Planned Course of Study. Algebra I Part 1 NORTHWESTERN LEHIGH SCHOOL DISTRICT 6493 ROUTE 309 NEW TRIPOLI, PA 18066

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1 Planned Course of Study Algebra I Part 1 NORTHWESTERN LEHIGH SCHOOL DISTRICT 6493 ROUTE 309 NEW TRIPOLI, PA 18066

2 NORTHWESTERN LEHIGH SCHOOL BOARD 2013 Darryl S. Schafer, President LeRoy Sorenson, Vice President Camille S. Bartlett, Secretary Willard G. Dellicker, Treasurer Christopher Ford Todd Hernandez Ronald L. Morrison Joseph J. Reiter Greg Sanders John E. Freund III, Esq., Solicitor ADMINISTRATION Dr. Mary Anne Wright, Superintendent Jennifer Holman, Assistant Superintendent Dr. Mark Scott, Director of Pupil Services Luann E. Matika, Director of Human Resources LeAnn M. Stitzel, Director of Curriculum Aileen Yadush, Secondary Principal Donald B. Allen, Assistant Secondary Principal Laurie Hoppes, Middle School Principal Amy Wahl, Middle School Assistant Principal Jill Berlet, Elementary Principal Marc Dobbs, Elementary Principal

3 INTRODUCTION The Algebra 1 Part 1 Mathematics curriculum guide contains planned course formats for the Northwestern Lehigh School District. The content of this document describes the objectives, activities, assessments, content, time frame, and standard alignment that serve as a guide to the specific units of study offered in Algebra 1 Part 1. The Algebra 1 Part 1 curriculum guide is the product of much diligent work on the part of the following staff members who contributed during the school year: Northwestern Lehigh High School Mathematics Department Ms. Jayme Baker Mr. Bob Biese Mrs. Kelly Bleam Mr. Greg Mitchell Mr. Duran Purrino Mrs. Erin Saulnier Mr. Jeremy Smoyer This document reflects their efforts to establish a well-defined and organized approach to teaching Mathematics in the Northwestern Lehigh School District. Approved by Northwestern Lehigh School District Board of Education 2013

4 Unit 1 Section A Curricular Topics Domains Common Core State Standards Relationships between Quantities Expressions, Equations, and Functions Pennsylvania State Standards: A1.1.1: Operations with Real Numbers and Expressions A1.2.1: Functions Anchor Descriptor A : Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents). A : Apply number theory concepts to show relationships between real numbers in problem solving settings. A : Use exponents, roots, and/or absolute values to solve problems. A : Use estimation strategies in problem-solving situations. A : Analyze and/or use patterns or relations. Common Core Standards: A.SSE.1a: Interpret parts of an expression, such as terms, factors and coefficients. A.SSE.2: Use the structure of an expression to identify ways to rewrite it. A.SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity. A.CED.1: Create equations and inequalities in one variable and use them to solve problems A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F.IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f (x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f (x).

5 Essential Curriculum Framing Questions Essential Questions: How can algebraic expressions be transformed? How can mathematical ideas be represented? Unit Questions: How can you write algebraic expressions? How would you use the order of operations? How do you solve equations? How would you represent and interpret relations and functions? How do you do use function notation? How do you interpret the graphs of functions? Content Questions: How do students: Write a verbal expression as an algebraic expression and an algebraic expression as a verbal expression? Evaluate numerical and algebraic expression using the order of operations? Recognize the properties of algebraic expressions? Use the distributive property to evaluate and simplify expressions? Solve equations with one variable? With two variables? Represent and interrupt relations using graphs? Determine whether a relation is a function? Find function values? Competencies Content Skills (What the students will be able to do by the end of the unit) The students will be able to: Materials (Including technology) Assessments (How will students demonstrate understanding of objectives? Identify when formative assessments will take place. Assessments may include projects, demonstrations, presentations, group work, writing pieces, checklists, etc.)

6 Mathematical Practice Standards Time Frame Make sense of problems and persevere in solving them. Reason abstractly and quantitatively Construct viable arguments and critique the reasoning Modeling with Mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning (Number of 80 Minute Blocks) * Represents Accelerated/Honors

7 Unit 1 Section B Relationships between Quantities Curricular Topics Linear Equations Domains Common Core State Standards Pennsylvania State Standards: A1.1.1: Operations with Real Numbers and Expressions A1.1.2: Linear Equations Anchor Descriptor A : Use exponents, roots, and/or absolute values to solve problems. A : Use estimation strategies in problem-solving situations. A : Write, solve, and/or graph linear equations using various methods. Common Core Standards: A.CED.1: Create equations and inequalities in one variable and use them to solve problems. A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters N.Q.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

8 Essential Curriculum Framing Questions Essential Questions: Why are equations and inequalities useful? Why is it helpful to represent the same mathematical idea in different ways? Unit Questions: How can variables be represented as an unknown amount when writing equations from a verbal sentence? How do you solve an equation by finding the value of the variable in an equation to make the equation true? How do you create equations that describe relationships? How do you solve multi-step equations that involve more than one operation? How do you use formulas and solve real-world problems? Content Questions: How do students: Translate sentences into equations? Translate equations into sentences? Solve equations by using addition and subtraction? Multiplication and division? Solve equations involving more than one operation? Solve equations involving consecutive integers? Solve equations involving more than one operation? Solve equations involving consecutive integers? Solve equations with variables on each side? Solve equations involving grouping symbols? Evaluate absolute value expression? Solve absolute value equations? Compare ratios? Solve proportions? Find the percent of change? Solve problems the percent of change? Solve equations for given variables? Use formulas to solve real world problems? Solve mixture problems? Solve uniform motion problems? Competencies Content Skills (What the students will be able to do by the end of the unit) The students will be able to:

9 Materials (Including technology) Assessments (How will students demonstrate understanding of objectives? Identify when formative assessments will take place. Assessments may include projects, demonstrations, presentations, group work, writing pieces, checklists, etc. Mathematical Practice Standards Time Frame Make sense of problems and persevere in solving them. Reason abstractly and quantitatively Construct viable arguments and critique the reasoning Modeling with Mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning (Number of 80 Minute Blocks) * Represents Accelerated/Honors

10 Unit 2 Section A Linear Relationships Curricular Topics Linear Functions Domains Common Core State Standards Pennsylvania State Standards: A1.1.1: Operations with Real Numbers and Expressions A1.1.2: Linear Equations A1.2.1: Functions A1.2.2: Coordinate Geometry Anchor Descriptor A : Use estimation strategies in problem-solving situations. A : Write, solve, and/or graph linear equations using various methods. A : Analyze and/or use patterns or relations. A : Interpret and/or use linear functions and their equations, graphs, or tables. A : Describe, compute, and/or use the rate of change (slope) of a line. Common Core Standards: F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description for the relationship F.IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) F.FI.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. F.LE.1a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. F.BF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. F.LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table). F.LE.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another

11 Essential Curriculum Framing Questions Essential Questions: Why are graphs useful? Why are linear functions useful? How do linear functions model the real world? Unit Questions: How do you identify linear equations, intercepts, and zeros? How do you graph and write linear equations? What is rate of change and how do you use it to solve problems? Content Questions: How do students: Identify linear equations, intercepts, and zeroes? Graph linear equations? Solve linear equations by graphing? Estimate solutions to a linear equation by graphing? Use rate of change to solve problems? Find the slope of a line? Write and graph direct variation equations? Solve problems involving direct variation? Recognize arithmetic sequences? Relate arithmetic sequences to linear functions? Recognize arithmetic sequences? Relate arithmetic sequences to linear functions? Competencies Content Skills (What the students will be able to do by the end of the unit) The students will be able to: Materials (Including technology) Assessments (How will students demonstrate understanding of objectives? Identify when formative assessments will take place. Assessments may include projects, demonstrations, presentations, group work, writing pieces, checklists, etc.)

12 Mathematical Practice Standards Time Frame Make sense of problems and persevere in solving them. Reason abstractly and quantitatively Construct viable arguments and critique the reasoning Modeling with Mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning (Number of 80 Minute Blocks) * Represents Accelerated/Honors

13 Unit 2 Section B Curricular Topics Domains Common Core State Standards Linear Relationships Equations of Linear Functions Pennsylvania State Standards: A1.1.1: Operations with Real Numbers and Expressions A1.1.2: Linear Equations A1.2.1: Functions A1.2.2: Coordinate Geometry Anchor Descriptor A : Use estimation strategies in problem-solving situations A : Interpret and/or use linear functions and their equations, graphs, or tables. A : Describe, compute, and/or use the rate of change (slope) of a line. A : Analyze and/or interpret data on a scatter plot. Common Core Standards: F.IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data F.BF.1: Write a function that describes a relationship between two quantities o Determine an explicit expression, a recursive process, or steps for calculation from a context. o Combine standard function types using arithmetic operations F.LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. *S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. S.ID.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models S.ID.6c: Fit linear function for a scatter plot that suggests a linear association. *S.ID.8: Compute (using technology) and interpret the correlation coefficient of a linear fit. *A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *F.BF.4a: Solve an equation of the form f (x) = c for a single function f that has an inverse and write an expression for the inverse.

14 Essential Curriculum Framing Questions Essential Questions: Why is math used to model real-world situations? How are patterns of change represented in functions? Unit Questions: How do you write and graph linear equations in various forms? How do you use scatter plots and linear of fit, and write equations of best-fit lines using linear regression? How do you find inverse linear functions? Content Questions: How do students: Write and graph linear equations in slope-intercept form? Model real world data with equations and slope-intercept form? Write an equation of a line in slope-intercept form given the slope and one point or given two points? Write equations of lines in point-slope form? Write linear equations in different forms? Write an equation of the line that passes through a given point parallel or perpendicular to a given line? Investigate relationships between quantities by using points on a scatter plot? Use lines of fit to make and evaluate predictions? *Write equations of best-fit lines using linear regression? *Find the inverse of a relation? *Find the inverse of a linear function? Competencies Content Skills (What the students will be able to do by the end of the unit) The students will be able to: Materials (Including technology) Assessments (How will students demonstrate understanding of objectives? Identify when formative assessments will take place. Assessments may include projects, demonstrations, presentations, group work, writing pieces, checklists, etc.)

15 Mathematical Practice Standards Time Frame Make sense of problems and persevere in solving them. Reason abstractly and quantitatively Construct viable arguments and critique the reasoning Modeling with Mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning (Number of 80 Minute Blocks) * Represents Accelerated/Honors

16 Unit 2 Section C Curricular Topics Domains Common Core State Standards Linear Relationships Linear Inequalities Pennsylvania State Standards: A1.1.1: Operations with Real Numbers and Expressions A1.1.3: Linear Inequalities Anchor Descriptor A : Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents). A : Use estimation strategies in problem-solving situations A : Write, solve, and/or graph linear inequalities using various methods. A : Use exponents, roots, and/or absolute values to solve problems. Common Core Standards: A.CED.1: Create equations and inequalities in one variable and use them to solve problems. A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters A.CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. A.REI.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

17 Essential Curriculum Framing Questions Essential Questions: How are symbols useful in mathematics? What mathematical symbols do you know? Why are equations and inequalities useful? Unit Questions: How do you solve one-step and multi-step inequalities? How do you solve compound inequalities and inequalities involving absolute value? How do graph inequalities in two variables? Content Questions: How do you solve linear inequalities by using addition and subtraction? How do you solve linear inequalities by using multiplication and division? How do you solve linear inequalities involving more than one operation or the Distributive Property? How do you solve compound inequalities containing the word AND, and graph their solution set? How do you solve compound inequalities containing the word OR, and graph their solution set? How do you solve and graph absolute value inequalities (less than)? How do you solve and graph absolute value inequalities (greater than)? How do graph linear equalities on a coordinate plane? How do you solve linear inequalities by graphing? Competencies Content Skills (What the students will be able to do by the end of the unit) The students will be able to: Materials (Including Technology) Assessments (How will students demonstrate understanding of objectives? Identify when formative assessments will take place. Assessments may include projects, demonstrations, presentations, group work, writing pieces, checklists, etc.)

18 Mathematical Practice Standards Time Frame Make sense of problems and persevere in solving them. Reason abstractly and quantitatively Construct viable arguments and critique the reasoning Modeling with Mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning (Number of 80 Minute Blocks)

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