Topic: Polygon of Constraints Instructor: Robyn Campbell Grade: MATH 506 Room: 5 Date: October 4, 2019 Period 7 (2:10-3:04) Having reviewed concepts from Sec 4 (second order inequalities, linear systems), students are now ready to consider polygons of constraints. They will be introduced to the idea of incorporating multiple inequalities on one plane, and some of the implications of doing so. They will be introduced also to finding the vertices of the polygon using systems of equations. After the introduction, students will be given time to practice these concepts in pairs or small groups. Mathematical instructional goals Goals for students’ learning of mathematical concepts: - Students will continue to review key concepts from Secondary 3-4, including linear equations, linear systems, and two-variable inequalities. - Students will understand a polygon of constraints as incorporating multiple constraints on one graph. - Students will recognize vertices of the polygon as intersection points of a linear system. Goals for students’ learning of mathematical processes: - Students will observe patterns in their findings and make conjectures about relationships between rules and concepts; - Students will, when faced with a problem requiring multiple steps, employ effective strategies to develop a solution; - Students will continue to develop problem solving abilities related to more abstract concepts and procedures; - Students will express their findings and strategies using mathematical language. Professional Competency Targeted: 4- To pilot teaching/learning situations that are appropriate to the students concerned and the subject content with a view to developing the competencies targeted in the programs of study o Focus on supporting of student learning by asking questions and providing frequent and relevant feedback to promote the integration and transfer of learning. This involves asking critical, open-ended problems, positioning students competently, and creating a supportive and inclusive learning environment. Curriculum Expectations and Competencies (including Evaluation criteria) Learning Content: Algebra: Linear Programming Specific Content: E1 Analyzes a situation to be optimized Competencies: C2: Uses Mathematical Reasoning - correct use of the concepts and processes appropriate to the situation - proper organization of the steps in an appropriate procedure Is there a Connection for Students? Connections to other Curricular Areas? Connections to Cross-Curricular Competencies? Polygons of constraints are used in many areas of science (will allude to applications in physics) where researchers must take into account a variety of constraints on parameters to narrow their search and to make conjectures. Cross Curricular Competencies: C2: Solves Problems C5: Adopts Effective Work Methods C8: Cooperates with Others C9: Communicates Appropriately Equity/ Diversity and Social Justice (Teacher Actions) Allow students to work in small groups (sorted by ability and personality) during independent work Permit extra time for students to copy notes, while posting slides and other materials on Google Classroom for student reference Expectations for students’ participation Students will wait until called upon to answer a question and listen to each other’s answers respectfully without interrupting. They should be prepared to elaborate on, rephrase, and question contributions made by their classmates. They will write notes during the lecture (possibly not directly from the slide) and will complete any formative assessment (i.e. exit ticket) given to the best of their ability. Part 1: Minds On (10 MINUTES) Questions to Ask - Introduce idea of polygon of constraints as coming from situations where multiple constraints need to be incorporated. Give some examples from physics - What would happen if you had to graph two inequalities on a graph? What would you shade? What is dark matter? How do scientists know how to search for it? Part 2: Action (35 MINUTES) Questions to Ask Do example of polygon of constraints (Use I-doone, we-do-one, you-do-one, you-do-many) - - Accommodations/ Modifications (content/process/product) What strategies might you use approaching a problem like this? How might you calculate one of the vertices of the polygon? - Materials Post PowerPoints online for student reference During given questions allow students to talk quietly with their partners Accommodations/ Modifications (content/process/product) - Post PowerPoints online for student reference During given questions allow students to talk quietly with their partners PowerPoint Materials - PowerPoint Part 3: Consolidate/Debrief (10 MINUTES) Questions to Ask Give homework questions (p45 #1) - N/A Accommodations / Differentiation (content/process/product) - N/A Materials Handouts, papers for exit card. Encourage students to submit work on Google Classroom for feedback. Assessment Tools (diagnostic/formative/summative) Diagnostic: Listen to student questions during lecture and gauge level of understanding. Can they make the connection with prior topics? Formative: Observe students as they work through questions and problems at end. Ask individual questions. Summative: None for this lesson. Next Steps Next lesson: More practice with polygons, then Optimization Self Reflection What went well? What didn’t go so well? What do I need to change?
