N.Negrello I.T.I. Malignani - Udine. Module: Integration Where: 5^ class I.T.I. A.Malignani Udine...

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

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 IntegralsU2: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.

Istituto Tecnico Industriale “A. Malignani”

Module: Integration

Time Table

Units Time

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 EPSILON 2 hour

TOTAL 18 hours

U.1.:Indefinite Integrals

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

U.1.:Lesson planning

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

Total Time 6 hours + 1 hour (test)

U.2.:Integration Techniques

What to know: Rules of substitution technique

Rules of integration by part

Rules of integration of rational functions

What to Do:Apply integration rules

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 activityWhole class teaching

Interactive teaching

Learning support

EPSILON

Total Time 8 hours + 1 hour (test)

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

EXERCISESIstituto Tecnico Industriale

“A. Malignani”Udine

1) Complete

This is………..

f(x)dx

We say: “ The integral be…….

Or easily…….

This is …….

f(x)dx

We’ll 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.

N.Negrello I.T.I. Malignani - Udine. Module: Integration Where: 5^ class I.T.I. A.Malignani Udine...

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