Abstract algebra

Learning Objectives: Cognitive- Students will be able to: • Apply the Associative property of multiplication to multiply. Psychomotor-Students will be able to: • Write the order of operation before applying the associative property to multiply. Affective-Students will be able to: • worked collaboratively and give each other help when needed. Academic Vocabulary: Associative property-- “When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors” (Banfill, 2009). Prior Knowledge: To teach this lesson, students should be familiar with: 1. Multiplication times table Teacher Preparation and Resources: 1. Interactive whiteboard 2. Tablets/Laptop 3. Cardboard with numbers and letters. 4. Individual worksheet 5. Group and self-evaluation rubric Procedure: Introduction/Motivation: According to Ormrod (2008), “People of all ages learn new information more effectively when they can relate it to what they already know” (p.253). For this reason, to introduce this lesson, I will select four students. While the chosen students are standing in front of the classroom, I will give each of the student a cardboard with a different number. For instance, the first student will have the number 13, the second student will have the number 4, the third student will have the letter X for multiplication and the fourth student will have the equal sign. After, I will have the class solve the problem and write the answer as well as the…

Abstract: This paper is a report on the development of algebra throughout time. It’s slow, but nevertheless, unyielding progression brings us to the algebra we know today. However, it was not always based on the abstract, rather, it was born out of necessity. The need to calculate unknown quantities gave rise to algebraic methods and techniques practiced and taught even today. And, even though nowadays, algebra is a rather abstract mathematics, this was not always the case. It was through…

Is Algebra Necessary? By The New York Times Algebra is necessary because it is the branch of mathematics that studies l combining elements of abstract structures according to certain rules . Originally these elements would put be interpreted as numbers or quantities, so that the algebra somewhat originally was a generalization . The adjective " algebraic " usually denotes a relationship with algebra , such as in algebraic structure . For historical reasons, it may also indicate a relationship…

Eq.\ref{Bi} is a projection of the attribute vector $I_i$ in the eigenspace spanned by the first $k_c$ eigenbackgrounds, being $\textbf{b}$ the coefficient vector of the combination. In the standard EIG method the number of eigenbackgrounds retained $k_c$ is chosen by fixing a threshold for the last eigenvalue $\lambda_{k_c}$ retained. The background obtained $B_i$ are then subtracted to the original image and a moving object is identified as the regions of the images in which $I_i-B_i$ is…

Abstract: - Mathematics is a fascinating subject filled with concepts and ideas that have been formed and developed throughout time. This paper focuses on the contributions made by Islamic mathematician Muhammad Al-Khwarizmi to the difference subjects of algebra, geometry and trigonometry. Ideas discovered by Al-Khwarizmi are discussed as well as other concepts that serve as proof of his understanding of various complex ideas we use nowadays. These concepts include simplifying equations,…

Different number were even believed to have a cosmic significance or magical powers. However the main thrust of Chinese mathematics came from the Empire’s desire to have administrators that were well versed in mathematics. Therefore in order to educate, a textbook called, “Nine Chapters on the Mathematical Art” was written. This important text became a vital part of Chinese education. This tool provided hundreds of problems in taxation, engineering and payment of wages. The text served as a…

Ms. Caldwell definitely deserves being teacher of the year. If you ask me why I will say many things, for example, math wasn’t a subject I valued until I had Ms. Caldwell for Algebra 1. She always helped us and made sure she answered the questions we had. She would make my classmates and I go early in the mornings to her office so we could explain what we had done wrong and if we didn’t understand the material she would explain the material in detail and say why the answer is right. Her…

There is also evidence of the use of decimal numbers in cuneiform mathematical texts most notably in several centuries older division exercise from the ancient city Ebla (Friberg 2000, 1986). On the front side of the hand tablet (UET 6/2 222) is a proverb, which is translated by Friberg to mean “when a dog bites, the morsels get into its mouth” (see figure 2). The presence of proverbs on one side of the tablet was common. On the reverse side of the tablet is an example of a square root of a…

their major requires it or not. This test has three different sections with a total of forty questions. The three sections are fifteen question Basic Skills Algebra, fifteen Algebra and Precalculus and ten quantitative reasoning questions. Once the test is complete, your schedule either consists of a math course in the first semester or the student will wait to take one in a later semester. During this test, you are not allowed to use any source besides your brain! James Madison’s math placement…

I continued on in high school with geometry, a second year of algebra, precalculus, trigonometry, and calculus. Thus far, my math courses in college have also been easy for me. My least favorite teacher was my calculus teacher, and it was not solely because of the tough subject matter. He was an engineer who took up teaching after retirement. He very simply could not teach well. He would stand in front of the board and talk through the problem at a pace that was almost impossible to follow. I…