Unit Overview - Tewksbury Township Schools



|Unit Overview |

|Content Area: Math |

|Unit Title: Expressions and Functions Unit: 4 |

|Target Course/Grade Level: Eighth Grade Timeline: 3/4 weeks |

|Unit 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 Technology |

|9.1 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 Innovation |

|Mathematical 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 Targets |

|Domain: Functions |

|Cluster: Define, evaluate, and compare functions. Use functions to model relationships between quantities. |

|Standard # | Standards |

|8.F.1 |Understand 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.3 |Interpret 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.5 |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. |

|8.SP.1 |Construct 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.4 |Understand 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.1 |Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and |

| |problem-solving skills. |

|9.1.8.A.2 |Implement problem-solving strategies to solve a problem in school or the community. |

|9.1.8.B.2 |Assess 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.1 |Determine an individual’s responsibility for personal actions and contributions to group activities. |

|9.1.8.C.2 |Demonstrate the use of compromise, consensus and community building strategies for carrying out different task, |

| |assignments and projects. |

|9.1.8.C.3 |Model leadership skills during classroom and extracurricular activities. |

|Unit Essential Questions |Unit Enduring Understandings |

|How can words, tables, graphs, and equations be used to show the |Coordinate geometry can be used to represent and verify |

|relationship between two quantities? |geometric/algebraic relationships. |

|How are functions, formulas, equations, tables, and graphs related? |The symbolic language of algebra is used to communicate and generalize |

|What are some ways in which functions and relations can be |the patterns in mathematics. |

|represented? |In order to make inferences about the world we communicate |

|How are the graphs of linear functions and quadratic functions |representations and generalizations of patterns verbally, numerically, |

|different? |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 Learning |

|Summative 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, Elmo |

|Teacher Instructional Resources: Textbook (TBD) |

|Study Island |

|Khan Academy Videos |

|Formative Assessments |

|Skill sheets |Homework |

|Quizzes/Tests |Math games |

|Student workbook |Study Island |

| |

|Integration 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: |

| |

| |

| – Interactive 2.0 instructional and practice site. Students can view instructional videos and complete practice |

|modules for additional practice/remediation. |

| |

| - Web-based instruction, practice, assessment and reporting built from NJ standards. |

| |

| - IXL 8th grade online interactive activities for the students to complete |

| |

| - AAA math 8th grade – online interactive activities and problems for the student to complete. |

| |

| – 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. Review |

|writing linear equations from tables and graphs. |

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