2014-2015 Curriculum Blueprint Grade: 7 Course: MJ2 ADV 10 Days Unit #14: Functions Learning Goal Students will be able to calculate the slope of a linear function, and determine where the line crosses the x and y axes in real-world problems. Students will also be able to solve systems of equations in real-world problems to determine a common solution. Link to Learning Scale: Functions, Interpret Functions    Essential Question(s) How do we recognize linear functions? When graphing real world data, what does the slope and intercepts tell us? When would a system of equations with two unknowns have no solution or an infinite number of solutions? Approximate Time: Unit Overview In this unit, the term function is formally introduced for both linear and non-linear functions. Students model functions in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) and interpret those representations qualitatively and quantitatively. For this unit, students will be introduced to non-linear functions so that they are able to identify whether or not a function is linear, but they will not be required to generate their own examples until later. Understanding how functions model (MP.4) relationships requires that student’s reason abstractly and quantitatively (MP.2) while looking for and making use of structure (MP.7). Focus Standards Vertical Progression: Bullets are the deconstructed standards These should be used to develop concise learning http://www.turnonccmath.net/ K-8 Learning Trajectories (This could be used to determine statements/daily objectives/scales. Standards below are not intended to be followed in the order they remediation needs or enrichment opportunities) are listed. See unit sequence for intended order. Grade 8 Mathematics Item Specifications 7th Grade - Students decide whether two quantities are in a proportional relationship. MAFS.8.F.1.1 (DOK 2): Understand that a function is a rule that assigns to each input exactly one output. The graph of a High School - Students will learn function notation, explore many examples of functions, interpret function is the set of ordered pairs consisting of an input and the corresponding output. functions, and translate between representations. MAFS.8.F.1.2 (DOK 2): Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.  Identify functions algebraically including slope and y-intercept.  Identify functions using graphs, tables and verbal descriptions.  Compare and contrast 2 functions with different representations.  Draw conclusions based on different representations of functions. Unit Sequence Be selective in choosing problems aligned to the standards within each lesson Slope, Intercepts, and Linear Functions Rule  McDougal Littell 7-7 – 7-8  Engage NY Module 5 Lesson 1 (Page 9) More Examples of Functions MAFS.8.F.1.3 (DOK 2): Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give  Engage NY Module 5 examples of functions that are not linear. For example, the function A = s² giving the area of a Lesson 4 ( Page 45) square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Graphs of Functions  Recognize that a linear function is graphed as a straight line.  Engage NY Module 5 Lesson 5 (Page 57)  Recognize the equation y = mx + b is the equation of a function whose graph is a straight line where m is the slope and b is the y-intercept.  Compare the characteristics of linear and nonlinear functions using various representations.  Provide examples of nonlinear functions using multiple representations.        Essential Vocabulary x-intercept y-intercept slope-intercept form linear function function notation systems of equations solutions of systems of equations    Higher Order Questions/Stems How did you identify the function? What are the characteristics of a __________? What are some different ways you can recognize a non-linear function?   Writing Connections Compare and contrast 2 functions. Compare the characteristics of linear and nonlinear functions. 2014-2015 Curriculum Blueprint Grade: 7 Course: MJ2 ADV 10 Days Unit #14: Functions MAFS.8.F.2.5 (DOK 3): Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.  Analyze a graph and describe the functional relationship between two quantities using the qualities of the graph.  Interpret the relationship between x and y values by analyzing a graph.  Sketch a graph, given a verbal description of its qualitative features. Mathematical Practice Standards Link to Mathematical Practice Standards Rubric MAFS.K12.MP.2.1: Reason abstractly and quantitatively. MAFS.K12.MP.4.1: Model with mathematics. MAFS.K12.MP.7.1: Look for and make use of structure. Approximate Time: Supplemental Resources 8th Grade Flip Book – A user-friendly resource for understanding the specifications of the Common Core Standards.  EngageNY Grade 8 Module 5 – Word documents can be found using this link *You can access all of the following material from the Module 5 page as the links below may be slow to load o Teacher Materials o Student Materials - The student materials consist of the student pages for each lesson in Module 5. o Copy Ready Materials - A collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials. Writing Template Tasks These template tasks are designed from the Mathematical Practice Standards. When filled in, these templates become teaching tasks that create opportunities for teaching literacy skills in mathematics. Georgia Unit 4: Functions Tasks aligned to 8.F.1.1 and 8.F.1.2: o Secret Codes and Number Rules – Page 9 o Foxes and Rabbits – Page 36 o The Vending Machine – Page 41 o Order Matters – Page 47 o Battery Charging – Page 57 o Which is Which? – Page 64 o Create Matching Function Cards – Page 72 o Sorting Functions – Page 100 Georgia Unit 5: Linear Functions Tasks aligned to 8.F.1.2 and 8.F.1.3 o Analyzing Linear Functions – Page 54 MARS Task: Modeling Situations with Linear Equations – a formative assessment lesson in which students will explore relationships between variables in everyday situations, find unknown values from known values, find relationships between pairs of unknowns, and express these as tables and graphs, find general relationships between several variables, and express these in different ways by rearranging formulae. (PowerPoint at the bottom of the page)  Draw conclusions based on different representations of functions. Explain how you verified that for each input there was exactly one output. Link to Problem Solving Rubric Link to Webb’s DOK Guide 2014-2015 Curriculum Blueprint Grade: 7 Course: MJ2 ADV Unit #14: Functions Math Formative Assessment System (MFAS) These formative assessments could be used before instructing a lesson on similar content to help formulate small groups or they may be used however PLCs see best for their students. Each formative assessment comes with a rubric and instructional implications based on the level of student understanding. Illustrative Mathematics – 8th grade tasks developed under the direction of writers of the CCSS at the University of Arizona. RTTT Item Specifications – page 45 Teaching Channel Video: Graphing Linear Equations Full Body Style – 4 minute video featuring students graphing a line given slopeintercept on a giant coordinate plane. Teaching Channel Video 2 minute video with a focus on Improving Participation with Talk Moves (Personalized Learning Opportunity). Approximate Time: 10 Days