—and make them as inexpensive as possible. They use a light meter to measure and compare light intensities through the commercial sunglasses and their prototype lenses. They consider the project requirements and constraints in their designs. They brainstorm and evaluate possible design ideas. They keep track of materials costs. They create and present advertisements to the class that promote the sunglasses benefits, using collected data to justify their claims. A grading rubric and reflection handout are provided.

Through this lesson and its series of hands-on mini-activities, students answer the question: How can we investigate and measure the inside of an object or its structure if we cannot take it apart? Unlike the destructive nuclear weapon test (!), nondestructive evaluation (NDE) methods are able to accomplish this. After an introductory slide presentation, small groups rotate through five mini-activity stations: 1) applying Maxwell’s equations, 2) generating currents, 3) creating magnetic fields, 4) solving a system of equations, and 5) understanding why the finite element method (FEM) is important. Through the short experiments, students become familiar with the science and physics being used and make the mathematical connections. They explore components of NDE and see how engineers find unseen flaws and cracks in materials that make aircraft. A pre/post quiz, slide presentation and worksheet are included.

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of different equations.

The aim of this video lesson is to introduce the concept of factorials, and to show students that everyday events in their lives have so much to do with factorials - even if they do not realize it! During this video, students will learn about the large number of ways to arrange people and objects using the mathematical concept of factorials. This video lesson will begin with a story of a family vacation to Pulau Pinang, an island located 330 km from the city of Kuala Lumpur in Malaysia. In this video, lessons about using factorials are demonstrated through several challenges this family encounters during their vacation. A prerequisite for this lesson is knowledge of the multiplication rule of counting. During the classroom activities, students are asked to carry out collaborative learning challenges in groups of 6. These activities require students to arrange cards to show different factorial arrangements that can be made. The materials needed for this activity are very simple. We only need to provide a few pieces of blank or colored paper for each student. The lesson will take about 40 – 50 minutes to complete.

All of us have felt sick at some point in our lives. Many times, we find ourselves asking, "What is the quickest way that I can start to feel better?" During this two-lesson unit, students study that question and determine which form of medicine delivery (pill, liquid, injection/shot) offers the fastest relief. This challenge question serves as a real-world context for learning all about flow rates. Students study how long various prescription methods take to introduce chemicals into our blood streams, as well as use flow rate to determine how increasing a person's heart rate can theoretically make medicines work more quickly. Students are introduced to engineering devices that simulate what occurs during the distribution of antibiotic cells in the body.

This project will be focused on designing, constructing and evaluating different containers to determine the optimal design for heat retention. After students have constructed their designs and collected and shared data, students will evaluate the class data to create an optimal design for our culminating event: warming ooey, gooey chocolate chip cookies to perfection! Through this activity, students will learn about energy transfer, engineering design process, data collection, graphing, rate of change, optimization, surface area and proportions. The students will test the effectiveness of their design using Vernier Probes to gather quantitative data and graphing the rate of temperature change. They will then create a poster presentation to share their data to the class. Students will use their mathematical skills to quantitatively analyze the strength and weaknesses of their designs while enjoying some delicious, toasty, warm cookies.

Working individually or in groups, students explore the concept of stress (compression) through physical experience and math. They discover why it hurts more to poke themselves with mechanical pencil lead than with an eraser. Then they prove why this is so by using the basic equation for stress and applying the concepts to real engineering problems.

Using the LEGO® NXT robotics kit, students construct and program robots to illustrate and explore the Fibonacci sequence. Within teams, students are assigned roles: group leader, chassis builder, arm builder, chief programmer, and Fibonacci verifier. By designing a robot that moves based on the Fibonacci sequence of numbers, they can better visualize how quickly the numbers in the sequence grow. To program the robot to move according to these numbers, students break down the sequence into simple algebraic equations so that the computer can understand the Fibonacci sequence.