Developed By: Gloria Quigley Name of Collaborative: Math 2 Curriculum Area: Mathematics Unit Title: The Great Quadratic Time Frame: 18 days Note: Each teacher keeps his/her own copy reflecting teacher’s unit plan | ||
Desired Results | ||
Content Standards ( # and brief description): Copy and paste from Picasso | ||
Element: MM2N1 Students will represent and operate with complex numbers. Element: MM2N1.a. Write square roots of negative numbers in imaginary form. Element: MM2N1.b. Write complex numbers in the form a + bi. Element: MM2N1.c. Add, subtract, multiply, and divide complex numbers. Element: MM2N1.d. Simplify expressions involving complex numbers. Element: MM2A3.a. Convert between standard and vertex form. Element: MM2A3.b. Graph quadratic functions as transformations of the function f(x) = x^{2}. Element: MM2A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change. Students will solve quadratic equations and inequalities in one variable. Element: MM2A4.a. Solve equations graphically using appropriate technology. Element: MM2A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Element: MM2A4.c. Analyze the nature of roots using technology and using the discriminant. Element: MM2A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities. Students will solve problems (using appropriate technology). Element: MM2P1.a. Build new mathematical knowledge through problem solving. Element: MM2P1.b. Solve problems that arise in mathematics and in other contexts. Element: MM2P1.c. Apply and adapt a variety of appropriate strategies to solve problems. Students will make connections among mathematical ideas and to other disciplines. Element: MM2P4.a. Recognize and use connections among mathematical ideas. Element: MM2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. Element: MM2P4.c. Recognize and apply mathematics in contexts outside of mathematics. | ||
Essential Questions: What provocative questions will foster inquiry, understanding, and transfer of learning? | ||
What are my roots? Why do I need to know how to factor? What happens if I move the parabola? What if it is not Real? What is the connection to other mathematics? | ||
Content (Unpack Nouns from Standards): Students will know… |
Skills (Unpack Verbs from Standards): Students will be able to… | |
Complex numbers Quadratic equations Inequalities Quadratic formula Standard form of a quadratic equation Vertex form of a quadratic equation Intercept form of a quadratic equation Discriminant Factor |
Students will represent and operate with complex numbers. Students will analyze and graph quadratic functions in the forms f(x) = ax^{2} + bx + c , f(x) = a(x - h)^{2} + k, and f(x) = (x – a )(x – b) Students will solve quadratic equations and inequalities in one variable. Students will solve quadratic equations by factoring, by the square root method, by completing the square, and by using the quadratic formula. Students will communicate mathematically. Students will make connections among mathematical ideas and other disciplines. | |
Essential Vocabulary: What critical vocabulary must be learned in order to master the content? · quadratic function · standard form · vertex form · intercept form · quadratic formula · discriminant · root · inequality · factor | ||
Assessment Evidence | ||
Summative (attach) |
Test .5 and Test 1 | |
Formative (build from Summative) |
Quizzes, Journals, Tasks, Worksheets, Problem sets, Board work, Verbal communication, Notebooks, Workbooks, Collaborative activities | |
Common/ Collaborative Goal: 75% or more of the assessment should be from the Summative Assessment |
Quizzes, Tasks, Note-taking workbooks, Worksheets, Tests, Problem Sets | |
Learning Plan | ||
Pacing Guide (weekly or daily) |
Days 1-2: Graphing quadratics and noting characteristics via performance tasks Day 3-4: Factoring many types of quadratic equations Days 5-6: Solving quadratics Days 7-8: Reinforce days 1-5 concepts and relate the topics to one another Day 9: Mid-Unit Test Days 10: Complex Number System Day 11: Using complex numbers to solve square roots Day 12: More complex number concepts Day 13: Completing the square Day 14: Quadratic Formula stressing the discriminant Day 15: Graphing quadratic inequalities in one variable Days 16-7: Reinforce days 1-15 concepts and relate the topics to one another Day 18: Test on unit 1 | |
Engagement (Highlight all that apply) |
Independent activities Pairing /small Groups Learning Stations Cooperative learning Hands on Whole group instruction Technology integration Project Lecture Peer tutoring Visuals Simulations/Role Play Discussion Performance Task Game Other: Other: Other: | |
Learning Activities |
What learning experiences and instruction will enable students to achieve the desired results? Create a list with a brief description. Protein Bar Learning Task-examines the process application for factoring quadratic equations Imagining a New Number Task-examines computations and uses for imaginary numbers Graphing Quadratic Equations Task- analyzes the properties of graphs of quadratic equations from standard, vertex, and intercept form Frayer’s model for vocabulary Model showing what student knows, needs to know, and has learned Word wall | |
Differentiation |
Enrichment activities vs.remediation activities. Group work/teacher directed vs independent study | |
Materials/Resources |
Textbook, note-taking workbook, worksheets, smartboard, whiteboard, tasks, concept maps, | |
Collaborative Reflection |
Weekly |