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# Xmss ict lesson on graphs of trigonometrical functions

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### Xmss ict lesson on graphs of trigonometrical functions

1. 1. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning SUBJECT AREA: Additional Mathematics GRADE LEVEL: Sec 3 Express Name of Teacher: Yeo Kuie Soo Annie / Pauline Wong LESSON TITLE: Graphs of Trigonometrical Functions TIME ALLOTTED: 2 x 50 minutes LESSON DESCRIPTION: (Write a concise description of what occurs in this lesson.) Essential Question Do the shape of y = a sin bx + c differ from y = sin x , y = a cos bx + c differ from y = cos x and y = a tan bx + c differ from y = tan x ? How do the values of a, b and c affect the shape of the graphs of , y = a sin bx + c , y = a cos bx and y = a tan bx respectively? Knowledge and Skills • At the end of this lesson, students should be able to state the magnitude/amplitude and the frequency of  a sine function of the form y = a sin bx + c or from the graph of a sine function  a cosine function of the form y = a cos bx + c or from the graph of a cosine function  a tangent function of the form y = a tan bx + c or from the graph of a tangent function • sketch the graph of  a sine function of the form y = a sin bx + c for 0° ≤ x ≤ 360° , where a, b and c are constants  a cosine function of the form y = a cos bx + c for 0° ≤ x ≤ 360° , where a, b and c are constants  a tangent function of the form y = a tan bx + c for 0° ≤ x ≤ 360° , where a, b and c are constants The lesson aims to help students acquire the relevant knowledge and skills using the following ACE – Learning system.  Video Lessons – The video lessons enables students to access lessons at their own pace. The step by step plotting of the graph is especially useful for lessons involving basic shape of y = sin x , y = cos x and y = tan x for 0° ≤ x ≤ 360°  Practice Drills – The system classifies practice questions into easy, normal and difficult. This feature enables differentiation to take place. Depending on their ability, students can attempt questions which challenge them suitably.  Interactive Labs – Some lessons have lab sessions that allow students to explore a concept further. In these lessons, students are able to explore y = a sin bx + c , y = a cos bx + c and y = a tan bx + c at his own pace. CLASSROOM LAYOUT AND GROUPING OF STUDENTS: (Where will the learning take place? How will the room be organized with the computers? How will the students be grouped (class group, individuals, pairs, small groups, etc…) The lessons take place in a computer lab or at home. Learning takes place through individual work.
2. 2. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning INSTRUCTIONAL OBJECTIVES: (Identification of the specific learning outcomes expected to happen based on Competency Standards.) a b c d Creativity & Innovation □ □ □ □ Communication & Collaboration □ □ □ □ Research and Fluency □ □ □ □ Critical Thinking, Problem Solving and Decision Making □ □ □ □ Digital Citizenship □ □ □ □ Technology Operations and Concepts □ □ □ □ ICT Creativity and Innovation Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students: a. apply existing knowledge to generate new ideas, products, or processes c. Use models and simulations to explore complex systems and issues Critical Thinking, Problem Solving, and Decision Making Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students: a. identify and define authentic problems and significant questions for investigation c. collect and analyze data to identify solutions and/or make informed decisions Digital Citizenship Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students: b. exhibit a positive attitude toward using technology that supports collaboration, learning and productivity c. demonstrate personal responsibility for lifelong learning Technology Operations and Concepts Students demonstrate a sound understanding of technology concepts, systems, and operations. Students: a. understand and use technology systems b. select and use applications effectively and productively
3. 3. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning MATERIALS, RESOURCES AND TECHNOLOGY: 1. Materials and Resources for this Lesson (special devices) Technology Components for this Lesson a. Computer with internet access 2. Web Site for this Lesson a. ACE Learning Website 3. Computer Software for this Lesson a. ACE Learning System STUDENT’S PRESENT LEVEL OF PERFORMANCE AND KNOWLEDGE: ( Do the students have the adequate knowledge to complete the lesson successfully? What pre-requisite skills must the students have to complete the lesson content? Include technology skills.) Students should be able to a. know the concepts of sine, cosine and tangent functions and values of sine, cosine and tangent of special angles ( 0° 30° , 45° , 60° and 90° ) b. know the basic graph of y = sin x , y = cos x and y = tan x c. navigate through the ace learning system
4. 4. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning INSTRUCTIONAL PROCEDURES: 1. Motivation: Explain the importance of the lesson to motivate the student. Relate lesson to previous lesson or real-life situation. This lesson seeks to provide a learner – centered environment for students to acquire the knowledge and skills Described. This lesson also seeks to demonstrate to students how they can systematically learn on their own using the ACE Learning platform. This lesson allows students to use the interactive lab to further explore y = a sin bx + c , y = a cos bx + c and y = a tan bx + c at his own pace. 2. Activities: (The sequential activities to happen in this lesson. It describes the teaching method to employ in learning the lesson.) a. Students first access the ACE Learning Website b. Students access the video lessons for (i) Graphs of y = sin x , y = cos x , y = tan x , (ii) Graphs of y = a sin x , y = a cos x (iii) Graphs of y = sin bx , y = cos bx (iv) Graphs of y = sin x + c , y = cos x + c
5. 5. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning
6. 6. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning
7. 7. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning d. Teacher will then reinforce the main concept presented in the video and address any questions e. Students select different problems from the question bank to practice. Differentiation takes place here. Depending on their abilities, students can attempt questions which challenge them suitably. The system gives immediate feedback to students after each attempt. Solutions will also be provided if an incorrect answer is submitted. This promotes independent learning. f. Teacher is then free to attend to students who might need more guidance. Peer coaching and learning can also take place. g. The next activity (interactive lab) allows students to further consolidate their understanding in the sketching of the graphs of y = a sin bx + c , y = a cos bx + c and y = a tan bx + c at his own pace. 3. Closure: Summary of the lesson and future lesson. The lesson is summarized by relating students’ learning experiences to the following findings: a. The changes of values of a, b and c affect the graphs of y = a sin bx + c , y = a cos bx + c and y = a tan bx + c b. The concept of amplitude, frequency and period of a trigonometrical graphs In this lesson, the “product” will be the trapeziums and parallelograms that students have drawn. STUDENT PRODUCTS: What artifact(s) or products will result from the lesson? (such as a report, newsletter, diagram, slideshow, drawing, etc.) a. Worksheets on Graphs of Trigonometry (See attached) b. Selected questions from the textbook are given to students as assignment. c. The primary objective in this lesson is for students understand and apply the concept of amplitude, frequency and period in sketching the trigonometrical graphs. d. The understanding that different values of a, b and c can affect the shapes of the trigonometrical graphs is less obvious and needs a bit more uncovering. The interactive lab in this lesson helps students to uncover and represent this understanding. Students are required to sketch graphs of different trigonometric functions. This allows students to apply what he has learnt in a novel way. At the same time, he has to self-adjust as he performs this task. e. The system provides immediate feedback to the student. The “ticks” or “crosses” also gives the teacher a quick and visual way to assess students’ understanding (The system generates a different question for each student, making it difficult for them to copy.) In this lesson, the ‘product’ will be the completion of the Worksheets.