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# Lesson Plan Rob Eldi

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A technology infused lesson for mathematic

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### Lesson Plan Rob Eldi

1. 1. Rob Eldi Technology Lesson Plan
2. 2. Transformation of Functions <ul><li>Grade Level: 9 th grade regular class </li></ul><ul><li>Subject Area: Math B </li></ul><ul><li>Tools used </li></ul><ul><ul><li>Notebook Software </li></ul></ul><ul><ul><li>TI-Smartview; TI-84 calculator </li></ul></ul><ul><ul><li>Geometer’s Sketchpad </li></ul></ul><ul><ul><li>www.fooplot.com </li></ul></ul>
3. 3. Description of Project <ul><li>Prior Knowledge: </li></ul><ul><ul><li>Students should have an understanding of the “parent functions” </li></ul></ul><ul><ul><ul><li>Basic sketch; Important points; Domain & Range </li></ul></ul></ul><ul><li>Purpose: </li></ul><ul><ul><li>Students will develop the knowledge and understanding about why functions transform the way they do </li></ul></ul><ul><ul><li>Students will construct the “rules” associated with each transformation </li></ul></ul><ul><ul><li>Students will be able to determine the new domain & range </li></ul></ul><ul><ul><li>Students will integrate the use of technology into their understanding of mathematical concepts. </li></ul></ul><ul><ul><li>Students will discuss concepts (student-to-student) through the use of technology </li></ul></ul>
4. 4. Description of Project <ul><li>Task: </li></ul><ul><ul><li>Students will construct the rules of transformations of functions through teacher led discussions as well as student-to-student discussions </li></ul></ul><ul><ul><ul><li>After each lesson, students will be given regular homework and will also be asked to create a transformed function using www.fooplot.com . The function will be copied to a word document, printed and brought to class to be used as do-nows for each small group in the beginning of each class </li></ul></ul></ul><ul><ul><li>After the 5 day sequence, students will create a unique design using at least one of each of the parent functions and their knowledge of parent functions </li></ul></ul><ul><ul><ul><li>We will spend one or two days in a computer lab so that the students can input their design into Geometer’s Sketchpad to create a final version of their design </li></ul></ul></ul>
5. 5. Procedures <ul><li>Day 1: </li></ul><ul><ul><li>Students will spend the entire first lesson constructing the rules for translations for the various functions. </li></ul></ul><ul><ul><li>We will focus on translation in the x-direction. We can list the inputs and outputs for each function to further determine that the function is backwards…meaning that if we go 3 right x gets replaced with (X – 3). </li></ul></ul><ul><ul><li>Demonstrations will be done using imported graphs created to match the grid on notebook software. This will allow us to move the functions manually about the coordinate plane. </li></ul></ul><ul><ul><ul><li>HOMEWORK: </li></ul></ul></ul><ul><ul><ul><ul><li>In addition to graphing translated functions and graphing them, you are to go to www.fooplot.com and plot a translated function. Copy this image and print it to bring to class. Make sure to retain the original function separate from the graph. As a do now tomorrow, students will trade papers within their 3-4 person group and they will try to determine the equation of the graphed function . </li></ul></ul></ul></ul>
6. 6. Procedures <ul><li>Day 2: </li></ul><ul><ul><li>Today we will focus on translations in the y-direction and by the end of the lesson we will have combined them both in one function. </li></ul></ul><ul><ul><li>Given the function translate and here is the end result what is the translation… </li></ul></ul><ul><ul><ul><li>HOMEWORK: </li></ul></ul></ul><ul><ul><ul><ul><li>In addition to graphing translated functions and graphing them, you are to go to www.fooplot.com and plot a translated function. Copy this image and print it to bring to class. Make sure to retain the original function separate from the graph. As a do now tomorrow, students will trade papers within their 3-4 person group and they will try to determine the equation of the graphed function. </li></ul></ul></ul></ul>
7. 7. Procedures <ul><li>Day 3: </li></ul><ul><ul><li>We will be looking at graphs of functions that have been reflected over the x-axis. We will find the rule. </li></ul></ul><ul><ul><li>We will also reflect over the y-axis and find the general rule. </li></ul></ul><ul><ul><ul><li>HOMEWORK: </li></ul></ul></ul><ul><ul><ul><ul><li>In addition to graphing reflected functions and graphing them, you are to go to www.fooplot.com and plot a reflected function. Copy this image, print it and to bring to class. Make sure to retain the original function separate from the graph. As a do now tomorrow, students will trade papers within their 3-4 person group and they will try to determine the equation of the graphed function. </li></ul></ul></ul></ul>
8. 8. Procedures <ul><li>Day 4: </li></ul><ul><ul><li>Composition of transformations of functions. </li></ul></ul><ul><ul><li>Given a parent function, here is the composition, graph it and write the new equation. </li></ul></ul><ul><ul><li>We will try some when we go backwards; here is the graph, what is the parent function and what composition of transformations occurred to get the result. </li></ul></ul><ul><ul><ul><li>HOMEWORK: </li></ul></ul></ul><ul><ul><ul><ul><li>In addition to graphing composed functions and graphing them, you are to go to www.fooplot.com and plot a composed function. Copy this image and print it to bring to class. Make sure to retain the original function separate from the graph. As a do now tomorrow, students will trade papers within their 3-4 person group and they will try to determine the equation of the graphed function. </li></ul></ul></ul></ul>
9. 9. Procedures <ul><li>Day 5: </li></ul><ul><ul><li>Review day. </li></ul></ul><ul><ul><li>Additionally explore the fact that if you reflect a function over the line Y = X the result is the inverse of that function. </li></ul></ul><ul><ul><li>We will explore the identity function. </li></ul></ul><ul><ul><li>We will also have a brief discussion on scaling, however, they are not responsible to know it. </li></ul></ul><ul><ul><li>Describe the project that they will be doing over the weekend. </li></ul></ul><ul><ul><ul><li>Project: </li></ul></ul></ul><ul><ul><ul><ul><li>Through your knowledge of transformations of functions, students will create a unique design, using at least one of each of the parent functions. Making sure to restrict the domains as necessary. Students will list all of the equations of the functions used and bring a sketch to class. We will meet in the computer lab on Monday and Tuesday to transfer these images into Geometers sketchpad to create the unique design. </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>For example: Design a slimily face; an animal, snowman; etc </li></ul></ul></ul></ul></ul>
10. 10. Resources <ul><li>The only resources required to teach this lesson are the technologies listed. Everything else has been created by me: </li></ul><ul><ul><li>Including worksheets; etc. </li></ul></ul>
11. 11. Teacher Preparation <ul><li>Teacher must have all parent functions pre-made and ready to use on the notebook software. </li></ul><ul><li>Homework worksheets must be created with ample examples, ranging in difficulty to ensure differentiated instruction possibilities. </li></ul><ul><li>Develop interesting AIMS; for example: </li></ul><ul><ul><li>How have our parents changed? </li></ul></ul><ul><ul><li>What’s up with our parent’s reflection? </li></ul></ul>
12. 12. Evaluation <ul><li>Link to the Rubric </li></ul><ul><li>Technology promotes learning. </li></ul><ul><ul><li>Hands-on activity provides motivation to learn the material while creating a design. </li></ul></ul><ul><ul><li>Students construct their own understanding. </li></ul></ul><ul><ul><li>Students develop a deeper understanding by creating their own problems on www.fooplot.com . </li></ul></ul>
13. 13. Higher Order Thinking <ul><li>Analysis </li></ul><ul><ul><li>Can students graph transformed functions based on their graph? </li></ul></ul><ul><ul><li>Can students determine the equation based on the graph? </li></ul></ul><ul><ul><li>Why does the function appear behave opposite to the equation? </li></ul></ul><ul><li>Synthesis </li></ul><ul><ul><li>Can students formulate their own examples to present to their groups? </li></ul></ul><ul><ul><li>Can students create a unique design? </li></ul></ul><ul><li>Evaluation </li></ul><ul><ul><li>Can students predict the behavior of the functions they created? </li></ul></ul><ul><ul><li>Can they fix the equation to behave accordingly? </li></ul></ul>
14. 14. New York Standards <ul><li>Problem Solving Strand </li></ul><ul><ul><li>A.PS.3 Observe and explain patterns to formulate generalizations and conjectures </li></ul></ul><ul><ul><li>A.PS.7 Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving </li></ul></ul><ul><li>Reasoning and Proof Strand </li></ul><ul><ul><li>A.RP.4 Develop, verify, and explain an argument, using mathematical ideas and language </li></ul></ul><ul><ul><li>A.RP.5 Construct logical arguments that verify claims or counterexamples that refute them </li></ul></ul><ul><ul><li>A.RP.10 Extend specific results to more general cases </li></ul></ul><ul><li>Communication Strand </li></ul><ul><ul><li>A.CM.1 Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explain for the steps used in solving a problem </li></ul></ul><ul><ul><li>A.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formula, functions, equations, charts, graphs, Venn diagrams, and other diagrams </li></ul></ul><ul><ul><li>A.CM.3 Present organized mathematical ideas with the use of appropriate standard notations, including the use of symbols and other representations when sharing an idea in verbal and written form </li></ul></ul><ul><li>Connections Strand </li></ul><ul><ul><li>A.CN.2 Understand the corresponding procedures for similar problems or mathematical concepts </li></ul></ul><ul><li>Representation Strand </li></ul><ul><ul><li>A.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts. </li></ul></ul><ul><ul><li>A.R.8 Use mathematics to show and understand mathematical phenomena(e.g., compare the graphs of the functions by the equationsY=x^2 and Y = -X^2 </li></ul></ul><ul><li>Geometry Strand </li></ul><ul><ul><li>A.G.8 Find the roots of a parabolic function graphically </li></ul></ul>
15. 15. ISTE Standards <ul><li>Basic operations and concepts </li></ul><ul><ul><li>Students demonstrate a sound understanding of the nature and operation of technology systems. </li></ul></ul><ul><ul><li>Students are proficient in the use of technology. </li></ul></ul><ul><li>Social, ethical, and human issues </li></ul><ul><ul><li>Students understand the societal issues related to technology. </li></ul></ul><ul><ul><li>Students practice responsible use of technology systems, information, and software. </li></ul></ul><ul><ul><li>Students develop positive attitudes toward technology uses that support lifelong learning, collaboration, personal pursuits, and productivity. </li></ul></ul><ul><li>Technology productivity tools </li></ul><ul><ul><li>Students use technology tools to enhance learning, increase productivity, and promote creativity. </li></ul></ul><ul><ul><li>Students use productivity tools to collaborate in constructing technology-enhanced models and producing other creative works. </li></ul></ul>