ࡱ>  0bjbjWW .==(&&&&&::::l4:;$pJJJJ%%%#######$Q&)p#&%%%%%#&&JJ#2%^&J&J#%#V !J@xZ! ~##<;$f!xs)Ms)!!s)&!%%%%%%%##%%%;$%%%%s)%%%%%%%%% :  Unit OverviewContent Area: MathUnit Title: Expressions and Functions Unit: 4Target Course/Grade Level: Eighth Grade Timeline: 3/4 weeksUnit Summary: Students are introduced to expressions, relations, and functions as they analyze words, tables, graphs, and equations. Patterns are used to help students write algebraic expressions and translate between verbal, tabular, graphical, and algebraic representations of linear functions. Students extend their analysis to nonlinear functions.Primary interdisciplinary connections: Language Arts and Technology9.1 21st-Centuries Life & Career Skills Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures. Strand: A. Critical Thinking and Problem Solving B. Creativity and Innovation C. Collaboration, Teamwork and Leadership Content Statement: 9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem solving skills to solve the problem is a lifelong skill that develops over time. 9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources, including global perspective, fosters creativity and innovative thinking. 9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals with greater efficiency. Leadership abilities develop over time through participation in group and or teams that that are engaged in challenging or competitive activities. 21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and Leadership, Creativity and InnovationMathematical Practices: 8.MP.1 Make sense of problems and persevere in solving them. 8.MP.2 Reason abstractly and quantitatively. 8.MP.3 Construct viable arguments and critique the reasoning of others. 8.MP.4 Model with mathematics. 8.MP.5 Use appropriate tools strategically. 8.MP.6 Attend to precision. 8.MP.7 Look for and make use of structure. 8.MP.8 Look for and express regularity in repeated reasoning.Learning TargetsDomain: Functions Cluster: Define, evaluate, and compare functions. Use functions to model relationships between quantities.Standard # Standards8.F.1Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.8.F.3Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a 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.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.8.F.5Describe 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.8.SP.1Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.8.SP.4Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?9.1.8.A.1Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem-solving skills.9.1.8.A.2Implement problem-solving strategies to solve a problem in school or the community.9.1.8.B.2Assess data gathered to solve problems for which there are varying perspective (e.g., cross cultural, gender specific, generational, etc.) and determine how the data can best be used to design the multiple solutions.9.1.8.C.1Determine an individuals responsibility for personal actions and contributions to group activities.9.1.8.C.2Demonstrate the use of compromise, consensus and community building strategies for carrying out different task, assignments and projects.9.1.8.C.3Model leadership skills during classroom and extracurricular activities. Unit Essential Questions How can words, tables, graphs, and equations be used to show the relationship between two quantities? How are functions, formulas, equations, tables, and graphs related? What are some ways in which functions and relations can be represented? How are the graphs of linear functions and quadratic functions different?Unit Enduring Understandings Coordinate geometry can be used to represent and verify geometric/algebraic relationships. The symbolic language of algebra is used to communicate and generalize the patterns in mathematics. In order to make inferences about the world we communicate representations and generalizations of patterns verbally, numerically, symbolically and graphically. Unit Learning Targets Students will ... Graph ordered pairs on the coordinate plane and use the coordinate plane to represent relations. Find a rule for a given pattern. Translate information in tables and graphs to expressions. Translate tables and graphs into linear equations. Determine whether a relation is a function. Complete function tables. Represent linear functions using function tables and graphs. Determine whether a function is linear or nonlinear. Graph quadratic functions.Evidence of LearningSummative Assessment Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations. Analyze domain and range. Given a table, graph, or verbal description, write an equation and make a prediction. Translate among verbal, tabular, graphical, and algebraic representations of linear functions. Determine whether a function is linear or nonlinear from a table. Compare the graphs of linear and nonlinear functions. Graph quadratic functions. Equipment needed: coordinate grids, number cubes, ruler, Smart Board, white boards, calculators, ElmoTeacher Instructional Resources: Textbook (TBD) Study Island Khan Academy VideosFormative AssessmentsSkill sheets Quizzes/Tests Student workbookHomework Math games Study IslandIntegration of Technology: Smart Board to play online games, utilize online resources, generate models with Smart Software. Kahn Academy Videos Elmo for demonstration Study Island Technology Resources:  HYPERLINK "http://www.purplemath.com" http://www.purplemath.com  HYPERLINK "http://www.khanacademy.org" http://www.khanacademy.org Interactive 2.0 instructional and practice site. Students can view instructional videos and complete practice modules for additional practice/remediation.  HYPERLINK "http://www.studyisland.com/" http://www.studyisland.com/ - Web-based instruction, practice, assessment and reporting built from NJ standards.  HYPERLINK "http://www.ixl.com/math/grade-8" http://www.ixl.com/math/grade-8 - IXL 8th grade online interactive activities for the students to complete  HYPERLINK "http://www.aaamath.com/grade8.html" http://www.aaamath.com/grade8.html - AAA math 8th grade online interactive activities and problems for the student to complete.  HYPERLINK "http://www.adaptedmind.com/Math-Worksheets.html?type=hstb" http://www.adaptedmind.com/Math-Worksheets.html?type=hstb Grade level material for practice, lessons, games, etc. Opportunities for Differentiation: Decelerate: Students create patterns of squares with sides 1, 2, 3, and so on, using toothpicks. Students make tables for perimeter, total number of squares, total number of toothpicks used, as they extend the pattern. Then they write the rule for each pattern. Students gather price information for snacks available in their cafeteria. Working in pairs, they create a table and then graph the data for the cost of buying one to six of the item. Students play the game Function or Not? Display a table of values. Students decide whether it is a function or not and are awarded points accordingly. Students use a template (showing all work) as they graph quadratic functions. Accelerated: Students bring in graphs from newspapers or magazines that represent real-world data. The graphs should represent a linear equation. The students will determine the linear equation using the text and examining the points. Give the graph to another student who will try to determine the equation. Given two equations, the students will determine the solution for the system. Students create different quadratic functions, graph them and then determine what in the function made the shape change.Teacher Notes: Before the chapter begins, review translating verbal phrases into algebraic expressions and then evaluating them. 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