Stage 1 Preparation (PLC)

Transcription

1 Teacher_harry henderson RRPS SECONDARY MATH UNIT/LESSON PLAN TEMPLATE Day(s) UNIT TITLE: spinning compass part Stage Preparation (PLC) Grade Level Content Standard(s)/Standard(s) for Mathematical Practice N-Q.2 Define appropriate qantities for the prpose of descriptive modeling. G-MG Modeling with Geometry, Apply geometric concepts in modeling sitations Resorces / Materials Needed compter with access to a mlti-core spercompter with OpenMP DOK levels and Learning Targets, 2, 3 Applying geometry law of sines and law of cosigns eqations to real world problem. Modifying agent based model into a serial code [C++] then paralellize. Another object is optimizing the code. Using technology to explore mathematical relations. Essential Qestion(s) How do we convert between agent based and serial? How do we optimize the code? How do we paralellize the code. This material is based pon work spported by the National Science Fondation nder the NSF EPSCoR Cooperative Agreement No. EPS with additional spport from the Loisiana Board of Regents Objectives: cover phase PHASE : Develop differential eqations to represent the physical object PHASE 2: Convert agent based code to serial code and se those eqations to bild the serial code in C++ PHASE 3: Optimize code sing gradient PHASE 4: Introdce and apply OpenMP to the serial code Prior knowledge: Familiarity with programming preferably with both agent based and serial coding. Geometry/trigonometry math backgrond. Stage 2 Implementation (PLC) Sggest ed Time/ Dates Setting ( Small Pairs, Independent ) Lesson/Unit Components Assessment options/how sed Provide premade serial codes if time or learning abilities are an isse.

2 Teacher_harry henderson RRPS SECONDARY MATH UNIT/LESSON PLAN TEMPLATE Day(s) UNIT TITLE: spinning compass part 5-0 Warm Up(s) Define vales on compass sing trigonometry β d f Resorces: / θ theta is amont of disk rotation α d the distance between the magnet and metal, sing law of cosines d = +r 2 (/ 2) 2 cos(α beta is fond sing law of sines sin(β)= sin (α) d, beta does not need to be solved for as sin(β) will be se below PHASE 2: Review gradient PHASE 3: Review parallel compting

3 Teacher_harry henderson RRPS SECONDARY MATH UNIT/LESSON PLAN TEMPLATE Day(s) UNIT TITLE: spinning compass part Phases can be done on different days if class periods are close to an hor or back to back if longer time slot is allowed Explicit Instrction: Core Lesson(s) Develop differential eqations, Review agent based model of the code and Finite difference, Eler's method: TO: vale new =vale old +time step differential eqation I will now define the inertia of the disk as: Ι= r I will present the Eler forms as: 0-20 θ new =θ new +Δt ω old +Δ t Ι τ(α θ new ) I will now compte the torqe as the orthogonal portion of the force times the radis, [for simplicity allow constants for f to be ] τ= sin (β)/d 2 WITH: We will now compte torqe by expanding the distance, d, sing the law of cosines from the review above τ= sin(α) 2 cos(α

4 Teacher_harry henderson RRPS SECONDARY MATH UNIT/LESSON PLAN TEMPLATE Day(s) UNIT TITLE: spinning compass part Gided and Independent Practice Opportnities BY: On yor own now expanding the the Eler forms with the complete form of torqe, stdents shold arrive at: Small Pairs, or Independent r +Δ t sin ((α θ new +r 2 2 cos((α θ new ) (3/2 ) for enrichment stdents can add friction and arrive at: r +Δ t [ sin ((α θ new ζω +r 2 2 cos((α θ new ) (3/2) old ] 2 Closre for Core Lesson(s) and Independent Practice add more than one piece of metal: θ new =θ old + Δt ω old n n= + Δt n= sin ((α n θ new 2 cos((α n θ new ) for enrichment stdents can also add more than one magnet: + v m= n = Δt sin(((α n ϕ m ) θ new 2 cos(((α n ϕ m ) θ new ) Stage 3 Individal Classroom Plan (Teacher) Differentiation & Strategies to Individalize Unit/Lesson Accommodations

5 Teacher_harry henderson RRPS SECONDARY MATH UNIT/LESSON PLAN TEMPLATE Day(s) UNIT TITLE: spinning compass part This lesson is to be sed with grades 0-2, depending on stdent poplation adjstments will need to be made to make the project level appropriate, these accommodations can also be sed to make accommodations within grade level differentiation [e.g. IEP, gifted, etc ] For lower levels provide prebilt eqation sheets/code and allow stdents to work in s. If the lesson needs to be shorter this option can be sed with pper level stdents also. Stage 4 Two Part Reflection (Teacher and PLC) Which one of the shifts did this nit/lesson best reflect? Explain how. X Rigor: In major topics prse conceptal nderstanding, procedral skill and flency, and application with eqal intensity. This project covers several key aspects of mathematics, ties in the scientific method and wraps everything together in a comprehensive experiment from start to finish inclding analysis all with a hands on real world application. Choose one of the following qestions to answer or create yor own: ) How did this nit/lesson spport 2 st Centry Skills? 2) How did this nit/lesson reflect academic rigor? 3) How did this nit/lesson cognitively engage stdents? 4) How did this nit/lesson engage stdents in collaborative learning and enhance their collaborative skills? This lesson seamlessly combines STEM together. Projects that incorporate math and science together not only teach both math and science they demonstrate the interconnections between the two and this yields a sm greater than the parts. Since this is a team project stdents bond over the importance of combined math and science project promoting the acceptance of STEM in a pblic fashion that is mostly absent in or society today.