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N.Negrello I.T.I. Malignani - Udine

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Module: Integration Where: 5^ class I.T.I. A.Malignani Udine Time: 3 hours a week in the first term Topics of the Module: U1:Indefinite Integrals U2:Integration techniques Methodology During the lessons students are asked to hypothesise, to discuss, to give opinions, to generalise and synthesise concepts. They are expected to use problem solving. Some lessons are done with the English teacher.

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine Module: Integration Time Table UnitsTime Indefinite integral Unit 1 Whole class teaching; Use EPSILON Test for monitoring understanding Scientific language Vocabulary reinforcement 3 hours 2 hours 1 hour 1 hour with the English teacher Integration techniques Unit 2 Whole class teaching; Use EPSILON Test for monitoring understanding Scientific language Vocabulary reinforcement Final test 4 hours 2 hours 1 hour 1 hour with the English teacher 1 hour Revising with EPSILON2 hour TOTAL18 hours

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine U.1.: Indefinite Integrals Aims What to know : The definition of the set of anti-derivatives of a function The relation between integration and derivation The definition of a definite integral The difference between indefinite and definite integral Properties of indefinite integrals Integration vocabulary What to do: Graphic identification of functions and anti-derivatives Apply the properties of indefinite integrals

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N.Negrello I.T.I. Malignani - Udine U.1.: Lesson planning Istituto Tecnico Industriale A. Malignani Udine Contents Definition of indefinite integral Relation of integration and derivation Recognise this relation in different contexts Cognitive Process Working out concepts and links. Asking for explanations Improving vocabulary Teacher activity Whole class teaching Interactive teaching Problem solving Learning support EPSILON B/B Total Time 6 hours + 1 hour (test)

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N.Negrello I.T.I. Malignani - Udine U.2.: Integration Techniques Istituto Tecnico Industriale A. Malignani Udine Aims What to know: Rules of substitution technique Rules of integration by part Rules of integration of rational functions What to Do: Apply integration rules

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine U.2.: Lesson planning Contents Integration by substitution Integration by part Integration of rational functions Integration of some irrational functions Cognitive Process Applying rules Asking for explanations Teacher activity Whole class teaching Interactive teaching Learning support EPSILON B/B Total Time 8 hours + 1 hour (test)

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine Examples of the use of EPSILON and of monitoring / understanding Epsilon = software multimedia Monach University – Melbourne- Australia Cristina Varsavsky Cristina.Varsavsky@sci.monash.edu.au exercises

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N.Negrello I.T.I. Malignani - Udine EXERCISES Istituto Tecnico Industriale A. Malignani Udine 1) Complete This is……….. f(x)dx We say: The integral be……. Or easily……. This is ……. a b f(x)dx Well read this as integral be….. Or easily…….. 2) Fill in the gaps Integration is the…….. process of differentiation. In order to …….. with confidence it is helpful to have a good knowledge of ……….. techniques, because when ……… a function, we often try to figure out what has been ……… to give that function.For ……….integration, …….. are given and a numerical value obtained. When there are no limits, the integration is known as ………., and it is necessary to include the integration …….., usually written C.

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine

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N.Negrello I.T.I. Malignani - Udine Istituto Tecnico Industriale A. Malignani Udine

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1 Duschl, R & Osborne, J. 2002. ”Supporting and Promoting Argumentation Discourse in Science Education” in Studies in Science Education, 38, 39-72 Ingeborg.

1 Duschl, R & Osborne, J. 2002. ”Supporting and Promoting Argumentation Discourse in Science Education” in Studies in Science Education, 38, 39-72 Ingeborg.

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