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
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.
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani”
Udine
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
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
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)
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
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 activityWhole class teaching
Interactive teaching
Learning support
EPSILON
B/B
Total Time 8 hours + 1 hour (test)
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
exercises
N.Negrello I.T.I. Malignani - Udine
EXERCISESIstituto Tecnico Industriale
“A. Malignani”Udine
1) Complete
This is………..
f(x)dx
We say: “ The integral be…….
Or easily…….
This is …….
ab
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
Istituto Tecnico Industriale “A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani”
Udine