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- 1. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 SUBJECT AREA: Mathematics GRADE LEVEL: Sec 3E Name of Teachers: Junie Lim/ Lillian Kuck LESSON TITLE: Functions and Graphs TIME ALLOTTED: 1 hour LESSON DESCRIPTION: (Write a concise description of what occurs in this lesson.) At the end of the lesson, students will be able to: 1. Interpret the shape of the graph based on the function y = ax n for n = −2, −1, 0,1, 2 and 3 2. Sketch the graph accurately. 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 lesson will take place in the computer lab. Students will work individually. 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 □ ■ □ □
- 2. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 Creativity and Innovation : a) apply existing knowledge to generate new ideas, products or processes Critical Thinking, Problem Solving and Decision Making : b) plan and manage activities to develop a solution or complete a project Digital Citizenship : b) exhibit a positive attitude toward using technology that supports collaboration, learning and productivity Technology Operations and Concepts : a) understand and use technology systems MATERIALS, RESOURCES AND TECHNOLOGY: 1. Materials and Resources for this Lesson (special devices) Technology Components for this Lesson Computer with graphing software 2. Web Site for this Lesson Nil 3. Computer Software for this Lesson Graphmatica 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.) Pre-requisite skills needed: 1. Knowledge to sketch graphs, ie the general shape of the graph as well as the essential points needed when applicable. 2. Knowledge of the use of the software, Graphmatica.
- 3. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 INSTRUCTIONAL PROCEDURES: 1. Motivation: Explain the importance of the lesson to motivate the student. Relate lesson to previous lesson or real-life situation. • This is an important topic in Mathematics as many real-life situations can be represented using graphs. • If we have all the essential points, ie x and y intercepts, maximum or minimum points, a line or curve can be sketched. 2. Activities: (The sequential activities to happen in this lesson. It describes the teaching method to employ in learning the lesson.) • Get the students to settle down in class. • Recall past knowledge about the sketching of line and curve, ie the general shape of the curve and the essential points required. • Teacher to give out worksheet to the class. Teacher to get the class to start their computer. Extract from the worksheet: Teacher to tell the class that they are going to Interpret the shape of the graph based on the function y = ax for n • n = −2, −1, 0,1, 2 and 3 . Teacher to ask the students to do the first 3 pages of the worksheet given to them. They are to explore the graphs, y = ax n for n = 0,1 and 2 , using the Graphmatica software and answer the questions. • The teacher to go through the questions with the students. Teacher to get the students to recall past knowledge
- 4. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 that is related to these 3 graphs. 1. y = ax is a horizontal straight line passing through a. 0 2. y = ax is a straight line passing through the origin. 3. y = ax is a quadratic curve. The line of symmetry for the curve is a vertical 2 straight line passing through the maximum or minimum point. • Teacher to ask the students to continue with the worksheet, pg 4. • Teacher to go through the worksheet with the students. Introduce a new term to the students: point of inflexion. Teacher is to elicit to the students why the general shape of the graph of y = ax 3 is as such. a • Teacher to get the students to continue with the worksheet, pg 5-8. Teacher to go through the graph of y = x a and y = . Through the guiding questions given in the worksheet, the teachers will explain to the students why x2 the general shape of the graphs is as such. 3. Closure: • Teacher to summarize what the students have learnt today by going through pg 7-8 of the worksheet. Teacher to pick students to come to the board and draw the general shape of y = ax n for n = −2, −1, 0,1, 2 and 3 . SUPPLEMENTAL ACTIVITIES: 1. Additional activities to expand the lesson 2. Remediation activities for the student needing more instruction and practices 3. Assignments Nil
- 5. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 ASSESSMENT AND EVALUATION: How will you measure the student’s success? Formally or informally? Formal evaluation of student work requires that a grade is taken while informal might be monitoring of work, or class discussion. This section should contain a description of the assessment process, the criteria for achievement, and performance levels. The criteria should directly align to objectives and instruction. Describe your plan for providing feedback to your students. During discussion, the teacher can pick on students to answer question. Can correct any misconceptions if they have any. For the summary of what they have learnt today, the teacher can also check for understanding by picking out weaker students to sketch the general shape of t y = ax n for n = −2, −1, 0,1, 2 and 3 . STUDENT PRODUCTS: What artifact(s) or products will result from the lesson? (such as a report, newsletter, diagram, slideshow, drawing, etc.) Completed Worksheet to be submitted for checking.
- 6. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 Name: ____________________ ( ) Date: ___________ Class: Sec 30( ) WORKSHEET 2 CHAPTER 5: FUNCTIONS AND GRAPHS INVESTIGATION ON GRAPHS OF POWER FUNCTION The function y = ax n , where a is a real constant and n is a rational number, is called a power function. Note: We are focusing on the function, y = ax n where n = −2, −1, 0,1, 2 and 3 . a. Case n = 0 Use Graphmatica to sketch the following graphs: Equation Graph y - intercept y = 3x 0 y = −2x 0 1. The graph of y = ax 0 can be re-written as _______________ . 2. Briefly describe the graphs above. b. Case n = 1
- 7. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 Use Graphmatica to sketch the following graphs: Equation Graph x and y - intercept y = 2x 1 y=− x 2 1. The graph of y = ax is known as a _____________ graph. 2. When a > 0 , the graph of y = ax has a __________ gradient. 3. When a < 0 , the graph of y = ax has a __________ gradient. 4. Briefly describe the graphs above. c. Case n = 2
- 8. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 Using Graphmatica, sketch the following graphs on the same axes. 1 2 1. y = x 2 2. y = 3x 2 3. y = − x 2 4. y = − x 2 Label all the graphs after you have sketched them. y x 0 1. The graph of y = ax 2 is known as a _____________ graph. 2. When a > 0 , the graph of y = ax 2 has a ___________ point. 3. When a < 0 , the graph of y = ax 2 has a ___________ point. 4. The graph of y = ax 2 will always has a line of _____________ passing through the maximum or minimum point. The line of symmetry is a ____________ straight line.
- 9. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 d. Case n = 3 Using Graphmatica, sketch the following graphs on the same axes. 1 3 1. y = x 3 2. y = 3x 3 3. y = − x 3 4. y = − x 2 Label all the graphs after you have sketched them. y x 0 1. The graph of y = ax 3 is known as a _____________ graph. 2. The graph of y = ax 3 has no turning point but it has a point of inflexion. (a) When a > 0 , the graph of y = ax 3 has a __________ gradient before and after the point of inflexion. (b) When a < 0 , the graph of y = ax 3 has a ___________ gradient before and after the point of inflexion. e. Case n = -1 Using Graphmatica, sketch the following graphs on the same axes.
- 10. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 1 3 1 1 1. y = 2. y = 3. y = − 4. y = − x x x 2x Label all the graphs after you have sketched them. y x 0 a 1. The graph of y = is known as a _____________ graph. x a 2. The graph of y = is defined for all real values of x, except when x = _______. Therefore, the ____ - x axis is known as an ____________ . a 3. There is _____ turning point for y = . x
- 11. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 1 4. As the positive value of x increases, the value of will ___________. Hence, the value of y x ___________ . The curve will get very close to the x-axis but it will never touch it. 5. Between 0 < x < 1 , the gradient of the graph has a very __________ gradient. This is due to the rapid ______________ in the value of y. 1 6. As the value of x becomes more negative, the value of becomes _________ negative. Hence, the value x of y becomes _________ negative. 7. Between − 1 < x < 0 , the gradient of the graph has a very __________ gradient. This is due to the rapid ______________ in the value of y. a 8. The 2 parts of the graph are mirror images of each other. There are 2 lines of symmetry for y = . The x equations are ______________ and ______________.
- 12. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 e. Case n = - 2 Using Graphmatica, sketch the following graphs on the same axes. 1 3 1 1 1. y = 2. y = 3. y = − 4. y = − x2 x2 x2 2x 2 Label all the graphs after you have sketched them. y x 0 a 1. The graph of y = is known as a _____________ graph. x2 a 2. The graph of y = is defined for all real values of x, except when x = _______. Therefore, the ____ - x2 axis is known as an ____________ . a 3. There is _____ turning point for y = . x2
- 13. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 1 4. As the positive value of x increases, the value of will ___________. Hence, the value of y x2 ___________ . The curve will get very close to the x-axis but it will never touch it. 1 5. As the value of x becomes more negative, the value of becomes _________ positive. Hence, the x2 value of y becomes _________ positive. 6. Between − 1 < x < 0 and 0 < x < 1 , the gradient of the graph has a very __________ gradient. This is due to the rapid ______________ in the value of y. 7. Since the values of y are always positive, therefore the curve lies entirely _________ the x –axis. a 8. The 2 parts of the graph are mirror images of each other. The curve, y = is symmetrical about the ___ x2 - axis.
- 14. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 In conclusion, the following are the graphs of the functions with the form y = ax n , where n = −2, −1, 0,1, 2 and 3 . y = ax 0 , a > 0 y = ax 0 , a < 0 y y x x 0 0 y = ax , a > 0 y = ax , a < 0 y y x x 0 0 y = ax 2 , a > 0 y = ax 2 , a < 0 y y x x 0 0 y y y = ax 3 , a > 0 y = ax 3 , a < 0 x x 0 0
- 15. XMSS LESSON PLAN TEMPLATE: Using ICT in Teaching and Learning 2010 a a y= , a>0 y y= , a<0 y x x x x 0 0 a a y= , a>0 y y= , a<0 x2 x2 y x 0 x 0

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