Algebra 2 Early 1 st Quarter

Transcription

1 Algebra 2 Early 1 st Quarter CCSS Domain Cluster A.9-12 CED.4 A REI.3 Creating Equations Reasoning with Equations Inequalities Create equations that describe numbers or relationships. Solve equations inequalities. Solve equations inequalities in one variable. Stard Statement 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. Solve linear equations inequalities in one variable, including equations with coefficients represented by letters. Days Clear Learning Target 2 I can solve formulas for a specified variable. 3 I can solve linear equations in one variable including equations with coefficients represented by letters. Vocabulary Equation Linear equation Linear inequality Coefficient Core Resource Chapter 1 Section 1.4 Chapter 1 Section 1.3, Additional Resource Quality Quality (Nee d page # s) Assessment Chapter 1 /or 2 Quiz Chapter 1 / or 2 Tests Chapter 1 /or 2 Quiz Chapter 1 /or 2 Tests I can solve linear inequalities in one variable including inequalities with coefficients represented by letters. F BF.3 Building Functions Build new s from existing s. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), f(x + k) for specific values of k (both positive negative); find the value of k given the 2 I can explain the translations of original graphs for right left shifts, vertical horizontal stretches shrinks. Amplitude Vertical shift Horizontal shift Period change Negative coefficient Appendix 1 Section pages Quality (Nee d page # s) Chapter 1 /or 2 Quiz Chapter 1 /or 2 Tests Daily Common Formative Assessment

2 graphs. Experiment with cases illustrate an explanation of the effects on the graph using technology. - Include recognizing even odd s from their graphs algebraic expressions for them. I can analyze the similarities differences between s with different values of k. I can recognize from a graph if the is even or odd Translation Function Translate Stretch Shrink Even Odd Y- axis symmetry Rotational symmetry F IF.4 F IF.6. Interpreting Functions Interpreting Functions Interpret s that arise in applications in terms of the context. Analyze s using different representations. Interpret s that arise in applications in terms of the For a that models a relationship between two quantities, interpret key features of graphs tables in terms of the quantities, sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the is increasing, decreasing, positive, or negative; relative maximums minimums; symmetries; end behavior; periodicity. Calculate interpret the average rate of change of a (presented symbolically or as a 6 I can define the relative maximum minimum as place where the transitions from decreasing to increasing vis- versa. I can define the positive negative end behavior as the trend of a s outputs. 2 I can define interval, rate of change, average rate of change. X- intercept Y- intercept Interval Increase Decrease Maximum Minimum Symmetry End Behavior Periodicity Function Rate of change Average rate of change Chapter 2 5 Section 2.1, 2.2, 2.3, 2.4, 2.5, 2.7, 2.8, 5.1 Chapter 2, 5 Quality (Need page # s) Quality Chapters 1/2/5 Quiz??? Chapters 1/2/5 Test Chapter 1/2/5 Quiz Chapter 1/2/5 Test Daily Common Formative Assessment

3 context. Analyze s using different representations. table) over a specified interval. Estimate the rate of change from a graph. I can calculate rate of change. Interval Section (Nee d page # s) F IF.9. Interpreting Functions Interpret s that arise in applications in terms of the context. Analyze s using different representations. Compare properties of two s each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic an algebraic expression for another, say which has the larger maximum. 2 I can compare properties of two s when represented in different ways. I can distinguish between s that model growth decay. Evaluate Function Coordinate plane Algebraically Graphically Numerically Verbally Chapter 2, 5 8 Section 2.1, 5.1, Quality (Nee d page # s) Chapter 1/25/8 Quiz Chapter 1/2/5/8 Test End Early 1 st Quarter (4.5 Weeks) District Short Cycle Assessment Daily Common Formative Assessment

4 Algebra 2 Late 1 st Quarter CCSS Domain Cluster Stard Statement Days Clear Learning Target Vocabulary Core Resource Additional Resource Assessment A CED.1. Creating Equations Create equations that describe numbers or relationships Create equations inequalities in one variable use them to solve problems. Include equations arising from linear quadratic s, simple rational s. 2 I can identify the variables quantities represented in a real- world problem. I can write an equation or inequality that best models the problem Linear Quadratic Rational Chapters 2 5 Section Quality Chapter 2/3 Quiz Chapter 2/3 Test A REI.12. Reasoning with Equations Inequalities Represent solve equations inequalities graphically Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half- planes. 2 I can define linear inequality, half- plane, boundary. I can graph a linear inequality systems of linear equalities. System of linear inequalities Solution Half- plane Boundary Intersection Coordinate plane Linear inequality Chapter 2 Section Quality Chapter 2/3 Quiz Chapter 2/3 Test A CED.2. Creating Equations Create equations that describe numbers or relationships Create equations in two or more variables to represent relationships between quantities; graph equations on 4 I can identify the variables quantities represented in a real- world situation. Linear Quadratic Coordinate axes Scale Labels Chapter 3 Section 3.1, 3.2, 3.5, 3.6 Quality Chapter 2/3 Quiz Chapter 2/3 Test Common Formative Assessment will be implemented daily

5 A CED.3. Creating Equations Create equations that describe numbers or relationships coordinate axes with labels scales. Represent constraints by equations or inequalities, by systems of equations /or inequalities, interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional cost constraints on combinations of different foods. I can graph equations on coordinate axes with appropriate labels scales. 3 I can write the system of equations /or inequalities that best models the problem. Constraints System of equations System of inequalities Linear Quadratic Scale Coordinate axes Labels Solutions Chapter 3 Section 3.1, 3.2, 3.3 Quality Chapter 2/3 Quiz Chapter 2/3 Test A REI.5. A REI.10. Reasoning with Equations Inequalities. Represent solve equations inequalities graphically. Reasoning with Equations Inequalities Represent Solve systems of equations Solve systems of equations Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation a multiple of the other produces a system with the same solutions. Underst that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a 2 I can solve systems of equations using elimination. 2 I can explain every point on the graph of an equation represents values that make System of equations Equivalent equations Elimination method X- axis X- coordinate Y- axis Y- coordinate Coordinate graph Chapter 3 Section 3.2 Chapter 3 5 Section Quality Quality Chapter 3 Quiz Chapter 3 Test Chapter 3 Quiz Chapter 3 Test Common Formative Assessment will be implemented daily

6 A REI.11. solve equations inequalities graphically. Reasoning with Equations Inequalities. Represent solve equations inequalities graphically. Solve systems of equations curve (which could be a line). Explain why the x- coordinates of the points where the graphs of the equations y = f(x) y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the s, make tables of values, or find successive approximations. Include cases where f(x) /or g(x) are linear, polynomial, rational, absolute value,, logarithmic s. the equation true. I can verify that any point on a graph will result in a true equation when their coordinates are substituted into the equation. 2 I can explain that point of intersection on the graph of a system of equations represents a solution to both equations. X- intercept Y- intercept X- coordinate Intersection Solution Linear Polynomial Rational Absolute value Logarithmic System of equations Substitution property Chapter 3 Section 3.1, 3.2, 3.3 Quality Chapter 3 Quiz Chapter 3 Test G MG.3. Modeling with Geometry Apply Geometric concepts in modeling situations Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy 2 I can create a visual representation of a design problem. Geometric model Graph Equation Table Chapter 3 Section 3.4 Quality Chapter 3 Quiz Chapter 3 Test Common Formative Assessment will be implemented daily

7 physical constraints or minimize cost; working with typographic grid systems based on ratios). I can solve problems, interpret results make conclusions based on a geometric model. Formula End Late 1 st Quarter (4.5 Weeks) District Short Cycle Assessment Common Formative Assessment will be implemented daily

8 Algebra 2 Early 2 nd Quarter CCSS Domain Cluster N.9-12 VM.6. (+) N.9-12 VM.7. (+) N.9-12 VM.8. (+) Vector Matrix Quantities Vector Matrix Quantities Vector Matrix Quantities Perform operations on matrices use matrices in applications. Perform operations on matrices use matrices in applications. Perform operations on matrices use matrices in applications. Stard Statement Use matrices to represent manipulate data, e.g., to represent payoffs or incidence relationships in a network. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. Add, subtract, multiply matrices of appropriate dimensions. Days Clear Learning Target 2 I can define categories for the rows column of a matrix. 2 I can multiply a given matrix by a given scalar to produce a new matrix. I can interpret how scalar multiplication of a matrix would change the situation that the matrix represents. 1 I can explain that two matrices can be added or subtracted only if both matrices have the same dimensions the resulting matrix will have the same dimensions as Vocabulary Matrix Dimension of a matrix Row Column Matrix Dimension of a matrix Row Column Scaler multiplication Scaler Matrix Dimension of a matrix Row Column Core Resource Chapter 4 Section 4.1 Chapter 4 Section 4.2 Chapter 4 Section Additional Resource Quality (Nee d page # s) Quality (Nee d page # s) Quality (Nee d page # s) Assessment Chapter 4 Quiz Chapter 4 Test Chapter 4 Quiz Chapter 4 Test Chapter 4 Quiz Chapter 4 Test Daily Common Formative Assessment

9 the original matrices. N.9-12 VM.9. (+) N.9-12 VM.10. (+) Vector Matrix Quantities Vector Matrix Quantities Perform operations on matrices use matrices in applications. Perform operations on matrices use matrices in applications. Underst that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative distributive properties. Underst that the zero identity matrices play a role in matrix addition multiplication similar to the role of 0 1 in the real numbers. The determinant of a square matrix is nonzero if only if the matrix has a multiplicative inverse. 0 I can explain demonstrate the matrix multiplication is not commutative. I can explain demonstrate why the associative distributive properties hold for matrix multiplication. 0 I can explain identity properties of addition multiplication under the set of real numbers. I can define identify a zero matrix. Matrix Dimension of a matrix Row Column Commutative property of X Associative property of X Distributive property Square matrix Matrix Dimension of a matrix Row Column Square matrix Identity property of + Identity property of X Zero matrix Identity matrix Determinant Inverse Chapter 4 Section 4.2 Chapter 4 Section Quality (Nee d page # s) Quality (Nee d page # s) Chapter 4 Quiz Chapter 4 Test Chapter 4 Quiz Chapter 4 Test N.9-12 VM.12. (+) Vector Matrix Quantities Perform operations on matrices use matrices in applications. Work with 2 2 matrices as transformations of the plane, interpret the absolute value of 3 I can organize ordered pairs in a matrix. I can perform transformations Transformation Translation Rotation Reflection Dilation Scaler Chapter 4 Quality Chapter 4 Quiz Chapter 4 Test Daily Common Formative Assessment

10 A.9-12 REI.8. (+) A.9-12 REI.9. (+) Reasoning with Equations Inequalities Reasoning with Equations Inequalities Solve Systems of Equations Find the inverse of a matrix if it exists use it to sole systems of linear equations; Underst solving equations as a process of reasoning an explain the reasoning. the determinant in terms of area. Represent a system of linear equations as a single matrix equation in a vector variable. Find the inverse of a matrix if it exists use it to solve systems of linear equations (using technology for matrices of dimension 3 3 or greater). on a point matrix using; addition, multiplication (reflect, rotate, dilate, scalar). 3 I can express a system of linear equations as a matrix equation. 2 I can define a matrix, dimensions of a matrix, inverse. End Early 2 nd Quarter (4.5 Weeks) Matrix Vertex Determinant Area Absolute value Matrix System of linear equations Vector variable Matrix Dimensions of a matrix Determinant of a matrix Inverse of a matrix Matrix equation System of linear equations Section 4.3 Chapter 4 Section Chapter 4 Section (Nee d page # s) Quality (Nee d page # s) Quality (Nee d page # s) Chapter 4 Quiz Chapter 4 Test Chapter 4 Quiz Chapter 4 Test District Short Cycle Assessment Daily Common Formative Assessment

11 Algebra 2 Late 2 nd Quarter CCSS Domain Cluster F IF.4 F IF.6. Interpreting Functions Interpreting Functions Interpret s that arise in applications in terms of the context. Analyze s using different representations. Interpret s that arise in applications in terms of the context. Analyze s using different representations. Stard Statement For a that models a relationship between two quantities, interpret key features of graphs tables in terms of the quantities, sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the is increasing, decreasing, positive, or negative; relative maximums minimums; symmetries; end behavior; periodicity. Calculate interpret the average rate of change of a (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Days Clear Learning Target 6 I can define the relative maximum minimum as place where the transitions from decreasing to increasing vis- versa. I can define the positive negative end behavior as the trend of a s outputs. 2 I can define interval, rate of change, average rate of change. I can calculate rate of change. Vocabulary X- intercept Y- intercept Interval Increase Decrease Maximum Minimum Symmetry End Behavior Periodicity Function Rate of change Average rate of change Interval Core Resource Chapter 2 5 Section 2.1, 2.2, 2.3, 2.4, 2.5, 2.7, 2.8, 5.1 Chapter 2, 5 Section Additional Resource Quality Quality Assessment Chapter 2/5 Quiz Chapter 2/5 Test Chapter 2/5 Quiz Chapter 2/5 Test Common Formative Assessment to be implemented Daily

12 F IF.9. A SSE.1 Interpreting Functions Seeing Structure in Expressions Interpret s that arise in applications in terms of the context. Analyze s using different representations. Interpret the structure of expressions Compare properties of two s each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic an algebraic expression for another, say which has the larger maximum. Interpret expressions that represent a quantity in terms of its context. 2 I can compare properties of two s when represented in different ways. I can distinguish between s that model growth decay. 2 I can define expression, term, factor, coefficient. I can interpret the real- world meaning of terms, factors, coefficients of an expression in terms of their units. Evaluate Function Coordinate plane Algebraically Graphically Numerically Verbally Expression Term Factor Coefficient Equivalent Chapter 2, 5 8 Section 2.1, 5.1, Chapter 5 Section 5.1 Quality Quality Chapter 2/5/8 Quiz Chapter 2/5/8 Test Chapter 5 Quiz Chapter 5 Test I can group the parts of an expression differently in order to better interpret their meaning. Common Formative Assessment to be implemented Daily

13 A SSE.2. Seeing Structure in Expressions Interpret the structure of expressions 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 ). 2 I can look for identify clues in the structure of expressions in order to rewrite it another way. I can explain why equivalent expressions are equivalent. Equivalent expressions Polynomials Chapter 5 Section 5.2 Quality Chapter 5 Quiz Chapter 5 Test A SSE.3. Seeing Structure in Expressions Interpret the structure of expressions Choose produce an equivalent form of an expression to reveal explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the I can apply models for factoring multiplying polynomials to rewrite expressions. 3 Part A: I can factor a quadratic expression to find the zeroes of the it represents. Part B: I can identify factor perfect- square trinomials. I can complete the square. I can predict whether a quadratic will have a minimum Quadratic expression Quadratic equation Zeros Perfect- square trinomial Complete the square Function Maximum Minimum Chapter 5 8 Section 5.2, 5.5, Quality Chapter 5/8 Quiz Chapter 5/8 Test Common Formative Assessment to be implemented Daily

14 it defines. or a maximum. c. Use the properties of exponents to transform expressions for s. For example the expression 1.15t can be rewritten as (1.151/12)12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Part C: I can define an. I can rewrite s using the properties of exponents. A REI.4. Reasoning with Equations Inequalities Solve equations inequalities in one variable Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square 2 Part A: I can identify a quadratic expression a perfect square. I can factor a perfect square complete the square. Part B: I can write complex number solutions for a quadratic equation. Quadratic equation Complete the square Inspection Square root method Quadratic formula Complex solution Factoring completely Radic Imaginary number Perfect square trinomial Chapter 5 Section 5.2, 5.3, 5.4, 5.5, 5.6 Quality Chapter 5 Quiz Chapter 5 Test Common Formative Assessment to be implemented Daily

15 roots, completing the square, the quadratic formula factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions write them as a ± bi for real numbers a b. Lorain City School District N.9-12 CN.1. N.9-12 CN.2. Complex Numbers Complex Numbers Perform arithmetic operations with complex numbers Perform arithmetic operations with complex numbers Know there is a complex number i such that i 2 = 1, every complex number has the form a + bi with a b real. Use the relation i 2 = 1 the commutative, associative, distributive properties to add, subtract, multiply complex numbers. 1 I can identify that i is a complex number. I can identify that a complex number is written in the form a + bi, where a b are both real numbers. 0 I can use the commutative associative properties to add subtract complex numbers to multiply complex numbers. I Complex number Real number i Complex number Commutative property Associative property Distributive property Real numbers Chapter 5 Section 5.4 Chapter 5 Section 5.4 Quality Quality Chapter 5 Quiz Chapter 5 Test Chapter 5 Quiz Chapter 5 Test Common Formative Assessment to be implemented Daily

16 N.9-12 CN.3. (+) N.9-12 CN.7. N.9-12 CN.8. (+) Complex Numbers Complex Numbers Complex Numbers Perform arithmetic operations with complex numbers Use complex numbers in polynomial identities equations. Perform arithmetic operations with complex numbers Find the conjugate of a complex number; use conjugates to find moduli quotients of complex numbers. Solve quadratic equations with real coefficients that have complex solutions. Extend polynomial identities to the complex numbers. For example, rewrite x as (x + 2i)(x 2i). 1 I can determine the conjugate of a complex number. I can explain why multiplying a complex number by its conjugate results in a real number. 1 I can determine when a quadratic equation in stard form, has complex roots by looking at a graph or by calculating the discriminant. 1 I can write the factors of polynomials using complex numbers. I can use complex numbers to rewrite a sum of squares as the product of complex numbers its conjugate. Conjugate Complex number Quotient Denominator Modulus Quadratic equation Factor Complete the square Quadratic formula Real number coefficient Complex solution Complex roots Discriminant Sum of squares Factor Real number Complex number Polynomial Chapter 5 Section 5.4 Chapter 7 Section 5.4 Chapter 5 Section 5.4 Quality Quality Quality Chapter 5 Quiz Chapter 5 Test Chapter 7/8 Quiz Chapter 7/8 Test Chapter 5 Quiz Chapter 5 Test Common Formative Assessment to be implemented Daily

17 F.9-12 IF.8. Interpreting Functions Analyze s using different representations Write a defined by an expression in different but equivalent forms to reveal explain different properties of the. a. Use the process of factoring completing the square in a quadratic to show zeros, extreme values, symmetry of the graph, interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for s. For example, identify percent rate of change in s such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, classify them as representing growth or decay. 2 I can explain that there are three forms of quadratic s. I can explain stard form, vertex form, factored form, graphs of quadratic s, parabolas. I can distinguish between s. Factor Polynomial Quadratic Vertex form Complete the square Vertex Extreme value Axis of symmetry Intercept form Zero Properties of exponents Expression growth decay Percent rate of change Chapter 5 8 Section 5.2, 5.3, 5.4, 5.5, 5.6, 8.1, 8.2 Quality Chapter 5/8 Quiz Chapter 5/8 Test Common Formative Assessment to be implemented Daily

18 F.9-12 LE.3. Linear, Quadratic, Models Construct compare linear, quadratic, models solve problems Observe using graphs tables that a quantity increasing ly eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial. 1 I can use graphs or tables to compare the output values of linear, quadratic, polynomial, s. I can estimate the intervals for which the output of one is greater than the output of another when given a table or graph. Evaluate Function Linear Quadratic Polynomial Rate Chapter 2,5 8 Section 2.1, 5.1, 8.1 Quality Chapter 2/5/8 Quiz Chapter 2/5/8 Test I can use technology to find the point at which the graphs of two s intersect use the points of intersection to precisely list the intervals for which the output of one is greater than the output of another. I can use graphs or tables to compare the rates of change of linear, Common Formative Assessment to be implemented Daily

19 quadratic, polynomial, s. I can explain why s eventually have greater output values than linear, quadratic, or polynomial s by comparing simple s of each type. End Late 2 nd Quarter (4.5 Weeks) District Short Cycle Assessment Common Formative Assessment to be implemented Daily

20 Algebra 2 Early 3 rd Quarter CCSS Domain Cluster Stard Statement Days N RN.2. The Real Number System Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals rational exponents using the properties of exponents. 2 Clear Learning Target I can apply the properties of exponents to simplify algebraic expressions with integer rational exponents. Vocabulary Exponent Laws of exponents Simplify Expression Integer Rational Core Resource Chapter 6 Section 6.1 Additional Resource Quality (Need page # s) Assessment Chapter 6 Quiz Chapter 6 Test N.9-12 CN.9. (+) Complex Numbers Use complex numbers in polynomial identities equations Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. I can write radical expressions as expressions with rational exponents radical expressions. I can explain the Fundamental Theorem of Algebra. I can use the Linear Factorization Theorem. I can solve a quadratic equation in factored form for its zeroes even if the zeroes are Fundamental theorem of algebra Linear factorization theorem Quadratic Polynomial Linear Factor Complex number Zeros Chapter 6 Section Quality (Need page # s) Chapter 6 Quiz Chapter 6 Test Daily Common Formative Assessment

21 complex. A.9-12 APR.1. A.9-12 APR.2. A.9-12 APR.3. Arithmeti c with Polynomi als Rational Expressio ns Arithmeti c with Polynomi als Rational Expressio ns Arithmeti c with Polynomi als Rational Expressio Perform arithmetic operations on polynomials; Underst the relationship between zeros factors of polynomials; re- write rational expressions Perform arithmetic operations on polynomials; Underst the relationship between zeros factors of polynomials; re- write rational expressions Perform arithmetic operations on polynomials; Underst the Underst that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, multiplication; add, subtract, multiply polynomials. Know apply the Remainder Theorem: For a polynomial p(x) a number a, the remainder on division by x a is p(a), so p(a) = 0 if only if (x a) is a factor of p(x). Identify zeros of polynomials when suitable factorizations are available, use the zeros to construct a I can apply the definition of an integer polynomial to explain why adding, subtraction or multiplying two polynomials always produces a polynomial. I can add, subtract multiply polynomials. I can divide polynomials using long division synthetic division apply the Remainder Theorem to check the answer or find the factor of a polynomial. I can identify the zeros of a factored polynomial. I can explain how Polynomial Closure property Integers Remainder theorem Polynomial Long division Synthetic division Divisor Factor Zeros Polynomial Factorization X- intercept Y- intercept Chapter 6 Section Chapter 6 Section Chapter 6 Section Quality (Need page # s) Quality (Need page # s) Quality Chapter 6 Quiz Chapter 6 Test Chapter 6 Quiz Chapter 6 Test Chapter 6 Quiz Chapter 6 Test Daily Common Formative Assessment

22 A.9-12 APR.4 A.9-12 APR.5 (+) ns Arithmeti c with Polynomi als Rational Expressio ns Arithmeti c with Polynomi als Rational Expressio ns relationship between zeros factors of polynomials; re- write rational expressions Perform arithmetic operations on polynomials; Underst the relationship between zeros factors of polynomials; re- write rational expressions Perform arithmetic operations on polynomials; Underst the relationship between zeros factors of polynomials; re- write rational expressions rough graph of the defined by the polynomial. Prove polynomial identities use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 =(x 2 y 2 ) 2 + (2xy) 2 Know apply the Binomial Theorem for the expansion of (x + y) n in powers of x y for a positive integer n, where x y are any numbers, with coefficients determined for example by Pascal s Triangle.* the multiplicity of the zeroes provides a clue as to how the graph will behave. I can factor polynomials by applying the polynomial identities. I can use the combination formula. I can write the binomial expansion of (a +b) n by applying the Binomial Theorem. I can generate Pascal's Triangle to find the coefficients of a binomial expansion. Multiplicity Polynomial Polynomial identity Factor completely Binomial theorem Binomial expansion Pascal s triangle Combinations Coefficient Chapter 6 Section Chapter 6 Section (Need page # s) Quality (Need page # s) Quality (Need page # s) Chapter 6 Quiz Chapter 6 Test Chapter 6 Quiz Chapter 6 Test Daily Common Formative Assessment

23 A.9-12 APR.6. Arithmeti c with Polynomi als Rational Expressio ns Perform arithmetic operations on polynomials; Underst the relationship between zeros factors of polynomials; re- write rational expressions Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. I can define rational expression. I can determine the best method of simplifying a given rational expression (inspection, long division, computer algebra system) I can simplify rational expressions using long division. Rational expression Dividend Divisor Quotient Remainder Degree Inspection Long division Chapter 6 Section Quality (Need page # s) Chapter 6 Quiz Chapter 6 Test I can write a rational expression a(x)/b(x) where a(x) is the dividend b(x) is the divisor in the form q(x) + r(x)/b(x) where q(x) is the quotient r(x) is the remainder. End Early 3 rd Quarter (4.5 Weeks) District Short Cycle Assessment Daily Common Formative Assessment

24 Algebra 2 Late 3 rd Quarter CCSS Domain Cluster Stard Statement Days A- REI.2. Reasoning with Equations Inequalities Underst solving equations as a process of reasoning explain the reasoning. Solve simple rational radical equations in one variable, give examples showing how extraneous solutions may arise. Clear Learning Target 2 I can define extraneous solution. I can determine which numbers cannot be solutions of a radical equation explain why. Vocabulary Rational equation Radical equation Extraneous solution Core Resource Chapter 7 Section 7.6 Additional Resource Quality Assessment Chapter 7 Quiz Chapter 7 Test N.9-12 RN.1. The Real Number System Extend the properties of exponents to rational exponents. 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 I can generate examples of radical equations with extraneous solutions. 3 I can apply the properties of exponents definition of nth root. I can apply the properties of exponents to simplify algebraic expressions with rational exponents. Exponent Law of exponents Simplify Expression Integer Rational Chapter 7: Section 7.1 7,2 Quality Chapter 7 Quiz Chapter 7 Test Common Formative Assessment to Be Implemented Daily

25 equal 5. F.9-12 BF.1. Building Functions Build a that models a relationship between two quantities Write a that describes a relationship between two quantities. - Determine an explicit expression, a recursive process, or steps for calculation from a context. - Combine stard types using arithmetic operations. For example, build a that models the temperature of a cooling body by adding a constant to a decaying, relate these s to the model. (+) Compose s. For example, if T(y) is the temperature in the atmosphere as a of height, h(t) is the height of a weather balloon as a 2 I can define explicit recursive expressions, quantities being compared in real- world problem, write explicit /or recursive expressions of a to describe a real- world problem. I can recall the parent s, apply transformations combine different s. Quantity Function Parent Transformatio n Composition of s Chapter 7 Section 7.3 Quality Chapter 7 Quiz Chapter 7 Test Common Formative Assessment to Be Implemented Daily

26 of time, then T(h(t)) is the temperature at the location of the weather balloon as a of time. Lorain City School District F.9-12 BF.4. Building Functions Build a that models a relationship between two quantities Find inverse s. - Solve an equation of the form f(x) = c for a simple f that has an inverse write an expression for the inverse. For example, f(x) =2 x 3 or f(x) = (x+1)/(x 1) for x 1. (+) Verify by composition that one is the inverse of another. 2 I can define an inverse. I can write explain the inverse of a. I can use the composition of s in stard notation. I can use the composition of s to verify inverses. Inverse Function Composition of s Horizontal line test Domain Invertible One- to- one Chapter 7 Section 7.4 Quality Chapter 7 Quiz Chapter 7 Test (+) Read values of an inverse from a graph or a table, given that the has an inverse. (+) Produce an invertible from a non- invertible by restricting the domain Common Formative Assessment to Be Implemented Daily

27 F IF.5 A REI.2. S.9-12 IC.1 Interpreting Functions Reasoning with Equations Inequalities Making Inferences Justifying Conclusions Interpret s that arise in applications in terms of the context Underst solving equations as a process of reasoning explain the reasoning. Underst evaluate rom processes underlying statistical experiments. Relate the domain of a to its graph, where applicable, to the quantitative relationship it describes. For example, if the 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.* Solve simple rational radical equations in one variable, give examples showing how extraneous solutions may arise. Underst statistics as a process for making inferences about population parameters based on a rom sample from that population. 1 I can explain how the domain of a is represented in its graph. 2 I can state the appropriate domain of a that represents a problem situation, defend my choice, explain why other numbers might be excluded from the domain. I can generate examples of rational or radical equations with extraneous solutions. I can solve rational radical equations in one variable. 1 I can define population, population parameter, rom sample, inference. Function Domain Rational equation Radical equation Extraneous solution Inference Population parameter Rom sample Population Statistics Chapter 7 Section 7.4 Chapter 7 9 Section Chapter 7 Section Quality Quality Quality Chapter 7 Quiz Chapter 7 Test Chapter 7 9/11/12 Quiz Chapter 7 9/11/12 Test Chapter 7 Quiz Chapter 7 Test Common Formative Assessment to Be Implemented Daily

28 S.9-12 IC.2 Making Inferences Justifying Conclusions Underst evaluate rom processes underlying statistical experiments. Decide if a specified model is consistent with results from a given data- generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? 1 I can choose a probability model for a problem situation. I can conduct a simulation of the model an determine which results are typical of the model an which result are considered outliers. Theoretical probability Experimental probability Simulation Model Event Chapter 7 Section 7.7 Quality Chapter 7 Quiz Chapter 7 Test I can decide if the data collected is consistent with the selected model or if another model is required. S IC.3 Making Inferences Justifying Conclusions Make inferences justify conclusions from sample surveys, experiments, observational Recognize the purposes of differences among sample surveys, experiments, observational studies; explain how romization relates I can pose a question that suggests a model la means of collecting data answer my question. 0 I can define sample survey, experiment, observational study romization. I can describe Sample survey Experiment Observational study Romization Chapter 7 Section 7.7 Quality Chapter 7 Quiz Chapter 7 Test Common Formative Assessment to Be Implemented Daily

29 S IC.4 Making Inferences Justifying Conclusions studies to each. the purpose of a sample survey, an experiment, an observational study. Make inferences justify conclusions from sample surveys, experiments, observational studies Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the simulation models for rom sampling. 1 I can define population mean, sample mean, population proportion, sample proportion. I can calculate the sample mean or proportion. Population mean Sample mean Population proportion Sample proportion Sample survey Margin of error Simulation model Rom sampling Confidence interval Chapter 7 Section 7.7 Quality Chapter 7 Quiz Chapter 7 Test S IC.5 Making Inferences Justifying Conclusions Make inferences justify conclusions from sample surveys, experiments, observational studies Use data from a romized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. 1 I can calculate the sample mean stard deviation of the two treatment groups the difference of the means. End Late 3 rd Quarter (4.5 Weeks) Sample Mean Treatment Simulation Stard deviation Histogram Extreme Parameters Significant Chapter 7 Section 7.7 Quality Chapter 7 Quiz Chapter 7 Test District Short Cycle Assessment Common Formative Assessment to Be Implemented Daily

30 Algebra 2 Early 4 th Quarter CCSS Domain Cluster Stard Statement Days F IF.9. A SSE.3. Interpreting Functions Seeing Structure in Expressions Interpret s that arise in applications in terms of the context. Analyze s using different representations. Interpret the structure of expressions Compare properties of two s each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic an algebraic expression for another, say which has the larger maximum. Choose produce an equivalent form of an expression to reveal explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the it defines. b. Complete the square in a quadratic expression to reveal Clear Learning Target 2 I can compare properties of two s when represented in different ways. I can distinguish between s that model growth decay. 3 Part A: I can factor a quadratic expression to find the zeroes of the it represents. Part B: I can identify factor perfect- square trinomials. I can complete the square. I can predict Vocabulary Evaluate Function Coordinate plane Algebraically Graphically Numerically Verbally Quadratic expression Quadratic equation Zeros Perfect- square trinomial Complete the Square Function Maximum Minimum Core Resource Chapter 2, 5 8 Section 2.1, 5.1, Chapter 5 8 Section 5.2, 5.5, Additional Resource Quality (Nee d page # s) Quality (Nee d page # s) Assessment Chapter 2/5/8 Quiz??? Chapter 2/5/8 Test Chapter 5/8 Quiz??? Chapter 5/8 Test Daily Common Formative Assessment

31 the maximum or minimum value of the it defines. c. Use the properties of exponents to transform expressions for s. For example the expression 1.15t can be rewritten as (1.151/12)12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. whether a quadratic will have a minimum or a maximum. Part C: I can define an. I can rewrite s using the properties of exponents. F.9-12 IF.8. Interpreting Functions Analyze s using different representations Write a defined by an expression in different but equivalent forms to reveal explain different properties of the. a. Use the process of factoring completing the square in a quadratic to show zeros, extreme values, symmetry of the graph, interpret 2 I can explain that there are three forms of quadratic s. I can explain stard form, vertex form, factored form, graphs of quadratic s, parabolas. I can distinguish between s. Factor Polynomial Quadratic Vertex form Complete the square Vertex Extreme value Axis of symmetry Intercept form Zero Properties of Exponents Expression Chapter 5 8 Section 5.2, 5.3, 5.4, 5.5, 5.6, 8.1, 8.2 Quality (Nee d page # s) Chapter 5/8 Quiz Chapter 5/8 Test Daily Common Formative Assessment

32 these in terms of a context. b. Use the properties of exponents to interpret expressions for s. For example, identify percent rate of change in s such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, classify them as representing growth or decay. growth decay Percent rate of change F.9-12 LE.3. Linear, Quadratic, Models Construct compare linear, quadratic, models solve problems Observe using graphs tables that a quantity increasing ly eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial. 1 I can use graphs or tables to compare the output values of linear, quadratic, polynomial, s. I can estimate the intervals for which the output of one is greater than the output of another when given a table or graph. Evaluate Function Linear Quadratic Polynomial Rate Chapter 2,5 8 Section 2.1, 5.1, 8.1 Quality (Nee d page # s) Chapter 2/5/8 Quiz Chapter 2/5/8 Test I can use Daily Common Formative Assessment

33 technology to find the point at which the graphs of two s intersect use the points of intersection to precisely list the intervals for which the output of one is greater than the output of another. I can use graphs or tables to compare the rates of change of linear, quadratic, polynomial, s. I can explain why s eventually have greater output values than linear, quadratic, or polynomial s by comparing simple s of each type. Daily Common Formative Assessment

34 F LE.1. Linear, Quadratic, Models Construct compare linear, quadratic, models solve problems Distinguish between situations that can be modeled with linear s with s. - Prove that linear s grow by equal differences over equal intervals, that s grow by equal factors over equal intervals. - Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. - Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 2 I can demonstrate that a linear has a constant rate of change (slope) an has a constant multiplier (common ratio). I can distinguish between situations modeled with linear s with s when presented with a real- world problem. Linear Function Evaluate Rate of change Slope Common Ratio Chapter 8 Section Quality (Nee d page # s) Chapter 7/8 Quiz Chapter 7/8 Test F LE.3. Linear, Quadratic, Models Construct compare linear, quadratic, models solve problems Observe using graphs tables that a quantity increasing ly eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as 0 I can use graphs or tables to compare the output values of linear, quadratic, polynomial, s. Evaluate Function Linear Function Quadratic Polynomial Chapter 2,5 8 Section Quality (Nee d page # s) Chapter 7/8 Quiz Chapter 7/8 Test Daily Common Formative Assessment

35 a polynomial. I can estimate the intervals for which the output of one is greater than the output of another when given a table or graph. I can use technology to find the point at which the graphs of two s intersect use the points of intersection to precisely list the intervals for which the output of one is greater than the output of another. I can use graphs or tables to compare the rates of change of linear, quadratic, polynomial, s. I can explain why s eventually have Rate Daily Common Formative Assessment

36 F LE.4. Linear, Quadratic, Models Construct compare linear, quadratic, models solve problems For models, express as a logarithm the solution to ab c = d where a, c, d are numbers the base b is 2, 10, or e; evaluate the logarithm using technology. greater output values than linear, quadratic, or polynomial s by comparing simple s of each type. 6 I can define logarithmic. I can write an equation ab ct =d in logarithmic form log b(d/a) = ct solve it for t. Logarithmic Logarithmic form Base Change of base Evaluate Chapter 8 Section 8.1, 8.2, 8.3, 8.4, 8.5 Quality (Nee d page # s) Chapter 7/8 Quiz Chapter 7/8 Test I can explain using the properties of s logarithms why ab ct = d log b(d/a) = ct are equivalent. I can use powers of 2 or 10 to estimate the value of log 2(x) or log 10(x). I can use a calculator to evaluate a Daily Common Formative Assessment

37 logarithm with a base of 10 or e. F.9-12 BF.5. (+) Building Functions Build new s from existing s. Underst the inverse relationship between exponents logarithms use this relationship to solve problems involving logarithms exponents. I can apply the change of base formula to evaluate the logarithm with a base of 2 using a calculator. 3 I can state that the inverse of an is a logarithmic ( vice- versa). I can explain the inverse relationship between exponents logarithms (y = b x is equivalent to log by = x). Inverse Exponent Logarithm Chapter 8 Section 8.3, 8.4, Quality (Nee d page # s) Chapter 7/8 Quiz Chapter 7/8 Test I can estimate or solve for the values of logarithms by evaluating powers of the base (e.g., log 525 = 2 log 530 is between 2 3). I can solve problems with Daily Common Formative Assessment

38 F.9-12 IF.7. Interpreting Functions Analyze s using different representations. Graph s expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. a. Graph linear quadratic s show intercepts, maxima, minima. b. Graph square root, cube root, piecewise- defined s, including step s absolute value s. c. Graph polynomial s, identifying zeros when suitable factorizations are available, showing end behavior. variables in an exponent or logarithm by applying the inverse relationship to logarithms exponents. 4 I can identify the x- intercept(s), y- intercept, increasing intervals, decreasing intervals, the maximums, minimums of a by looking at its graph. I can sketch identify the various characteristics of a quadratic, a square root, cube root, a piecewise, an absolute value, step s, polynomial s, rational s, Evaluate Function Domain Input Equation Parent Transformation Slope X- intercept Y- intercept Linear Coordinate plane Vertex Quadratic Maximum Minimum Square root Cube root Piecewise Step Absolute value Factor Polynomial Synthetic division Polynomial Chapter 2,5,6,8,9,10 Section 8.1, 8.2, 9.1, 9.2, 9.3 Quality (Nee d page # s) Chapter 9/11/12 Quiz?????? Chapter 9/11/12 Test Daily Common Formative Assessment

39 d. (+) Graph rational s, identifying zeros asymptotes when suitable factorizations are available, showing end behavior. e. Graph logarithmic s, showing intercepts end behavior, trigonometric s, showing period, midline, amplitude. s. End behavior Turning point Zero Multiplicity Rational Removable discontinuity Non- removable discontinuity Vertical asymptote Horizontal asymptote Logarithmic form form Logarithmic Trigonometric Period Midline Amplitude End Early 4 th Quarter (4.5 Weeks) District Short Cycle Assessment Daily Common Formative Assessment

40 Algebra 2 Late 4 th Quarter CCSS Domain Cluster Stard Statement Days Clear Learning Target Vocabulary Core Resource Additional Resource Assessment F.9-12 IF.7. Interpreting Functions Analyze s using different representations. Graph s expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. a. Graph linear quadratic s show intercepts, maxima, minima. b. Graph square root, cube root, piecewise- defined s, including step s absolute value s. c. Graph polynomial s, identifying zeros when suitable factorizations are available, showing end behavior. d. (+) Graph rational s, identifying 4 I can identify the x- intercept(s), y- intercept, increasing intervals, decreasing intervals, the maximums, minimums of a by looking at its graph. I can sketch identify the various characteristics of a quadratic, a square root, cube root, a piecewise, an absolute value, step s, polynomial s, rational s, s. Evaluate Function Domain Input Equation Parent Transformation Slope X- intercept Y- intercept Linear Coordinate plane Vertex Quadratic Maximum Minimum Square root Cube root Piecewise Step Absolute value Factor Polynomial Synthetic division Polynomial End behavior Turning point Zero Chapter 2,5,6,8,9,10 Section 8.1, 8.2, 9.1, 9.2, 9.3 Quality Chapter 9/11/12 Quiz Chapter 9/11/12 Test Common Formative Assessment To Be Implemented Daily

41 A REI.2. N RN.3. Reasoning with Equations Inequalities The Real Number System Underst solving equations as a process of reasoning explain the reasoning. Use properties of rational irrational numbers. zeros asymptotes when suitable factorizations are available, showing end behavior. e. Graph logarithmic s, showing intercepts end behavior, trigonometric s, showing period, midline, amplitude. Solve simple rational radical equations in one variable, give examples showing how extraneous solutions may arise. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number an irrational number is irrational; 2 I can generate examples of rational or radical equations with extraneous solutions. I can solve rational radical equations in one variable. 1 I can explain why the sum or product of two numbers (either rational or irrational) is rational or Multiplicity Rational Removable discontinuity Nonremovable discontinuity Vertical asymptote Horizontal asymptote Logarithmic form form Logarithmic Trigonometric Period Midline Amplitude Rational equation Radical equation Extraneous solution Real number Rational number Irrational number Sum Product Chapter 7 9 Section Chapter 9 Quality Quality Chapter 7 9/11/12 Quiz Chapter 7 9/11/12 Test Chapter 9/11/12 Quiz Chapter 9/11/12 Test Common Formative Assessment To Be Implemented Daily