COLLEGE-PREP ALGEBRA I Course #042 Course of Study Findlay City Schools 2013
TABLE OF CONTENTS 1. Findlay City Schools Mission Statement and Beliefs 2. College-Prep Algebra I Course of Study 3. College-Prep Algebra I Pacing Guide Course Description: Students will work extensively with linear equations including solving, graphing, analyzing and solving practical problems. The language and notation for functions will be used. Students will also explore systems of equations and quadratic equations. Other topics will include polynomial operations, factoring, exponents and radicals. COLLEGE-PREP ALGEBRA I Course of Study Writing Team Ellen Laube Karen Ouwenga Carrie Soellner Text: Algebra I, Common Core, 2012 edition; Pearson (publisher); ISBN #9780133185492; Cost: $97.10
Mission Statement The mission of the Findlay City Schools, a community partnership committed to educational excellence, is to instill in each student the knowledge, skills and virtues necessary to be lifelong learners who recognize their unique talents and purpose and use them in pursuit of their dreams and for service to a global society. This is accomplished through a passion for knowledge, discovery and vision shared by students, families, staff and community. Beliefs Our beliefs form the ethical foundation of the Findlay City Schools. We believe. every person has worth every individual can learn family is the most important influence on the development of personal values. attitude is a choice and always affects performance motivation and effort are necessary to achieve full potential honesty and integrity are essential for building trust. people are responsible for the choices they make. performance is directly related to expectations. educated citizens are essential for the survival of the democratic process. personal fulfillment requires the nurturing of mind, body and spirit. every individual has a moral and ethical obligation to contribute to the well-being of society. education is a responsibility shared by students, family, staff and community. the entire community benefits by investing its time, resources and effort in educational excellence. a consistent practice of shared morals and ethics is essential for our community to thrive.
FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Subject(s) CP Algebra I Grade / Course 9 th Grade Unit of Study Chapter 1 - Foundations of Algebra Pacing 12 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS 1.1 Algebra uses symbols to represent quantities that are unknown or that vary. Mathematical phrases and real-world relationships can be represented using symbols and operations. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. 1.2 Powers can be used to shorten the representation of repeated multiplication. When simplifying an expression operations must be performed in the correct order. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. 1.3 The definition of square root can be used to find the exact square roots of some nonnegative numbers. The square roots of other nonnegative numbers can be approximated. Prepare for N.RN.3 1.4 Relationships that are always true for real numbers are called properties, which are rules used to rewrite and compare expressions. Prepare for N.RN.3 1.7 The distributive property can be used to simplify the product of a number and a sum or difference. An algebraic expression can be simplified by combining the parts of the expression that are alike. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients.
1.9 Sometimes the value of one known quantity can be found if the values of another is known. The relationship between the quantities can be represented in different ways, including tables, equations and graphs. A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 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). Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills (Students need to be able to do) Interpret (A.SSE.1) Unwrapped Concepts (Students need to know) Parts of an expression: Terms Factors Coefficients Bloom s Taxonomy Levels Understand Create (A.CED.2) Equations in two or more variables Apply Graph (A.CED.2) Understand (A.REI.10) Equations on a coordinate plane with labels and scales The graph of an equation in two variables is the set of all its solutions Create Understand
Vocabulary 1.1 Quantity, Variable, Algebraic Expression, Numerical Expression Resources Textbook with Supplementals 1.2 Power, Exponent, Base, Simplify, Evaluate 1.3 Square Root, Radicand, Radical, Perfect Square, Set, Element of a Set, Subset, Rational Numbers, Natural Numbers, Whole Numbers, Integers, Irrational Numbers, Real Numbers, Inequality 1.4 Equivalent Expressions, Deductive Reasoning, Counterexample 1.7 Distributive Property, Term, Constant, Coefficient, Like Terms 1.9 Solution of an Equation, Inductive Reasoning Essential Questions Understanding/Corresponding Big Ideas 1. How can you represent quantities, patterns, and Students will learn to write and evaluate expressions relationships? with unknown values. 2. How are properties related to Algebra? Properties are used to simplify expressions.
FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Subject(s) CP Algebra I Grade / Course 9 th Grade Unit of Study Chapter 2 Solving Equations Pacing 20 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS 2.1 Equations can describe, explain, and predict various aspects of the real world. Equivalent equations are equations that have the same solution(s). A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 2.2 Equations can describe, explain, and predict various aspects of the real world. Equivalent equations are equations that have the same solution(s). A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 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. 2.3 Equations can describe, explain, and predict various aspects of the real world. Equivalent equations are equations that have the same solution(s). A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 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.
2.4 Equations can describe, explain, and predict various aspects of the real world. Equivalent equations are equations that have the same solution(s). A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 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. 2.5 Equations can describe, explain, and predict various aspects of the real world. Equivalent equations are equations that have the same solution(s). 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.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR to highlight resistance R. 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. 2.6 Ratios and rates can used to compare quantities and make conversions. 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. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
2. 7 If two ratios are equal and a quantity in one of the ratios is unknown, the unknown quantity can be found by writing and solving a proportion. 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.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 2.8 Proportional reasoning can be used to find missing side lengths in similar figures. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 2.9 Percents represent another application of proportions. The percent proportion can be used to solve for any one of the missing components and to solve percent increase and percent decrease problems. Prepares for N.Q.3 2.10 Percents represent another application of proportions. The percent proportion can be used to solve for any one of the missing components and to solve percent increase and percent decrease problems. N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning
Unwrapped Skills Unwrapped Concepts Bloom s (Students need to be able to do) (Students need to know) Taxonomy Levels Create (A.CED.1) Equations and inequalities in one variable Apply Use (A.CED.1) To solve problems involving equations and inequalities in one variable Apply Solve (A.REI.3) Linear equations and inequalities with one variable Apply Explain (A.REI.1) The process of solving equations Understand Justify (A.REI.1) The solution to an equation can be supported with mathematical properties Create Use (N.Q.1) Appropriate units for solutions Understand Choose (N.Q.1) Interpret (N.Q.1) Appropriate units and scales: Formulas Graphs Data Displays Appropriate units and scales: Formulas Graphs Data Displays Apply Analyze Define (N.Q.2) Appropriateness of data Understand Choose (N.Q.3) A level of accuracy Understand Rearrange (A.CED.4) Formulas to highlight a quantity of interest Create
Vocabulary 2.1 Equivalent equations, Addition Property of Equality, Subtraction Property of Equality, Isolate, Inverse Operations, Multiplication Property of Equality, Division Property of Equality Resources Textbook with Supplementals 2.4 Identity 2.5 Literal Equations, Formula 2.6 Ratio, Rate, Unit Rate, Conversion Factor, Unit Analysis 2.7 Proportion, Cross Products, Cross Products Property 2.8 Similar Figures, Scale Drawing, Scale, Scale Model 2.10 Percent Change, Percent Increase, Percent Decrease, Relative Error, Percent Error Essential Questions 1. Can equations that appear to be different be equivalent? Understanding/Corresponding Big Ideas Students will find equivalent equations using inverse operations and simplification.
2. How can you solve equations? Students will solve equations using addition, subtraction, multiplication or division. Students will use the distributive property to simplify expressions and solve equations. Students will use the multiplication property of equality and the cross products property to solve proportions. 3. What kinds of relationships can proportions Students will calculate unit rates. represent? Students will use proportions to solve problems involving percents, measurements in similar figures, and indirect measurement. Students will use scale drawings such as maps.
Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 CP Algebra I 9 th Grade Chapter 3 Solving Inequalities 9 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS 3.2 Just as properties of equality can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). Just as equivalent equations can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). Just as equations can be solved using properties of equality, inequalities (including multi-step and compound inequalities) can be solved using the properties of inequality. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 3.3 Just as properties of equality can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). Just as equivalent equations can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). Just as equations can be solved using properties of equality, inequalities (including multi-step and compound inequalities) can be solved using the properties of inequality. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 3.4 Just as properties of equality can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). Just as equivalent equations can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). Just as equations can be solved using properties of equality, inequalities (including multi-step and
compound inequalities) can be solved using the properties of inequality. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 3.6 Just as properties of equality can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). Just as equivalent equations can be used to solve equations, properties of inequality can be used to solve inequalities (including multi-step and compound inequalities). Just as equations can be solved using properties of equality, inequalities (including multi-step and compound inequalities) can be solved using the properties of inequality. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 3.7 An equivalent pair of linear equations or inequalities can be used to solve absolute value equations and inequalities. Absolute value equations and inequalities can solved by first isolating the absolute value expression, if necessary, then writing an equivalent pair of linear equations or inequalities. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning
Unwrapped Skills Unwrapped Concepts Bloom s (Students need to be able to do) (Students need to know) Taxonomy Levels Create (A.CED.1) Equations and inequalities in one variable Apply Use (A.CED.1) To solve problems involving equations and inequalities in one variable Apply Solve(A.REI.3) Linear equations and inequalities with one variable Apply Define (N.Q.2) Appropriateness of data Understand Interpret (A.SSE.1) Parts of an expression: Terms Factors Coefficients Understand Vocabulary 3.2 Equivalent, Inequalities Resources Textbook with Supplementals 3.6 Compound Inequality, Interval Notation Essential Questions Understanding/Corresponding Big Ideas 1. How do you represent relationships between Students will learn to write and graph inequalities. quantities that are not equal? 2. Can inequalities that appear to be different be Students will use properties to generate equivalent equivalent? inequalities. 3. How can you solve inequalities? Equivalent inequalities are generated by using the properties of inequalities. Inequality symbols are reversed when multiplying or dividing both sides of an inequality by a negative number.
Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 CP Algebra I 9 th Grade Chapter 4 An Introduction to Functions 12 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS 4.1 Graphs can be used to visually represent the relationship between two variable quantities as they change. Prepares for F.IF.4 4.2 The value of one variable may be uniquely determined by the value of another variable. Such relationships may be represented using words, tables, equations, sets of ordered pairs, and graphs. 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.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 of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 4.3 Functions (linear and nonlinear) are a special type of relation where each value in the domain is paired with exactly one value in the range. Some functions can be graphed or represented by equations. 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.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 of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
4.4 Functions (linear and nonlinear) are a special type of relation where each value in the domain is paired with exactly one value in the range. Some functions can be graphed or represented by equations. The set of all solutions of an equation forms it s graph. A graph may include solutions that do not appear in a table. A real world graph should show only points that make sense in the given situation. 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.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.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 4.5 Functions (linear and nonlinear) are a special type of relation where each value in the domain is paired with exactly one value in the range. Some functions can be graphed or represented by equations. Many real world functional relationships can be represented by equations. Equations can be used to find the solution of given real world problems. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 4.6 Functions (linear and nonlinear) are a special type of relation where each value in the domain is paired with exactly one value in the range. Some functions can be graphed or represented by equations. 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). 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.
4.7 Arithmetic sequences have function rules that can be used to find any term of the sequence. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 1. F.BF.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. 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 (include reading these from a table). Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills Unwrapped Concepts (Students need to be able to do) (Students need to know) Define (N.Q.2) Appropriateness of data Understand Bloom s Taxonomy Levels Interpret (A.SSE.1) Parts of an expression: Terms Factors Coefficients Understand
Understand (A.REI.10) The graph of an equation in two variables is the set of all its solutions Understand Use (N.Q.1) Appropriate units for solutions Understand Choose (N.Q.1) Interpret (N.Q.1) Appropriate units and scales: Formulas Graphs Data Displays Appropriate units and scales: Formulas Graphs Data Displays Apply Analyze Create (A.CED.2) Equations in two or more variables Apply Graph (A.CED.2) Equations on a coordinate plane with labels and scales Create Interpret (F.IF.4) Key features of graphs and tables Evaluate Sketch (F.IF.4) Graphs showing key features given a verbal description of the relationship Create Relate (F.IF.5) The domain of a function to its graph in context Understand Understand (F.IF.1) What defines a function and the domain and range of the function Understand Use (F.IF.2) Function notation Apply Evaluate (F.IF.2) Functions or domains Evaluate
Interpret (F.IF.2) Functions in context Analyze Recognize (F.IF.3) That sequences are functions Understand Write (F.BF.1) A function modeling data Create Determine (F.BF.1a) Write (F.BF.2) An explicit expression, a recursive process, or steps for calculation Arithmetic and geometric sequences both recursively and explicitly to model situations Create Create Translate (F.BF.2) Between explicit and recursive forms Analyze Construct (F.LE.2) Linear and exponential functions including arithmetic and geometric sequences given: A Graph A description of a relationship A table of values Create Vocabulary 4.2 Dependent variable, Independent variable, Input, Output, Function, Linear Function Resources Textbook with Supplementals 4.3 Nonlinear Function 4.4 Continuous Graph, Discrete Graph 4.6 Relation, Domain, Range, Vertical Line Test, Function
Notation 4.7 Sequence, Term of a Sequence, Arithmetic Sequence, Common Difference, Recursive Formula, Explicit Formula Essential Questions Understanding/Corresponding Big Ideas 1. How can you represent and describe functions? Students will represent functions using tables, equations, and graphs. Students will use function notation. Students will represent arithmetic sequences using function rules. 2. Can functions describe real world situations? Graphs will be used to relate two quantities. Students will model real world situations that are continuous and real world situations that are discrete.
FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Subject(s) CP Algebra I Grade / Course 9 th Grade Unit of Study Chapter 5 Linear Functions Pacing 18 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS 5.1 Ratios can be used to show a relationship between changing quantities, such as vertical and horizontal change. F.IF.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.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 5.2 If the ratio of two variables is constant, then the variables have a special relationship, called a direct variation. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 5.3 A line on a graph can be represented by a linear equation. Forms of linear equations include the slope-intercept, point-slope, and standard forms. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. 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. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). 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.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 of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. F.BF.1 Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 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.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. 5.5 A line on a graph can be represented by a linear equation. Forms of linear equations include the slope-intercept, point-slope, and standard forms. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). 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.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 of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. F.BF.1 Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. 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.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. 5.6 The relationship between two lines can be determined by comparing their slopes and y-intercepts. G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. 5.7 Two sets of numerical data can be graphed as ordered pairs. If the two sets of data are related, a line on the graph can be used to estimate or predict values. 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. F.LE.5 Interpret the parameters in a linear or exponential function 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. a. 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 and exponential models. c. Fit a linear function for a scatter plot that suggests a linear association. S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. S.ID.9 Distinguish between correlation and causation. 5.8 Absolute value equations can be graphed quickly by shifting the graph of y = F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b. Graph square root, cubed root, piecewise-defined functions, including step functions and absolute
value functions. F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills Unwrapped Concepts Bloom s (Students need to be able to do) (Students need to know) Taxonomy Levels Define (N.Q.2) Appropriateness of data Understand Interpret (A.SSE.1) Parts of an expression: Terms Factors Coefficients Understand Use (N.Q.1) Appropriate units for solutions Understand Choose (N.Q.1) Appropriate units and scales: Formulas Graphs Data Displays Apply Interpret (N.Q.1) Appropriate units and scales: Analyze
Formulas Graphs Data Displays Create (A.CED.2) Equations in two or more variables Apply Graph (A.CED.2) Equations on a coordinate plane with labels and scales Create Interpret (F.IF.4) Key features of graphs and tables Evaluate Sketch (F.IF.4) Graphs showing key features given a verbal description of the relationship Create Use (F.IF.2) Function notation Apply Write (F.BF.1) A function modeling data Create Determine (F.BF.1a) Construct (F.LE.2) An explicit expression, a recursive process, or steps for calculation Linear and exponential functions including arithmetic and geometric sequences given: A Graph A description of a relationship A table of values Create Create Create (A.CED.2) Equations in two or more variables Apply Graph (A.CED.2) Equations on a coordinate plane with labels and scales Create Calculate (F.IF.6) Average rate of change Analyze
Interpret (F.IF.6) Average rate of change Analyze Estimate (F.IF.6) Average rate of change Apply Recognize (F.LE.1b) Direct variation Understand Use (A.SSE.2) Properties of exponents to transform expressions Apply Graph (F.IF.7) Identify (F.BF.3) Functions by showing key features: By hand With technology The effects of transformations on a function using function notation Create Understand Interpret (F.LE.5) Functions in context Analyze Compare (F.IF.9) Prove (G.GPE.5) Properties of two functions: Algebraically Graphically Numerically in tables Verbally Relationships between parallel and perpendicular lines using slopes Analyze Analyze Represent (S.ID.6) Data on a scatter plot Create Fit (S.ID.6) A function to the data Create Interpret (S.ID.7) Slope and intercept of a linear model Analyze
Compute (S.ID.8) The correlation coefficient of a linear fit using technology Apply Interpret (S.ID.8) The correlation coefficient of a linear fit Analyze Distinguish (S.ID.9) Between correlation and causation Analyze 5.1 Rate of Change, Slope Vocabulary Resources Textbook with Supplementals 5.2 Direct Variation, Constant of Variation for a Direct Variation 5.3 Parent Function, Linear Parent Function, Linear Equation, Y-Intercept, Slope-Intercept Form 5.5 X-Intercept, Standard Form of Linear Equation 5.6 Parallel Lines, Perpendicular Lines, Opposite Reciprocals 5.7 Scatter Plot, Positive Correlations, Negative Correlation, No Correlation, Trend Line, Interpolation, Exterpolation, Line of Best Fit, Correlation Coefficient, Causation 5.8 Absolute Value Function, Piecewise Function, Step Function, Translation
Essential Questions Understanding/Corresponding Big Ideas 1. What does the slope of a line indicate about the line? Students will find slope using a formula. Students will find slope using a graph. Students will analyze various slopes and describe their meaning. 2. What information does the equation of a line give you? 3. How can you make predictions based on a scatter plot? The equation of a line gives its slope. The equation of a line gives its y-intercept. Students will find the line of best fit. Students will analyze trend lines and scatter plots.
FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Subject(s) CP Algebra I Grade / Course 9 th Grade Unit of Study Chapter 6: Systems of Equations and Inequalities Pacing 18 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS 6.1 Systems of linear equations can be used to model problems. Systems of equations can be solved by graphing, substitution, or eliminating a variable. Some problems can be modeled by systems of linear equations. A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 6.2 Systems of linear equations can be used to model problems. Systems of equations can be solved by graphing, substitution, or eliminating a variable A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 6.3 Systems of linear equations can be used to model problems. Systems of equations can be solved by graphing, substitution, or eliminating a variable A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 6.4 Systems of linear equations can be used to model problems. Systems of equations can be solved by graphing, substitution, or eliminating a variable. Some problems can be modeled by systems of linear equations. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of
linear equations in two variables. 6.5 A linear inequality in two variables has an infinite number of solutions. These solutions can be represented in the coordinate plane as the set of all points on one side of a boundary line. The solutions of a system of linear inequalities can be represented by the region where the graphs of the individual inequalities overlap. A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 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. 6.6 A linear inequality in two variables has an infinite number of solutions. These solutions can be represented in the coordinate plane as the set of all points on one side of a boundary line. The solutions of a system of linear inequalities can be represented by the region where the graphs of the individual inequalities overlap. 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. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills (Students need to be able to do) Solve (A.REI.6) Unwrapped Concepts (Students need to know) Systems of linear equations focusing on linear equations in two variables Bloom s Taxonomy Levels Apply
Prove (A.REI.5) Given a system of two equations in two variables, solving using either addition or multiplication, will produce the same solution. Analyze Define (N.Q.2) Appropriateness of data Understand Choose (N.Q.3) A level of accuracy Understand Represent (A.CED.3) Constraints by equations or inequalities, and by systems of equations or inequalities Understand Interpret (A.CED.3) Solutions are viable or nonviable options in context Evaluate Graph (A.REI.12) The solution : To a linear inequality in two variables as a half plane To a system of linear inequalities Create Vocabulary 6.1 System of Linear Equations, Solution of a System of Linear Equations, Consistent, Independent, Dependent, Inconsistent Resources Textbook with Supplementals 6.2 Substitution Method 6.3 Elimination Method 6.5 Linear Inequality, Solution of a Linear Inequality
6.6 System of Linear Inequalities, Solution of a System of Linear Inequalities Essential Questions 1. How can you solve a system of equations or inequalities? 2. Can systems of equations model real world situations? Understanding/Corresponding Big Ideas Students will learn to solve systems of equations or inequalities by graphing. Students will learn to solve systems of equations or inequalities by substitution. Students will learn to solve systems of equations or inequalities by elimination. Students will write equations and inequalities to represent situations. Students will examine constraints placed on real world situations.
Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 CP Algebra I 9 th Grade Chapter 7 Exponents and Exponential Functions 11 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS 7.1 The idea of exponents can be extended to include zero and negative exponents. Prepares for N.RN.1 and N.RN.2 7.2 Properties of exponents make it easier to simplify products or quotients of powers with the same base or powers raised to a power or products raised to a power. N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5( 1/3 ) 3 to hold, so (5 1/3 ) 3 must equal 5. 7.3 Properties of exponents make it easier to simplify products or quotients of powers with the same base or powers raised to a power or products raised to a power. N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5( 1/3 ) 3 to hold, so (5 1/3 ) 3 must equal 5. 7.4 Properties of exponents make it easier to simplify products or quotients of powers with the same base or powers raised to a power or products raised to a power. N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5( 1/3 ) 3 to hold, so (5 1/3 ) 3 must equal 5. 7.5 Properties of exponents make it easier to simplify products or quotients of powers with the same base or powers raised to a power or products raised to a power. N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills Unwrapped Concepts Bloom s (Students need to be able to do) (Students need to know) Taxonomy Levels Explain (N.RN.1) The notation of rational exponents vs. radical form. Explain Rewrite (N.RN.2) Expressions involving radicals and rational exponents. Using the properties of exponents Understand 7.5 Index Vocabulary Resources Textbook with Supplementals Essential Questions 1. How can you represent numbers less than 1 using exponents? 2. How can you simplify expressions involving exponents? Understanding/Corresponding Big Ideas Students will learn to represent numbers using negative exponents. Students will define and use zero and negative exponents. Students will learn the rules for multiplying powers. Students will learn the rules for dividing powers.