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INTRODUCTION TO DIFFERENTIAL CALCULUS

INTRODUCTION TO DIFFERENTIAL CALCULUS. ITET «L.EINAUDI», Bassano del Grappa A.S. 2015/2016. LESSON PLAN. 1° lesson : Brainstorming (15 minutes) speaking / writing Pair work (10 minutes) reading / speaking Video introduction (8 minutes) listening / writing

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INTRODUCTION TO DIFFERENTIAL CALCULUS

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  1. INTRODUCTION TO DIFFERENTIAL CALCULUS ITET «L.EINAUDI», Bassano del Grappa A.S. 2015/2016

  2. LESSON PLAN 1° lesson: • Brainstorming (15 minutes) speaking/writing • Pair work (10 minutes) reading/speaking • Video introduction (8 minutes)listening/writing • Video comprehension (15 minutes) listening/writing Homework: watch video and studyvocabulary 2° lesson: Jigsawmethod: activitygroupreading/speaking/writing 3° lesson: Practiceat LIMspeaking/writing 4° lesson: Phasetesting 5° lesson: Test correction and reinforcement

  3. Brainstorming ACTIVITY 1: Teacherputs a word at LIM and studentshave to suggestmathconceptsconnected to it Examples of words Students’ suggestions: x-axes / y-axes /variables / domain /points .. Students’ suggestions: Intervals of increasing-descreasing/ maximum / minimum / GRAPH FUNCTION 1°LESSON TYPES OF FUNCTIONS Students’ suggestions: Parabola/ hyperbole/squareroot/exponential/logarithm..

  4. INTEGRATED VOCABULARY Students work in pair to complete the box with the right word. Thentheyread the expressionsaloud. ACTIVITY 2: Complete the following boxes with the options below WORDS: equal / plus / minus / x squared / f(x) over g(x) / squareroot 1°LESSON

  5. A VIDEO ABOUT DIFFERENTIAL CALCULUS Teachersuggests a video at the web page: https://www.youtube.com/watch?v=cRfNOg9Q22U ACTIVITY 3: Reorder the phasesyouhavewatched in the video : Visual/geometricinterpretation of derivative 1°LESSON Definition of derivative as The slope of the secant line and the slope of tangent line Differentinterpretations of derivative likespeed of somethingmoving , marginalcost…

  6. 1.Given a continuosfunction, 2. If ( s is a distance and a function of time) , is the speed of somethingmooving on thatdistance 3. is the slope of the tangent line to a graph of a function 4. As the width of the intervalbecomessmaller, approachesthe slope of the tangent line at the point x ACTIVITY 4: Accordingto the video are the followingsTrue or false? T F T F T F 1°LESSON T F

  7. DERIVATIVE APPLICATIONS ACTIVITY 5: Jigsaw Method Class isdividedintofivegroups of fourstudents. Eachstudent in the groupisgivenonesheetcontainingtheoryexplanations and examplesreguardingone of the followingtopics: • the definition of derivative and itsgeometricinterpretation, • how to calculate derivative of differentfunctionsusing the definition, • how to calculate derivative of differentfunctionsusinggivenrules and properties, • how to calculate the slope of the tangent line to a givenpoint c and representit. 2°LESSON

  8. DERIVATIVE APPLICATIONS ACTIVITY 5: Jigsawmethod First step: New groups are formed: eachgroupisnowmadeofstudents with same material. Theymustexplaineachotherwhattheyhaveunderstoodbytheirstudy. Students discuss and find out a common explanation and theywrite in theircopybooks. Secondstep: The originalgroups of students are composedagain and eachstudentexplainshistopic. The otherstudentslisten and write in theircopybooks. Teacherhastoobserve the activity and supports the differentgroups. 2°LESSON

  9. DERIVATIVE APPLICATION: MATERIAL PROPOSED • Read aloudthe derivative rules 2°LESSON

  10. DERIVATIVE APPLICATION: MATERIAL PROPOSED • Readaloudthe derivative rules 2°LESSON

  11. DERIVATIVE APPLICATIONS Students work at the blackboard and explain the ruleswhilesolving the exercises. Exercises/materialproposed • Givenfunction, which isits derivative at a pointusing the definition? • Givenfunction, which isits derivative at the point2? Whatisitsgeometricinterpretation? • Find the tangent line atpointof the function Reppresent it. • Calculate the derivatives of the following functionsusingderivativesrules . Read aloud the expressions 3°LESSON

  12. Math’s test

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