Simultaneous Equations vs Dear Aunt Sally

Simultaneous Equations are a set of equations with two or more variables for which there are values that can satisfy all the equations simultaneously. The Simultaneous Equations app is an interactive tool designed to help teachers introduce the concepts related to simultaneous equations and demonstrates two methods for solving them. It provides students with an interactive learning device to help them better understand these important concepts. While using the app students set up the definitions of two lines. The lines are plotted on a coordinate grid. The coordinate pair for the intersection of the two lines represents the solution for the simultaneous equations. The Elimination and Substitution Methods are demonstrated. Designed in California by Dr. Fred Ventura, Simultaneous Equations is one of the apps in the Math Power Series. Simultaneous Equations turns your iPad into a mathematical playground for introducing the coordinate plane, ordered pairs, slope, y-intercept, and the graphical, substitution and elimination methods for solving simultaneous equations. The primary objective for this app is to provide a method for students to visualize simultaneous equations graphed on a coordinate grid and to learn the substitution and elimination methods for finding a solution algebraically. Tap the table icon and begin defining an equation by using a slider to specify the slope and y-intercept of a line. Tap the plot button to graph the equation. Use the same procedure to define a second equation. Tap either the substitution or elimination icon to open a note and see the algebraic steps involved in finding the solution. Tap the question mark icon to start the quiz and measure a students understanding using randomly generated problems. Tap the notebook icon to begin reading an illustrated lesson that includes information about real-world applications for simultaneuos equations.. Simultaneous Equations turns your iPad into a power tool for teaching the concepts related to solving simultaneous equations using the graphical, substitution and elimination methods. Use Simultaneous Equations to create a presentation while illustrating and discussing the key principles of analytic geometry. Simultaneous Equation is perfect for algebra students in middle school and high school classrooms. Enrich your mathematics curriculum with the power of Simultaneous Equations!

PEMDAS is an acronym that is taught in school classrooms across the nation. It helps students remember the priority, or Order of Operations, used to solve expressions involving strings of numbers and operators. It stands for: P(arenthesis) E(xponent) M(ultiplication) D(ivision) A(ddition) S(ubtraction) A familiar mnemonic widely used in place of PEMDAS is: Please Excuse My Dear Aunt Sally. Thus the name of this application... Kind of an inside joke for the mathematical types. Computers, including smart phone calculators, desktops, etc. have built in functionality to properly interpret such expressions so we don't have to. But have you ever wondered what algorithms the CPU executes to get the right answer every time? This app demonstrates one such algorithm called the Shunt Yard, developed a few years back by Professor Edsger W. Dijkstra. We’re going to take a closer look under the hood at Order of Operations algorithms. It will interest programmers and school students alike; for programmers, the use of queues and stacks will reinforce previous computer science learning; for students, it allows them to write an expression, then analyze it using Order of Operations rules, step by step. The Quiz mode generates random expressions of user selected lengths and magnitudes and checks the student's answer. Incorrect answers can be examined using the same step by step process. In the SOLVE mode, algebraic expressions are entered free hand using an internal keyboard which limits entries to the five common mathematical operators (+ - / * ^) as well as one level of parenthesis. There is a maximum term limit of ten variables, but no limit to their magnitude in this mode. In the QUIZ mode, between two and ten variables can be selected, their maximum value and which operators that are eligible. The program then randomly generates an algebraic expression using these parameters. Both modes make available an analysis page which is used to step through the solution. Stack/Queue dynamics are displayed.