Road to Alphabetical Mathematics - Assignment Example

IPD TASK 4 UNIT ROAD TO ALPHABETICAL MATHEMATICS An Introduction to Algebra Grade level: 5-6 Time required: 4 Periods (3 hours) Objectives Developing a strong foundation in algebraic concepts Students should be able to perform basic mathematical operations Students are expected to comprehend algebraic expressions Students to able to recognize equality in algebraic expression To eliminate the fear of alphabets in mathematics for students entering secondary school Students should acknowledge the difference between an algebraic expression and an arithmetical expression Students should understand the role of alphabets as mere replacement of numbers Students are required to learn some basic rules of algebra To enable the students to utilize their analytical skills Students should be able to relate objects with numbers Students should comprehend the behavior of pan balance in situations of equality and inequality Students should utilize the concepts while solving worksheets To incorporate technology in mathematics Using computer software effectively to bring about a better understanding of mathematics Students should be able to use the Software adequately in order to understand the concepts of algebra Use of other experimental resources to elaborate concepts Summary The unit incorporates the use of computer software to convey the basic concepts of algebra, these include the equality of expressions, the rule of BODMAS i.e. which operator to be solved first, moreover simple computations of expressions and other operations in basic algebra are concisely reviewed. Learning Activities Use of Computer technology to teach the concept of equality in algebra Different colored blocks are balanced as a first step to understand equivalence amongst objects Solving algebraic equations consisting of different mathematical operator. An introduction to rules of operators Resources utilized Computer Software Calculators White board Activity Sheets Standards satisfied by the unit The above unit has been specifically designed for students beginning their venture into the secondary school; these students are already intimidated by the world algebra that sounds like an ancient Greek monster, to start with. Under these circumstances it is very important to provide students a platform to motivate them in going further with the subject and hence the pan balance experiment procedure has been proposed. The above procedure would definitely challenge, motivate and actively involve the students. Establishment of physical classroom environment to support the type of teaching has also been considered and the class would be undertaken in a computer lab and use of technology has been kept in mind with utilizing software to promote understanding. The students would be instructed to perform experiment on the software individually and in teams of two's and three's, the teacher would then visit each student/group and ask their conclusion, which would be then challenged, as the case may be, to bring about a better understanding. Finally, multiple assessment techniques would be utilized to monitor the student's performance and level of understanding these methods include observation, worksheets, experimental results, presentations by students etc. Assessment of the unit The unit will be assessed through a number of sources these would include the following: Observation of the instructor Worksheets Solutions to problems Experimental results tabulated Presentation of the students assignment which would be then graded by the Class LESSON 1 Concept of balancing equation using shapes Time Allotted: 2 periods (1.5 hours) Subject: Introducing Equality Grade/level: 6-7 The lecture described below belongs to the unit of essential algebraic concept and in this the student will balance shapes on the computer software to study equality, essential to understanding algebra. Corresponding relationships will be recognized when the pans balance, signifying the properties of equality. Objectives Students will: develop an understanding of equality using shape and a computer software's pan balance; Pertain the properties of equality to show that the stability is maintained; Explore the Reflexive, Symmetric, Multiplication/Division, Transitive, and Addition and Subtraction Properties of Equality; Recognize the connection between the balance in the software and an equation; Illustrate conclusion base upon the patterns in a table Resources Profile Pan Balance Recording leaf Pan Balance-Computer software Optional: Pan Balance from science department or homemade version Summary This lesson will develop algebraic perceptive through an easy study of equality. A two arm balance pan in the software, shown in the classroom borrowed from the technology department, or build with a meter stick balancing on an eraser will assist students to make out when the pans are balanced; the left plane of the balance equals the right plane. The important notion in algebra will be armored as students operate shapes in the pan balance in the software. Learning Context The following lesson helps in the developing the concepts of equality, which is the starting point in algebra. Progress in algebra is not possible without having a clear understanding of the equality of variables, even the simplest of the operations, i.e. addition cannot be carried out if a student fails to understand the concept. Procedure To exhibit how this software works, project the Computer software balance tool. Position a block on the left side of the scale; the balance is no longer poised and tilts to the left. This is unbalanced or an inequality situation in the arithmetical terms. Place an identical block on the right side to show equality. Next put a red circular shape on the right and a blue circle block on the left and don't forget to show students the method of placing the shapes in either scales until the balance is poised, adding circles, red on right, blue on left, in a speckled order, until equality is attained. When the balance is poised, demonstrate to the students how equivalent relationships are written up in the table on the computer screen, and will continue there until you click new query, which modifies the weights for each of the shapes, and the balancing procedure is restarted altogether. Students should be encouraged to use Retune Scales to keep the same weights as before, and this does not delete the table, but clears the scales which now are empty. Next, students are given a chance to survey the computer software individually or groups of two' or three's as per caliber of the student. As the teacher moves around and monitors the students' work, he/she also asks students to elucidate their discovery, at the same time challenging their answers to increase understanding. Following up with the survey, the teacher is required to facilitate a discussion with the class of the results of each student for about 25 minutes. Students may present their discoveries by using their lap tops with the projector. Instructional Material Handouts would be given to the students and they would be provided with complete instructions to go about the software Assessment of the Unit The Profile Recording Leaf may be gathered to assess student's commitment and success with using this software to learn the properties of equality in the arithmetical terms. Moreover students' answers to important questions will assist the teacher determine student understanding of similarity and whether or not he/she got the jest of the entire topic. LESSON 2 Corresponding Arithmetic Perceptive Subject: Comprehending Equivalence of Expression Time Allotted: 2 periods (1.5 hours) Grade/level: 5-6 The lecture described below belongs to the unit of basic algebraic perception .By using balancing software in the classroom is a primary step to algebraic comprehension. Utilizing this balance numbers software to practice the order of operation in simplifying arithmetical expressions and to reveal the rules of using algebraic rationale in solving or dealing with expressions Objectives Students will: Extend their understanding of equality in algebraic expressions use the software balance (in number) to determine equality of numeric expressions involving the order of operations also including the exponential expressions; build up their algebraic understanding as expressions will be simplified and noted down finally be introduced to algebraic expressions, with numeric values assigned to each variable master the art of solving algebraic expressions with numeric values and this will be the final goal of the entire unit Resources Computer Software-Numbers Kit Systematic Calculators Solving Expressions Drill Exercises Solving Algebraic Expression with numeric values for variables WHO has got the knack of it Ascertain the Flaws! Summary Students often defy solving expressions as these: 17+824. He/she may say I know its 21, but most of the times they would incorrectly answer it as 13.5. The software used in concurrence with this lesson will reveal algebraic knowledge, and convince students that mathematicians, and the computer, rationally display one rung at a time, beneath each other. This leads students to success with algebra. Learning Context The lesson highlights and corrects some very common mistakes that are committed by the students in dealing with algebra. The rule of BODMAS is revised and the lesson trains the student who can march on to solve expressions and make his way towards problems. Procedure Use the scenario on the Expenses, "Who has got the knack of it to express the significance of following the order of operations when ascertaining the number of tiles needed to remodel a bathroom. Who has got the knack of it Worksheet is shown to the students. Ask the students "Which of the pupil is able to determine the correct cost Show how you know." A student will get a correct answer only if he uses the correct order of operations which is as follows B BRACKETS O OF D DIVISION M MULTIPLICATION A ADDITION S SUBTRACTION A common flaw that students will come up is ignoring the rules of operations in algebra and conventionally solving from left to right of the expression 6+74+510=6+28+510 6+74+510=6+28+50 6+74+510=34+50 6+74+510=84 The question is given as input to the software and the students view the step-by-step solution of the problem as shown above. Numerous examples will be shown to students before dispatching them to work in groups Students are able to see algebraic logic, noting down each step at a time, and the significance of the left side of an equation being equal to the right side of the expression. Students should not be focusing on the final solution, which is shown in the solution box, but the steps of validation which show THE STEPS that resulted in the solution. Another common error made by students is that of performing multiplication before division, and the solution to a question looks like this 252510=110 =10 and not the solution on the next page 252510=25250=1/10! Once the students are through the basic questions they should be challenged with increasingly difficult example before introducing algebraic expression. For example 8*(9+5)-6=8*(14)-6 =112-6 =106 If the two sides are equal then the equation is correct. Following this up with algebraic expressions where rules followed are identical the only different lies in the introduction of alphabets, numerical values are provided for these alphabets and students how to incorporate them into alphabets. The explanatory lecture is followed up with a work sheet, having questions in the increasing order of difficulty. As a final activity, 'Ascertain the Flaws!' is shown to the students. This document gives solutions to the answers in the above worksheet. Assessment The Ascertain the Flaws will be a quick and easy assessment method which can be used at the end of the lesson. Provide questions such as 8196. If the student is correctly able to answer the above question give him/her the algebraic expression's sheet to solve. Having questions such as ab + c, where a=2, b=2 & c= 4 Once through this sheet the student is through the Basic Algebra. IPD TASK 11 Adaptations in Lesson 1 Suppose lesson plan 1 is also utilized by students who are learning disabled under these circumstances adaptations would be made irrespective of the type of disability, but some specific changes will also be made. The primary modification that would be made will be to keep a separate class for these children as they will require a greater amount of attention and time. Moreover the concepts of equality would be explained using a physical balance and object rather than exposing to technology right away. Or an alternative to this could the introduction of voice communication, where the system itself reminds the students for the necessary buttons to be pressed for e.g. 'Reset' to adapt to their mental lag. Apart from these universal changes, some specific modifications can be adopted for specific disabilities, use of special keyboards for students who are visually handicapped. Use of homogeneous and heterogeneous cooperative learning groups can be used to enhance learning for everyone if special students and average students are to study together. As the stronger ones will be able help those who are weak. A greater use of visuals is again a recommended act in making things easier for special students and at the end of the day everyone will be able to learn something if not everything. Adaptations in Lesson 2 Students who are gifted and talented have a greater understanding power, hence steps need to be taken to keep them motivated. In order to this a number of changes are required. Primarily the number of assessments and the depth of knowledge conveyed to them are increased; it is done in order to nurture the student's talent and this can be done by giving these students more worksheets even those having questions of a greater difficulty level. Another change would be to give unrestricted questions i.e. instead of asking them to identify the error, asking the bright students to check the questions and to see if there is any error at all. Such questions fuel higher order judgment skills and give students opportunities to prove their worth. Unrestricted questions involve analytical skills such as assessment, combination, imminence, creativity, and integration. Another strategy for lesson modification would be the choice for students to take up standard worksheets or higher challenges, this way there skills and passion both would be nurtured and they would be motivated rather than bored in the class. A variety of instructional approaches would be utilized to meet the standard of the gifted students and to their level and explain, that will be to tell them about the rule of operations and right away give them questions to be solved. IPD TASK 7 Standard: Uses multiple teaching/learning strategies that are appropriate to student development level and actively engages students in individual and cooperative learning experiences. Goals & Objectives 1. To use alternative methods of conveying knowledge 1. To at least two methods of explaining a question to the class 2. To make sure that all students are able to master at least one of the methods 3. To provide worksheets to be solved using all the methods taught in the class 2. To make sure each every member of the class learns something from the lecture if not everything 1. To adopt various ways of teaching according to the needs of the members of the class 2. To hold a Query session at the end of every class to solve the problems if any 3. To make a assessment on daily basis 3. To promote teamwork 1. To make students work in the team of two's or four's while doing class activities 2. Partners to be different all the times 3. Grading to be done on the group basis Explanation 1. At least two methods will be required in order to cater to the diversity of the class, i.e. to accommodate special as well as gifted students. Once this has been done it is the important to see that the students have conveyed at least one of the methods, and the methods designed should be such that at least one of them is suitable enough to be understood by all. Finally it is imperative to see whether students are comfortable with at least one of the ways so that the question solving phase can be started. 2. All students are not of the same caliber and all of them would ultimately not be able to grasp everything that is taught in the class it is therefore necessary for the teacher to make sure that at least the important parts of the lecture are understood by all i.e. basics to clear to all. And this can only be made sure by assessing the class 3. Teamwork is the key, as it is the mode of practice in the modern day industry; teachers are therefore required to nurture this habit in the students from the grass root level. Secondly it is important to cater the needs of weaker students and teams are made so as to encourage co-operation amongst students and to develop flexibility and adaptability within them. Bibliography 1. Naylor, Rhonda (2000). Everything Balances out in the end. Retrieved June 8, 2007, from Illuminiations:everything balances out in the end Web site: http://illuminations.nctm.org/LessonDetail.aspxID=L641 2. Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28, 14-18. 3. Exceptional children, council (2000). teacher version lesson plans adaptables and more. Retrieved June 8, 2007, from adaptation and modification for special need students Web site: http://www.teachervision.fen.com/special-education/resource/5347.html Read More