Graphing Radical Function Lesson for “Graphing Calculator” By Yevgeniy Pavlovskiy

Yevgeniy Pavlovskiy

MTHE 605

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Touro College School of Education and Psychology, Graduate Division MTHE 605 Prof. Strassfeld Yevgeniy Pavlovskiy Spring 2011 March 7, 2011

Lesson Plan Title: Graphing Radical Function By Yevgeniy Pavlovskiy Subject: Mathematics, Algebra II Grade Level: 10 Duration: 45 min. Aim: How can we graph Radical Functions by using translation? Standards: Prior Knowledge: Graphing a relation and its inverse; radical functions; performing operations with radicals; graphing quadratic and polynomial functions; How to use “TI Graphing Calculator”. Materials: Students’ “TI Graphing Calculators” Vocabulary words: Radical Function, Inverse, Square Root Function, Cube Root Functions. Teaching and Instructional Strategy: (5-10 min.) Do now (5-10 min.) Setting up the Project/Research (15-20 min.) Group/Partner Activity (5-10 min.) Presentations of findings (5-10 min.) Extension of the Findings (5 min.) Summary and Homework

Yevgeniy Pavlovskiy

MTHE 605

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Do now (5-10 min.) Students will be presented with the following tasks: Graph each equation: y=(x+2)2 y=-x2-1 y=(x-6)2+4 y=-(x+2)2+1 Graph using table: 𝑦= 𝑥 After 5 min students will be asked to present their answers with additional explanations if needed. Setting up the Project/Research (5-10 min) Class will be divided into groups. Depending on the overall population of the class, groups can be either of mix abilities or split based on the abilities. Students will be encouraged to recall how the graph of a parabola translates/shifts horizontally, vertically, or shrinks/expands based on the changes of the different coefficients in the Vertex Form based on the examples in the “Do Now”. Then students will be asked to hypothesize based on their prior knowledge how the graph 𝑦 = 𝑎 (𝑥 − ℎ) + 𝑘 would shift, shrink or expand from the original 𝑦 = 𝑥 form, when a, h, and k≠0. Group/Partner Activity (10-15 min.) Individual groups will be asked to investigate some of those predictions, when one of those coefficients is not equal to zero and either positive or negative. Students will be asked to first graph 𝑦 = 𝑥 function using “Y=” button on their “Graphing calculators”. Then they will be asked to input same function with one of the coefficients present, depending on the group. Then utilizing ”GRAPH” button they will be asked to note the changes in the graph based on the numerical and sign changes in the coefficient. They will be encouraged to change those values as many times as needed to prove or disprove their hypothesis.

Yevgeniy Pavlovskiy

MTHE 605

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Presentations of Findings (10-15 min.) Students’ groups will present their findings and start to develop rules on how shape and placement of the graph of “Square Root Function” changes based on the changes in coefficients.

Extension of the Findings (5-10 min.) Students and teacher together will develop rules and procedures how to graph 𝑦 = 𝑎 (𝑥 − ℎ) + 𝑘 function. And how those rules can be extended to the “higher” order Radical Functions, for example “Cube Root Functions”: 𝑦 = 𝑎 3 (𝑥 − ℎ) + 𝑘. Summary and Homework (5 min.) Student will be asked in their own words to summarize what they learned and given homework. Assessment: During the group projects activity teacher will observe class and individual students’ work, answer students’ questions, and conduct individual student conferences. Teacher will take short notes of student progress during group projects and later presentations of their findings or the lack of there off. The result of this assessment will be used for the class participation component of the grade and as the information for the future lessons. Homework: Students will be given following homework: Graph each function on the graph paper: 𝑦= 𝑥+1 𝑦= 𝑥−3 𝑦= 𝑥−4 𝑦= 𝑥+6 𝑦 =3 𝑥+1+4