MA5.3-11NA Logarithms.doc.docx - Weebly



MA5.3-11NALogarithm | Mathematics Stage 5.2/5.3 Year 10 2014Summary of sub strandsDuration 2 weeksStage 4 IndicesStage 5 Indices and surdsStart Date:Completion Date:Teacher and Class:Unit overviewOutcomesBig Ideas/Guiding QuestionsStudents will study the fascinating laws of logarithms and learn to apply these laws in expression and equations.MA5.3-11NA uses the definition of a logarithm to establish and apply the laws of logarithmsMA5.3-1WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjecturesMA5.3-3WM uses deductive reasoning in presenting arguments and formal proofsHow can we solve exponential equations?Key Words/ LanguageIndex, power, base, deduce, expression, exponent, exponential, growth, decay, logarithm, ruleCatholic PerspectivesSchool Free Design MacKillop College Bathurst is a Catholic faith community, dedicated to the education of young women. The Mathematics teachers undertake to uphold the ethos and teachings of the Catholic church and to support the liturgical life of the College. They promote in the classroom a sense of compassion, respect between students and staff and a positive and supportive learning environment.Numeracy operates within a variety of social contexts. From a Catholic perspective, numeracy must be infused with a vision of the innate dignity of all students, as created in the image and likeness of a loving, generous and creating God. Teachers of Mathematics have an obligation to not only teach their students the skills and knowledge to be numerate, but to teach from a Catholic perspective. Teachers are called to challenge their students to use the skills and knowledge they have acquired to bring about social change in the world.Assessment Overview As an assessment have the student create an old fashion log table. Pen and paper tests would also be useful in determining a student’s comprehension. ContentTeaching, learning and assessment Resources At the end of this unit the student should be able to:Stage 5.3 - Logarithms #Students:Use the definition of a?logarithm to establish and apply the laws of logarithms (ACMNA265)define 'logarithm': the logarithm of a number to any positive base is the?index when the number is expressed as a power of the base, ie where a?>?0, y?>?0translate statements expressing a number in index form into equivalent statements expressing the logarithm of the number, eg? deduce the following laws of logarithms from the laws of indices:?establish and use the following results: ? apply the laws of logarithms to simplify simple expressions, eg?, ? , ? , ? , ? simplify expressions using the laws of logarithms, eg?simplify draw and compare the graphs of the inverse?functions ?and Solve simple exponential equations (ACMNA270)solve simple equations that involve exponents or logarithms, eg?, ? , ? , ? Present the definition of Base so that the definition of the logarithm will make sense through the following discussion:-Write on a board 32 = 9 Ask the students the following questions “ 3 to which power is equal to 9”In this example 3 is the base and 2 is the power; therefore, the log of 9 with a base of 3 is two.Hence: if 3 2 = 9 then log 3 9 = 2 Present multiple example until the students show understanding of the concepti.e. solve: log28=3, log10100=2 ….Help students to draw a conclusion for these laws with numerical example such as:Present similar example for the other laws Read the article (referenced in the resources) to develop a historical perspective and importance of logarithms relate logarithms to practical scales, eg?Richter, decibel and pH scales (Problem Solving)compare and contrast exponential and logarithmic graphs drawn on the same axes,?eg?, ? , ? , ? ?(Communicating, Reasoning) Adjustment Refer students to mathsonline or Khan academy for logarithm tutorials. Have the students complete a group project to create class presentations on the history and application of logs in the real world.Use Geogebra to have students create and compare different graphsArticle: Calculator: ................
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