FLIPPED CLASSROOM ACTIVITY CONSTRUCTOR – USING EXISTING CONTENT

Table of Contents SECTION SLIDE # ABOUT YOU 3 OUT-OF-CLASS SEGMENT 5 IN-CLASS SEGMENT 10 EVALUATION 18 COMMUNITY BUILDING

About you Hello everyone We have a team of 3 members as follows: Prof. Mahesh Biradar Prof. Ashwin Chavan Prof. Ramkishan Bhise We belong to Engineering Mathematics domain. We have selected a topic “Laplace Transform” of Engineering Mathematics for Flipped classroom activity.

Replace Header with your Name Laplace Transform Engineering Mathematics Mathematics 2nd YEAR UG STUDENTS IN ENGINEERING University of Mumbai

Out-of-class Activity Design -1 Learning Objective(s) of Out-of-Class Activity At the end of watching the videos student should be able to LO.1: Explain the procedure of finding Laplace transform of given function LO.2 : Evaluate Laplace Transform of given function. LO.3 : Recall the Laplace Transform of standard functions Key Concept(s) to be covered Definition of Laplace Transform Laplace of Standard functions.

Guidelines for Video Selection - 1 First check in National Repositories NPTEL Videos (https://www.youtube.com/watch?v=DPg5T-YBQjU) NPTEL Youtube Channel (https://www.youtube.com/user/nptelhrd) Second Look in International Repositories OER Commons (https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-tutorial/v/laplace-transform-1)

Out-of-class Activity Design - 2 Main Video Source URL https://www.youtube.com/watch?v=r1Ei6gOcy_s License of Video CC-BY-SA (reuse allowed) Mapping Concept to Video Source CONCEPT VIDEO SEGMENT DURATION (in min) Introduction and Definition of Laplace transform V1 - 0:00 – 0.45 0.45 min L.T of First eat V1 - 0:45 – 3.00 2.15 min L.T of Standard functions V1: 3.00 – 8.45 5.45 min Summary V1: 8.45 – 8.55 0.10 min TOTAL DURATION: 8.55 min

Out-of-class Activity Design – 3(a) Aligning Assessment with Learning Objective Learning Objective Assessment Strategy Expected duration (in min) Additional Instructions (if any) Use of definition of Laplace transform Find Laplace Transform of e2t & e-3/2t 10 min Watch video from V1: 0.00 to 3.00 min

Out-of-class Activity Design – 3(b) Aligning Assessment with Learning Objective Learning Objective Assessment Strategy Expected duration (in min) Additional Instructions (if any) Apply formula to evaluate Laplace Transform of new function of t Find Laplace Transform of sinat, cosat, 10 min Watch video from V2: 3.00 to 8.00 min Find Laplace Transform of t3/2, sinhat, coshat Total activity duration: 30 min

In-class Activity Design -1 Learning Objective(s) of In - Class Activity At the end of the class, students will be able to, Solve Laplace Transform of given function. Apply the concept of Laplace Transform to find L.T of new function Explain the transformation of time domain to frequency domain Key Concept(s) to be covered Laplace Transforms, Time domain, Frequency domain

In-class Activity Design -2 Active Learning activity(ies) that you plan to do Think-Pair-Share Explain the strategy by giving details of What Teacher will do: Explained on slide 13 & 14 What Student will do: Explained on slide 15 Justify why the above is an active learning strategy Explained on slide 20

In-class Activity Design -2 Active Learning activity(ies) that you plan to do Evaluating Laplace transform of Higher powers of sine and cosine Think-Pair-Share Concept clarification using. Peer Instruction

In-class Activity Design -2 Peer Instruction Strategy – What Teacher Does Pose the two PI questions at the start of the class and provide summary of basic identities and expression simplification. Q 1:Which method do you use to expand the higher power of (a+b)^5? Binomial Theorem Use of Pascal triangle for coefficients in the expansion Actual Expansion method

In-class Activity Design -2 Peer Instruction Strategy – What Teacher Does  Q 2: Which of the following method is more efficient to expand higher powers ? Binomial Theorem Use of Pascal triangle for coefficients in the expansion Actual Expansion method

In-class Activity Design -2 Peer Instruction Strategy – What Student Does For each question students will first vote individually. Then students will discuss with peers and come to conclusion. Listen to instructor’s explanation.

In-class Activity Design -2 TPS Strategy – What Instructor does: Instructor explains sine and cosine functions and their exponential forms. Also he explains the basic identities of sine and cosine functions and their relations. Problem: Find the Laplace Transform of (Sint)5

In-class Activity Design -2 TPS Strategy – What Instructor does Think (~2 minutes) Instruction: Think individually and identify the best suitable method to expand (Sint)5 from the following: Binomial Theorem Use of Pascal triangle for coefficients in the expansion Actual Expansion method

In-class Activity Design -2 TPS Strategy – What Instructor does Pair (~5 minutes) Instruction: Now pair up and compare your answers. Agree on one final answer. While students are pairing and discussing, instructor goes to 2~3 sections to see what they are doing. Students are also instructed on what parameter answers to be compared as Simplicity, length of the calculation, time consumption.

In-class Activity Design -2 TPS Strategy – What Instructor does Share (~8 minutes): Instructor asks a group to share their answer with class and see whether there are different answers. After sharing is done, instructor gives feedback on the feasible solution and how minimizations of calculation using Pascal Triangle play a major role in the expansion of higher powers like (a+b)n In the next iteration of TPS, in the Think Phase we ask students to (cost)8 (sint)3 In the pair phase we ask students to compare the answers. In the share phase again the different answers are sought.

In-class Activity Design -2 Justify why the above is an active learning strategy In both the above strategies, students are required to go beyond mere listening and execution of prescribed steps. They are required to think deeply about the content they were familiarized in out-of-class and do higher order thinking. There is also feedback provided (either through peer discussion or instructor summary)