Geometry Concepts vs Dear Aunt Sally

Geometry Concepts is an interactive learning system designed to provide instruction in mathematics at 7th grade through adult levels. The instructional goals for Geometry Concepts include several objectives. The primary objective for this app is to provide basic information about geometry through interactive lessons. Tap the notebook icon open dynamically illustrated lessons on each of the seven topics: Basic Concepts, Circles, Angles and Triangles, Lines and Planes, Area and Perimeter, 2-Dimensional Figures and 3-Dimensional Figures. Our goal in designing this app is to incrementally build an understanding of fundamental concepts by providing an easy-to-use format for exploring geometry. Tap the magnifying glass icon to explore a topic more deeply. Each of the images are interactive. Tap to reveal terms and key concepts. Tap the more info icon for detailed information about the highlighted term. We hope to support the development of a sense of confidence in each user's mathematical ability through a variety of educational approaches. Geometry Concepts includes a reference system, lessons, randomly generated quiz questions and an exploratory tool for open-ended investigations. Tap the tool icon on the main navigation screen to access a set of 12 interactive tools for exploring geometry concepts. Icons on the sides of the screen are used to change the investigation. Manipulated the tools to learn more about each concept. We think your students will enjoy learning with Geometry Concepts.

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.