Understanding by Design

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

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: □ Complete template pages – Stages 1, 2, and 3 (Review use)

□ 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 ______) □ Revised draft (date ______)

□ Peer reviewed □ Content reviewed □ Field tested □ Validated □ Anchored

Notes: 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 = ax3); 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)2 = a2 + 2 ab + b2 What understandings are desired? (a – b)2 = a2 – 2 ab + b2

(a + b) (a – b) = a2 – b2 ; represent geometrically. 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… Students will be able to do… The differences between different types of Graph functions of all types functions (i.e. quadratic, linear, exponential) Make connections between functions using How roots and x-intercepts are related. tables, graphs, equations How to determine if a solution is correct or Apply common formulas for multiplying incorrect. binomials Solve various problems using factoring, roots, Determine roots and their relationship to the x- and graphs. intercepts of a graph Understanding of what a change in one variable Factor quadratics does to the other variable in a quadratic 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 16 Day 17 Day 18 Day 19 Day 20 FFPC 1.1 FFPC 1.2 (Day 1) FFPC 1.2 (Day 2) FFPC 1.3 (Day 1) FFPC 1.3 (Day 2) • Begin an introduction • Make connections • Write an equation that to quadratic between the patterns in a describes the relationships table and graph of a relationship between the by looking at a table and quadratic relationship length and area of graph • Use tables and graphs to rectangles with a fixed predict the fixed perimeter perimeter and maximum • Use a quadratic equation area for a family of to describe the graph rectangles with a fixed and table of a quadratic perimeter relationship • Use the equation, graph, and table to solve problems about quadratic relationship Day 21 Day 22 Day 23 Day 24 Day 25 Distributive Property FFPC 2.1 FFPC 2.2 (Day 1) FFPC 2.2 (Day 2) FFPC 2.3 (Day 1) Review • Introduce the concept of • Continue the use calculator to view • Expand the context of equivalent quadratic exploration of equivalent graphs area of rectangles to expressions quadratic expressions of write equivalent the form ax2 + bx quadratic expressions for • Represent a quadratic the relationship in expanded area of a rectangle x2 + and factored forms as two bx + c equivalent ways to • Use the area model to write an expression for review the Distributive the area of a rectangle Property that has been subdivided • Use the area model and into two Distributive Property rectangles to multiply two binomials Milwood Magnet School Biotechnology Magnet Curriculum Math 8 Unit 3, Guide 1 Day 26 Day 27 Day 28 Day 29 Day 30 FFPC 2.3 (Day 2) FFPC 2.4 (Day 1) FFPC 2.4 (Day 2) Quiz 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

Marking Period 4 Day 1 Day 2 Day 3 Day 4 Day 5 FFPC 2.5 (Day 1) FFPC 2.5 (Day 2) FFPC 2.5 (Day 3) FFPC 4.1 FFPC 4.2 • Make a connection • Make a connection • Make a connection • Examine patterns of • Examine patterns of between a quadratic between a quadratic between a quadratic change associated with change associated with equation in equation in equation in quadratic situations that quadratic situations that factored/expanded form factored/expanded form and factored/expanded form are represented by are represented by and its graph its graph and its graph equations in expanded equations in expanded • Predict the shape and • Predict the shape and • Predict the shape and form, such as the height form, such as the height features of a graph from features of a graph from features of a graph from of a ball over time that is of a ball over time that is the expanded and the expanded and factored the expanded and factored thrown in the air thrown in the air factored form of a form of a quadratic form of a quadratic • Predict the maximum or • Predict the y-intercept quadratic equation equation minimum point from from an equation, graph equation an equation, graph or or table table • Interpret the information that the y- intercept represents Day 6 Flex Days Day 7 Flex Days Day 8 Flex Days Day 9 Unit Test Day 10 Unit Test