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Milwood Magnet School Biotechnology Magnet Curriculum Math 8 Unit 3, Guide 1 Understanding by Design: 6-page Template, page 1 Unit Title: Alternative Energy & Medical Biotechnology (first half) Grade level: 8 Subject/Topic Areas: Frogs Fleas and Painted Cubes - representing quadratic relationships Key Words: function, parabola, quadratic relationship, factored form (product), expanded form (sum), distributive property, quadratic expressions, factoring, roots, line of symmetry, vertex, vertex form, intercept, maximum value, minimum value Designed by: Jennifer Pinckney & James Roth Time Frame: 5 weeks (MP 3 weeks 4-6 & MP 4 week 1-2) School District: Kalamazoo Public Schools School: Milwood Magnet School Brief Summary of Unit (including curricular context): In this unit students will be introduced to quadratic relationships by looking at tables, graphs, and equations. They will make connections between the patterns presented in each representation. Equations will be examined in both expanded and factored form. (This particular guide of this unit does not have direct ties to the thematic topic of Cap and Trade, however look for creative ways to support the theme as you explore these concepts.) Unit design status: (Review use) □ Complete template pages – Stages 1, 2, and 3 □ Completed blueprint for each performance task □ Completed rubrics □ Directions to students and teachers □ Materials and resources listed □ Suggested accommodations □ Suggested Extensions Status: □ initial draft (date _______ ) □ Peer reviewed Notes: □ Content reviewed □ Revised draft (date __________) □ Field tested □ Validated □ Anchored Milwood Magnet School Biotechnology Magnet Curriculum Math 8 Unit 3, Guide 1 6-Page Template, Page 2 Stage 1 – Identify Desired Results Established Goals: A.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions including inversely proportional relationships (y = k/x); cubics (y = ax 3); roots (y = √x ); and exponentials (y = ax , a > 0); using tables, graphs, and equations.* A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others. A.RP.08.04 Use the vertical line test to determine if a graph represents a function in one variable. A.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs, and vice versa; in particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic function. A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x-axis and the coordinates of the vertex; use words “parabola” and “roots”; include functions in vertex form and those with leading coefficient –1, e.g., y = x2 – 36, y = (x – 2)2 – 9; y = – x2; y = – (x – 3)2. A.FO.08.07 Recognize and apply the common formulas: (a + b) = a + 2 ab + b2 What (a – b)understandings 2 = a2 – 2 ab + b2 are desired? (a + b) (a – b) = a2 – b2 ; represent geometrically. 2 2 A.FO.08.08 Factor simple quadratic expressions with integer coefficients, A.FO.08.09 Solve applied problems involving simple quadratic equations. Students will understand the… Tables, graphs, and equations of quadratic functions can be used to represent/understand patterns and characteristics. What essential questions will be considered? How do outside factors impact decision making? Scaffolding Questions: How are graphs, equations, and tables related and what information can be gathered from each? What real world examples can be represented by quadratic functions? What are the similarities and differences between linear and quadratic functions? What key knowledge and skills will students acquire as a result of this unit? Students will know… The differences between different types of functions (i.e. quadratic, linear, exponential) How roots and x-intercepts are related. How to determine if a solution is correct or incorrect. Solve various problems using factoring, roots, and graphs. Understanding of what a change in one variable does to the other variable in a quadratic Students will be able to do… Graph functions of all types Make connections between functions using tables, graphs, equations Apply common formulas for multiplying binomials Determine roots and their relationship to the xintercepts of a graph Factor quadratics Solve quadratics with roots and/or by factoring and verify solutions Milwood Magnet School Biotechnology Magnet Curriculum Math 8 Unit 3, Guide 1 6-Page Template, Page 3 Stage 2 – Determine Acceptable Evidence What evidence will show that students understand? Unit Test * Complete a Performance Task Blueprint for each task (see next page) Other Evidence (quizzes, tests, prompts, observations, dialogues, work samples): Bell Work, Vocabulary, Summary, Class Discussion, Binder (Investigations), Quizzes/Check-Ups Student Self-Assessment and Reflection: Exit Slip, Reflections Milwood Magnet School Biotechnology Magnet Curriculum Math 8 Unit 3, Guide 1 6-Page Template, Page 4 Performance Task Blueprint Supplement to Stage 2 performance task What understanding and goals will be assessed through this task? Writing quadratic equations in factored and expanded form. Identify quadratic functions by looking at tables, graphs, and functions What criteria are implied in the standards and understandings regardless of the task specifics? What qualities must student work demonstrate to signify that standards were met? Student can fluently move between representations of quadratic function. Students can justify why a table, graph, or equation is quadratic or linear. Through what authentic performance task will students demonstrate understanding? What student products and performances will provide evidence of desired understandings? Weekly probes Unit Test By what criteria will student products and performances be evaluated? Milwood Magnet School Biotechnology Magnet Curriculum Math 8 Unit 3, Guide 1 6-Page Template, Page 5 Stage 3 – Plan Learning Experiences and Instruction Consider the WHERETO elements: WHERETO elements: W – Introduce performance task at beginning of unit so as instruction and learning occur they can be connected, and recorded, as tools for the task. H – Performance task has a real world connection. While not every student may be able to relate to farming, framing the context from a business perspective gives students an accessible practical application. E – Using textbook examples as their experiences have students reflect on how the content they are working might apply to the project. R – Performance task is planned for two days. Day two begins with questions that arose from Day one’s work. Based on the discussion students have the opportunity to revise their work, E – This summative assessment is the foundational knowledge for solving simultaneous linear equations by substitution and combination. So based on their results students will be able to reflect on their strengths and weaknesses and use that information to help them prepare for the second part of the unit. T – The integrated assessment which pulls content from the four core areas of instruction allows students to determine the format and content of their final project. O – Graphic Organizer created for students to keep final product together. Milwood Magnet School Biotechnology Magnet Curriculum Math 8 Unit 3, Guide 1 6-Page Template, Page 6 Stage 3 – Plan Learning Experiences and Instruction Marking Period 3 Day 18 FFPC 1.2 (Day 2) Day 16 FFPC 1.1 Day 17 FFPC 1.2 (Day 1) Day 19 FFPC 1.3 (Day 1) • Begin an introduction • Make connections • Write an equation that to quadratic relationships by looking at a table and graph between the patterns in a table and graph of a quadratic relationship • Use tables and graphs to predict the fixed perimeter and maximum area for a family of rectangles with a fixed perimeter describes the relationship between the length and area of rectangles with a fixed perimeter • Use a quadratic equation to describe the graph and table of a quadratic relationship • Use the equation, graph, and table to solve problems about quadratic relationship Day 21 Distributive Property Review Day 22 FFPC 2.1 Day 23 FFPC 2.2 (Day 1) • Introduce the concept of • Continue the equivalent quadratic expressions exploration of equivalent quadratic expressions of the form ax2 + bx • Represent a quadratic relationship in expanded and factored forms as two equivalent ways to write an expression for the area of a rectangle that has been subdivided into two rectangles Day 24 FFPC 2.2 (Day 2) use calculator to view graphs Day 20 FFPC 1.3 (Day 2) Day 25 FFPC 2.3 (Day 1) • Expand the context of area of rectangles to write equivalent quadratic expressions for the area of a rectangle x2 + bx + c • Use the area model to review the Distributive Property • Use the area model and Distributive Property to multiply two binomials Milwood Magnet School Biotechnology Magnet Curriculum Math 8 Unit 3, Guide 1 Day 26 FFPC 2.3 (Day 2) Day 27 FFPC 2.4 (Day 1) Day 28 FFPC 2.4 (Day 2) Day 29 Quiz Day 30 Flex Day • Use the area model and Distributive Property to rewrite an expression that is in expanded form into an equivalent expression in factored form Day 1 FFPC 2.5 (Day 1) Day 2 FFPC 2.5 (Day 2) Marking Period 4 Day 3 FFPC 2.5 (Day 3) Day 4 FFPC 4.1 Day 5 FFPC 4.2 • Make a connection • Make a connection • Make a connection • Examine patterns of • Examine patterns of between a quadratic equation in factored/expanded form and its graph • Predict the shape and features of a graph from the expanded and factored form of a quadratic equation between a quadratic equation in factored/expanded form and its graph • Predict the shape and features of a graph from the expanded and factored form of a quadratic equation between a quadratic equation in factored/expanded form and its graph • Predict the shape and features of a graph from the expanded and factored form of a quadratic equation change associated with quadratic situations that are represented by equations in expanded form, such as the height of a ball over time that is thrown in the air • Predict the maximum or minimum point from an equation, graph or table change associated with quadratic situations that are represented by equations in expanded form, such as the height of a ball over time that is thrown in the air • Predict the y-intercept from an equation, graph or table • Interpret the information that the yintercept represents Day 6 Flex Days Day 7 Flex Days Day 8 Flex Days Day 9 Unit Test Day 10 Unit Test