Algebraic Reasoning, Algebraic Expressions and Equations - Essay Example

RUNNING HEAD: LESSON PLAN ON ALGEBRAIC REASONING The following are seven lesson plans using the Madeleine Hunter Modelthat discusses concepts important to Algebraic Reasoning. In particular, the lessons will be about algebraic expressions and equations, simplifying algebraic equations, methods of solving algebraic equations, the Cartesian plane, and graphing of functions. "Algebraic Reasoning" Subject 1 - Algebraic Expressions and Equations What is the lesson objective The main motive of this assignment is to make the Middle School students start learning about abstract reasoning. Representing unknown quantities using variables is a good start. 30 minutes shall be allotted to the lecture; another 30 minutes for interactions; and the last 30 minutes for work sheet activities. Standards addressed and expectations of students: Knowledge is imparted based on classroom lectures. But students will be given a worksheet to apply immediately the concepts. Anticipatory Set: For creating interest, the students will see a demonstration using two sets of cubes: one set is red, the other is green. For example, if the number of red cubes on the left side is 8 and the number of green cubes on the right side is 5, how much green cubes must be added to make it 8 and equal to the number of red cubes Teaching/Instructional Process: The teacher will first show a concrete demonstration before moving to the abstract portion. The teacher should answer questions of clarification as he teaches so misunderstandings would be avoided. Guided practice and monitoring: The teacher will test for understanding orally, but he shall stress the written outputs in the worksheet. Closure: The teacher will explain the importance of abstraction not only of mathematics but in other areas. He shall ask students to think of further applications. Independent Practice: The teacher will ask the students to write reflective journals on the lesson learned. This should be typewritten. The teacher will gather everything before the next lesson starts. This way, the teacher could offer feedbacks and assess how the students feel about the subject and teaching style. "Algebraic Reasoning" Subject 2 - Simplifying Algebraic Expressions What is the lesson objective The main motive of this lesson is to make students simplify algebraic expressions. This is a fundamental skill. The lecture will be done within 30 minutes, so that the remaining time will be devoted to answering the worksheet and exercise sets. Standards addressed and expectations of students: Knowledge is imparted via a lecturer. Students will learn by doing. Several easy and difficult examples shall be given, and the fundamental importance of this skill shall be emphasized. Anticipatory Set: For creating interest, the students shall watch a short clip of how a jigsaw puzzle looks like when unarranged. When the pieces are put together, a coherent and beautiful picture appears. This will be the analogy that shall be imparted as to why algebraic expressions should be simplified. Teaching/Instructional Process: The teacher shall quickly discuss algebraic axioms and properties. Using these, he shall give simple and difficult examples of expressions that need to be simplified. The above shall be done in 30 minutes. After which, the students shall be given work sheets to ask. Students are free to ask questions if they encounter problems, or that the nature of a problem is beyond what the teacher has taught. Guided practice and monitoring: The teacher shall provide personalized tutoring during the work sheet activity. Closure: The students shall reiterate the importance of keeping things simple. Independent Practice: The teacher will ask the students to write reflective journals on the lesson learned. This should be typewritten. The teacher will gather everything before the next lesson starts. This way, the teacher could offer feedbacks and assess how the students feel about the subject and teaching style. The teacher will encourage the students to look for other references and online resources to reinforce learning. In particular: http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut11_simp.htm http://www.wisc-online.com/objects/index_tj.aspobjID=GEM1804 "Algebraic Reasoning" Subject 3 - Basic Methods of Solving Algebraic Equations What is the lesson objective The main motive of this lesson is to integrate all previous lessons in the basic skill of solving an equation. Several problem solving activities shall be employed, but things will be simple to develop a good feeling. Standards addressed and expectations of students: Knowledge is imparted based on classroom studies. The teacher shall explain and give exercise sets from the textbook. Anticipatory Set: For creating interest, the teacher will give a physical reward for the top 5 students that would be able to solve the most problems neatly and correctly. Teaching/Instructional Process: The teacher will spend the first 30 minutes discussing algebraic equations, plus word problems that could be solved using the basic method. After which, the teacher will assign problems from the textbook. Students shall be provided with blank papers to be used. Guided practice and monitoring: The teacher will observe if the students are following instructions. He will quickly correct a student if he immediately sees a problem or difficulty. Closure: The teacher shall emphasize that Mathematics is about finding solutions to a problem. The best method, he should emphasize, is the simplest way of doing it. Independent Practice: The teacher will ask the students to write reflective journals on the lesson learned. This should be typewritten. The teacher will gather everything before the next lesson starts. This way, the teacher could offer feedbacks and assess how the students feel about the subject and teaching style. "Algebraic Reasoning" Subject 4 - Advance Methods of Solving Algebraic Equations 1 What is the lesson objective The main motive of this lesson is to introduce most of the advance methods of solving algebraic equations. The textbook shall be used extensively, since this is the start where the teacher will emphasize independent learning. Standards addressed and expectations of students: Knowledge is imparted based on classroom studies. Lectures and interaction shall be utilized. Anticipatory Set: The teacher will emphasize independence by giving a picture of the signing of the Declaration of Independence. He will emphasize values that make Americans great. Teaching/Instructional Process: The teacher will lecture all through the period. Enough examples shall be given. He shall be open for questions, but the students will have to answer problems for themselves. There shall be no worksheet activity. Guided practice and monitoring: The teacher will ask students questions. Uncertain answers will be deemed indicative of lack of understanding. Closure: By explaining the importance of learning independently and more complex methods, the teacher will set the stage which will help students learn those skills and attitudes that the teacher cannot teach. Independent Practice: The teacher will ask the students to write reflective journals on the lesson learned. This should be typewritten. The teacher will gather everything before the next lesson starts. This way, the teacher could offer feedbacks and assess how the students feel about the subject and teaching style. Furthermore, the teacher will assign exercise sets from the textbook, which must be submitted on the next meeting. "Algebraic Reasoning" Subject 5 - Advance Methods of Solving Algebraic Equations 2 What is the lesson objective The main motive of this lesson is to assess the extent which the students can do unguided learning. For this day, the students must learn synthetic division. Standards addressed and expectations of students: Anticipatory Set: For creating interest, the teacher will emphasize the difficulty of regular division in simplifying algebraic expressions and equations. He will pose problems that would normally take much time, but will be easier to solved using the method in this lesson. Teaching/Instructional Process: The teacher shall leave the room for 45 minutes, where the students must answer problems requiring synthetic division. Students shall read from the textbook, and answer problems in the worksheet. After the students have answered, the teacher will emphasize the need for independent learning once students are able to pursue higher education. The teacher shall lecture and answer questions about synthetic division. Guided practice and monitoring: The teacher will clarify concepts if there are found difficulties, after the independent learning session part is over. Closure: The teacher will re-iterate the importance of discovering new and better methods of doing math. Independent Practice: The teacher will ask the students to write reflective journals on the lesson learned. This should be typewritten. The teacher will gather everything before the next lesson starts. This way, the teacher could offer feedbacks and assess how the students feel about the subject and teaching style. "The Madeline Hunter Model" Subject 6 - Points and the Cartesian plane What is the lesson objective The main motive of this lesson is to move the student to more concrete applications of algebra, which is the coordinate system of points. Standards addressed and expectations of students: Knowledge is imparted based on classroom studies. The lecture will be brief but activities and hands-on learning shall be emphasized. Anticipatory Set: For creating interest in the students, the teacher shall demonstrate a map showing the coordinates of locations. This is a practical application, in order to show the importance of the topic. Teaching/Instructional Process: The teacher will quickly lecture and the necessary terms of the Cartesian plane. But, hands-on activities and board works shall be given. Learning by doing is essential to master this lesson. Guided practice and monitoring: The teacher shall monitor the progress of each student in the work sheet activities. He will also coach a student doing board works in order to impart the proper way of plotting points. Closure: By explaining the importance of the Cartesian plane, the students will have to understand and appreciate various graphs and pictures. Independent Practice: The teacher will ask the students to write reflective journals on the lesson learned. This should be typewritten. The teacher will gather everything before the next lesson starts. This way, the teacher could offer feedbacks and assess how the students feel about the subject and teaching style. "Algebraic Reasoning" Subject 7 - Functions and Graphs What is the lesson objective The main motive of this lesson is to reiterate the importance of independent learning. Graphs shall be viewed as products of functions. Standards addressed and expectations of students: Knowledge is imparted based on classroom studies. The teacher shall lecture, and the students shall read the text book for further details. Anticipatory Set: The teacher will input a function in a Computer Algebra System, and the students shall see a graph generated from it. Teaching/Instructional Process: The teacher shall lecture quickly the mathematical definition of functions and graphs. However, the students will have to learn independently the graphs of different functions by reading the textbook. The teacher will be present to facilitate the group answering of work sheets and exercise sets. Guided practice and monitoring: The teacher shall monitor the progress of each group. Closure: The teacher will emphasize graphs and mathematical models are important in real life. He will cite several examples in the real world. Independent Practice: The teacher will ask the students to write reflective journals on the lessons learned throughout the unit. This should be typewritten. The teacher will gather everything before the major examination starts. Read More