Download Algebra 2 Map 2014

CURRICULUM MAP TEMPLATE
Priority Standards = Approximately 70%
Supporting Standards = Approximately 20%
Additional Standards = Approximately 10%
INTEGRATED ALGEBRA 2: COURSES 234/233/220
Essential Questions
&
Content
Sept/
Oct
UNIT 1: The Complex Number System Essential Question: How does the complex number system help solve real-­‐world problems? Prerequisite Concepts: Students should already be able to: • Simplifying and combining radicals including rationalization of square roots • Converting terminating and non-­‐
terminating decimals to a/b to show rational relationship • Combining like terms • Solve linear equations • Apply the properties of integer exponents • Apply area and volume problems for cylinders, pyramids, cones and spheres. • Solve equations involving radicals on one side of the equation. (220 only) • Solving linear inequalities Unit 1 Concepts: • Identify rational/irrational numbers • Simplify and evaluate numerical expressions Framework
Standard
Skills
N.CN.1 N.RN.3 G.GMD.3 N.CN.2 N.CN.3 N.RN.1 N.RN.2 N.RN.3 A.SSE.3 A.CED.1 MP.2 MP.4 MP.7 MP.8
Students will be able to: Use properties of rational and irrational numbers 1.1 Subsets of a + bi and how to determine rational vs. irrational numbers (a/b conversions) (N.CN.1) 1.2 Simplification and evaluation of numerical expressions with real numbers. 1.2.a Simplify complicated numerical expressions that contain rational and irrational numbers, and involve the order of operations and real number properties. 1.2.b Introduce closure property by explaining why the sum of or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. (220 only) (N.RN.3) 1.2.c Explain volume formulas (cylinders, pyramids, cones, and spheres) and use them to solve problems (G.GMD.3) 1.3 Radicals, including simplification, rationalization, square roots, cube roots (don’t do 4th root, 5th root, etc. simplication) Perform arithmetic operations with complex numbers 1.4 a. Definition of i (N.CN.1) b. Simplification and operations on complex numbers (N.CN.2) c. Conjugate of a complex number to rationalize (N.CN.3) Assessment &
Learner Expectations
Formative/Summative: ● Written section assessments ● Review games ● Practice exercises ● Ticket to Leave ● White board demonstrations ● Lab activities ● Unit 1 Common assessment ● Technology assessments ● Quick Quizzes ● Graded Classwork ● Flipped Classroom Instruction Text/Resources McDougall Littell Algebra 2 text 2007 edition Chapter 1 (1.1, 1.2, 1.6), Chapter 4 (4.5, 4.6) Chapter 6( 6.1, 6.2, 6.6) Technology TI Nspire Labs: • Complex Numbers • Extraneous Solutions Graphing Calculator: • Square root command
• Simplify and rationalize square and cube roots • Simplify and perform operations on complex numbers • Find conjugate of complex numbers • Apply properties of exponents to rational exponents including negative exponents • Solve radical and exponential equations • Create equations and inequalities Vocabulary Critical Terms: ● Exponent ● Linear ● Quadratic ● Rational ● Exponential ● Radical ● Extraneous Supplemental Terms: ● Real number ● Rational number ● Irrational number ● Integer ● Sum ● Product • Expression Extend the properties of exponents to rational exponents 1.5 Conversion of radicals to rational exponents to solve problems 1.5.a. Definition of rational exponents and their relationship to radicals 1.5.b. Simplify numbers raised to rational exponents by converting them to radical form. Include negative exponents (N.RN.1) 1.5.c. Use properties of exponents to rewrite expressions containing radicals (N.RN.2) 1.5.d Solve equations involving radicals and rational exponents (old 6.6) (A.SSE.3) 1.5.e Solve exponential equations containing rational and negative exponents (old exponential sheet 1 in ch 6) 1.6 Create equations and inequalities in one variable and use them to solve problems (A.CED.1) 1.6.a Linear relationships 1.6.b Quadratic (parabolic) relationships
• Math- cube root
• Mode- Complex number
Oct/
Nov
UNIT 2-­‐ Polynomial Relationships Essential Questions: How do the arithmetic operations on numbers extend to polynomials? What do the factors of a quadratic reveal about the function? What does completing the square reveal about a quadratic function? What is the graph of a quadratic function? What are its properties? What do the key features of a quadratic graph represent in a modeling situation? What new information will be revealed if this equation is written in a different but equivalent form? How do you create an appropriate function to model data or situations given within context? Prerequisite Concepts: Students should already be able to: • Identify linear relationships (1st degree equations) • Formulate point-­‐slope linear equations and identify slope, points and intercepts • Graph linear equations in the form of two variables • Solve linear equations with real numbers • Use laws of exponents to simplify monomials • Factor perfect squares and trinomials with lead coefficients of 1 Unit 2 Concepts: ● Add, subtract, multiply and divide polynomials. ● Interpret expressions in terms of its context. ● View complicated expressions by A.SSE.1 A.SSE.2 A.SSE.3 A.CED.1 A.CED.2 A.APR.1 F.IF.6 F.IF.7 F.IF.8 F.IF.9 A.APR.2 A.REI.4 N.CN.7 MP.2 MP.5 MP.7 Students will be able to… Perform arithmetic operations on polynomials. 2.1 Add and subtract polynomials; Multiply by distributive property 2.2 Dividing of polynomials: Long division and synthetic division Graph Quadratic Functions 2.3 Characteristics and properties of a Quadratic Function in Standard Form 2.3.a Vocabulary ( include minima, maxima, minimum and maximum values (extreme values), increasing and decreasing intervals, zeros) 2.3.b Parent functions (compare to 𝑦 = 𝑥 ! a positive/negative, narrow/wide, vertex: x = -­‐b/2a) 2.4 Graph and label vertex, axis of symmetry, minimum and maximum values without a graphing calculator 2.5 Graph and write quadratics in vertex form Understand the relationship between zeros and factors of polynomials 2.6 Know and apply the Remainder Theorem by choosing appropriate method(s) 2.6.a Factoring (2, 3, and 4 terms) 2.6.b Quadratic formula (including complex number solutions; using determinant) 2.6.c Solve by square rooting 2.6.d Completing the square 2.6.e Graphing calculator 2.6.f Synthetic division to find zeros 2.7 Compare properties of two quadratic functions each represented in a different way (algebraically, graphically, numerically in tables or by verbal descriptions) Vocabulary Critical Terms: Formative/Summative: ● Written section assessments ● Review games ● Practice exercises ● Ticket to Leave ● White board demonstrations ● Lab activities ● Unit 2 Common assessment ● Technology assessments ● Quick Quizzes ● Graded Classwork ● Flipped Classroom Instruction ● 4 Methods Project(234 only) ● Projectile Motion PBL(233 only) Text/Resources McDougall Littell Algebra 2 text 2007 edition Chapter 4 (4.1, 4.2, 4.3, 4.4,4.5, 4.7,4.8) Chapter 5 (5.2, 5.3, 5.4, 5.5, 5.8) Technology TI Nspire Labs • Completing the Square • Completing the Square Algebraically • Standard form of a Quadratic • Vertex and Factored Form of Quadratic Functions • Discriminant Testing • Exploring Polynomials: ●
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its parts. Use the structure of an expression to identify ways to rewrite it. Factor a quadratic expression. Complete the square on a quadratic function. Show zeros, extreme values, and symmetry of the graph of a quadratic function, and interpret these in terms of a context. Create equations in one, two or more variables to represent relationships between quantities. Graph a quadratic function and show intercepts, maxima and minima. Compare properties of two quadratic functions each represented in a different way (algebraically, graphically, numerically in tables or by verbal descriptions). Write a quadratic equation and/or function to model a real-­‐
life situation. Use a quadratic model to interpret information about physical phenomena. Translate among representations of quadratic functions including tables, graphs, equations, and real-­‐
life situations. Rewrite quadratic functions to reveal new information. Determine an explicit expression, a recursive process, or steps for calculation from a context. Combine standard function types using arithmetic operations. Interpret complicated expressions by viewing one or more of their parts as a single entity. Define appropriate quantities when modeling ● Quadratic ● Parabola ● Factor (as both a noun and a verb) ● Zero (of a function) ● Complex Number ● Discriminant ● Factor ● Zero ● Root ● X-­‐intercept Supplemental Terms: ● Vertex form ● Intercepts ● Maximum ● Minima ● Vertex ● Extreme values ● Interval ● Polynomial ● Quadratic ● Parabola ● Completing the Square ● Quadratic Formula ● Standard form ● Intercepts ● Intervals ● Relative maximums ● Relative minimums ● Symmetries ● End behavior ● Periodicity Factors, Roots and Zeros • Factoring Trinomials • Sums and Differences of Cubes • Applications of Polynomials • Watch Your P’s and Q’s • End Behavior of a Polynomial Function • Multiplicity of Zeros of Functions Graphing Calculator: • 2nd Calc Zero • 2nd Calc Intersect with Y2 = 0 • 2nd Calc Max/ Min • Table • Graph Quadratics ●
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Nov/
Dec
Explain their reasoning in solving equations Solve quadratic equations by taking square roots. Solve quadratic equations by completing the square. Solve quadratic equations by factoring. Solve quadratic equations using the quadratic formula. Derive the quadratic formula by completing the square. UNIT 3-­‐ Functions Essential Question: How does a function model model real world problems? Prerequsite Concepts: Students should already be able to: • Graph linear functions • Graph functions by using a T-­‐table • Graph functions by using a graphing calculator (Y= and Graph commands) • Find x-­‐ and y-­‐ intercepts • Find slope between two points • Graph a quadratic function Unit 3 Concepts: • Determine if a relation is a function • Domain and Range • Apply the vertical line test • Evaluate functions using function notation • Evaluate compositions • Identify different types of functions (linear, quadratic, trigonometric, exponential, logarithmic, piece-­‐wise, absolute value, radical and rational) • Identify and graph linear and quadratic functions and identify key F.IF.1 F.IF.2 F.IF.MA.10 F.IF.7abc F.IF.8 F.IF.9 F.BF.1 MP.1 MP.4 MP.5 MP.7 Students will be able to: 3.1 Determine the Domain and ranges of functions (F.IF.1) 3.2 Determine a function, i.e. Vertical Line Test, and utilize function notation by evaluating functions of all types. (F.IF.2) 3.2.a Apply the Vertical Line Test (Use circle equation as a counter-­‐example: graphing calculator) 3.2.b Evaluate with function notation 3.2.c Evaluate composition of functions 3.3 Identify types of functions and their characteristics including linear, polynomial (with degree), trigonometric, exponential, logarithmic, piece-­‐wise, absolute value, radical, and rational. (F.IF.MA.10) 3.4 Identify and graph functions using the key characteristics (F.IF.7 a b c) 3.4.a By Hand: Linear and quadratic: Intercepts (quadratics-­‐ simple factoring and quadratic formulas), max/mins with vertex 3.4.b With GC: Square root, cube root, absolute value functions, rational (with asymptotes: domain and factoring denominators), exponential and logs. 3.4.c By Hand: Piece-­‐wise defined (Course 233: linear/quadratic, Course 220: Include absolute value) 3.5 Understand and find relations, domain Formative/Summative: ● Written section assessments ● Review games ● Practice exercises ● Ticket to Leave ● White board demonstrations ● Lab activities ● Unit 3 Common assessment ● Technology assessments ● Quick Quizzes ● Graded Classwork ● Flipped Classroom Instruction Text/Resources McDougall Littell Algebra 2 text 2007 edition Chapter 2 (2.1, 2.2, 2.7) Chapter 6 (6.3, 6.5) Chapter 7 (7.1, 7.2, 7.4,) Chapter 8 (8.3) Technology TI Nspire Labs: • Function Composition • Application of Function characteristics by hand • Identify and graph all functions using key characteristics using a graphing calculator Vocabulary Critical Terms: ● Relation ● Function ● Function notation ● Domain ● Range ● Composition ● Vertical Line Test ● Intercepts ● Maximums ● Minimums ● Set Builder notation ● Interval notation ● linear ● quadratic ● exponential ● absolute value ● radical ● rational ● parabola ● asymptote Supplemental Terms: ● trigonometric ● logarithmic ● piece-­‐wise ● square root ● cube root ● natural logarithm UNIT 4-­‐ Interpretations of Functions Jan/
Feb
Prerequisite Concepts: Students should already be able to: • Build off unit 3 function concepts • Solve exponential equations Unit 4 Concepts: and range of a function, both with and without the graphing calculator. Composition • Domain and Range 2 • Exploring Power Functions1 • Exploring Power Functions2 • Graphs of Rational Functions • Rational Functions • Exploring Vertical Aymptotes • Crossing the Asymptote Graphing Calculator: • Graphing of Rational equations-­‐ Dot mode or decimal zoom • Trace • Table F.BF.4 F.BF.5 A.SSE.3c F.IF 4 F.IF.5 F.IF.6 F.IF.9 S.ID.6 A.REI.7 Students will be able to… Analyze functions using different representations 4.1 Find inverse functions (F.BF.4.a, F.BF.5) 4.1.a Show graphically how inverses are related 4.1.b Write expressions for inverses by interchanging x and y’s 4.2 Evaluate logs, rewrite logs in exponential form and apply log properties (A.SSE.3c) Formative/Summative: ● Written section assessments ● Review games ● Practice exercises ● Ticket to Leave ● White board demonstrations ● Lab activities ● Unit 4 Common • Show graphically how inverses are related • Write expressions for inverses • Evaluate logs • Rewrite logs in exponential form • Apply log properties • Simplify rational expressions and complex fractions • Compare properties of two functions each represented in a different way • Compare two functions in different ways • Apply average rate of change • Represent data using a scatterplot • Fit a function to data by identifying the model and completing a regression using a graphing calculator • Make predictions using the regression equation • Solve simple systems with linear, quadratic and circle equations Vocabulary inverse function logarithm Horizontal line test intercepts increasing intervals decreasing intervals positive position negative position relative max/mins scatterplot outlier regression MP.1 MP.2 MP.3 MP.4 MP.6 4.2.a Definition of a logarithm and conversion from logs to exponential form 4.2.b Understand inverse relationship between exponential and log functions (include line reflection and interchanging of x and y) 4.2.c Simplify log expressions 4.2.d Solve log equations for a variable 4.3 Rational Expressions and Complex Fractions 4.3.a Simplifying rational expressions and complex fractions 4.3.b Solve rational equations Interpret functions in applications 4.4 Interpret key features of graphs and tables of all types of functions to answer applications. (F.IF 4, F.IF.5) 4.4.a Intercepts 4.4.b Increasing, decreasing intervals 4.4c Positive or negative position (above or below independent axis, i.e. projectile motion) 4.4.d Relative max/mins 4.5 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal description (F.IF.9) 4.6 Apply average rate of change of all types of function by calculating slope between two points on the curve: tabular, graph, algebraic. (F.IF.6) 4.7 Represent data from two-­‐variable equations by using a scatter plot (S.ID.6) 4.7.a Describe the relationship of the two variables in context of the problem 4.7.b Fit the function to the data by first identifying if the model is linear, quadratic, exponential or log(graph calc regression command) 4.7.c Make predictions with data and assess ●
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assessment Technology assessments Quick Quizzes Graded Classwork Flipped Classroom Instruction Text/Resources McDougall Littell Algebra 2 text 2007 edition Chapter 2 (2.6) Chapter 3 (3.1, 3.2) Chapter 6 (6.4) Chapter 7 (7.4, 7.5. 7.6) Technology TI Nspire Labs: • Functions and Inverses • Power Function Inverses • Airport Impact Study • Exponential vs. Power • Exponential Transformations • Graphing Exponentials • What is log? • Log Transformations • Graph Log • Properties of Log • Solving Exponential Equations • Solving Log Equations • Polynomial Rollercoaster • How Many Solutions 2 • Solving Systems Using Elimination • Systems of Linear Inequalities 1 • Systems of Linear Inequalities 2 Feb/
March
the fit by analyzing outliers 4.8 Solve simple systems of equations and inequalities with linear, quadratic and circles(non-­‐function, but meets entire standard-­‐ graph calc activity) (A.REI.7) 4.8.a. Algebraically by substitution 4.8.b Graphically by finding points of intersection UNIT 5 – Create Equations and Build Functions Prerequisite Concepts: Students should already be able to: • Simplify proportional relationships • Label linear, area and volume quantities with correct units • Use problem solving strategies to formulate equations • Translate literal expressions into algebraic expressions • Solve literal equations for a given variable Unit 5 Concepts: • The parent graphs for linear, quadratic, and exponential functions. • Write a function to model a real-­‐
life situation. • Use a model of a function to interpret information about a real-­‐
life situation. • Use and compare multiple representations of quadratic functions including tables, graphs, equations and real-­‐life situations. • Distinguish between linear, exponential and quadratic functions from multiple N.Q.1 N.Q.2 G.MG.4 G.MG.2 N.Q.3 A.SSE.1 A.SSE.2 A.CED.1 A.CED.2 A.CED.3 A.SSE.3 A.CED.4 ASSE.MA.4 MP.1 MP.2 MP.3 MP.4 MP.6 Students will be able to… Reason quantitatively and use units to solve problems 5.1 Use units as a way to understand problems and to guide the solution of multi-­‐step problems, and define appropriate quantities for descriptive modeling (N.Q.1, N.Q.2) 5.1.a. Use dimensional analysis to solve problems (G.MG.MA.4) 5.1.b. Apply concepts of density based on area and volume (G.MG.2) 5.2 Choose a level of accuracy when reporting quantities (N.Q.3) Interpret the structure of expressions 5.3 Interpret expressions that represent a quantity in terms of its context (A.SSE.1) 5.4 Use structure of an expression to identify ways to rewrite it (A.SSE.2) Create equations that describe numbers or relationships 5.5 Create equations and inequalities in one variable to solve problems (A.CED.1) 5.5.a From linear and quadratic models 5.5.b From simple rational models 5.5.c From simple exponential models 5.6 Create equations in two or more variables to represent relationships between quantities, and graph them on a coordinate plane with labels and scales. (A.CED.2) 5.7 Represent constraints by equations or inequalities, graph as a system and interpret viable and non-­‐viable options, i.e. linear programming. (A.CED.3) Graphing Calculator: • Stat Plot/Stat/Edit • Graphs of logs/ ln/ exponentials • 2nd Calc Max/min • Stat-­‐Calc-­‐Regressions • 2nd Calc Intersect • Graphing circles with two functions Formative/Summative: ●
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Written section assessments Review games Practice exercises White board demonstrations Lab activities Ticket to Leave Unit 5 Common assessment Technology assessments Quick Quizzes Graded Classwork Flipped Classroom Instruction Text/Resources McDougall Littell Algebra 2 text 2007 edition Chapter 4 (4.10) Chapter 5 (5.9) Chapter 7 (7.7) Technology TI Nspire Labs: • Transformations: Dilating Functions • Transformations: Translating Functions • Families of Functions • Modeling with a Quadratic Function representations. • Rewrite quadratic and exponential functions in different forms to reveal new information. • Compare two functions represented in different ways (such as an equation compared to a table or graph). • Fit a linear, quadratic, or exponential model to data. Write expressions in equivalent forms to solve problems. 5.8 Create expressions/equations to reveal or explain properties of the quantity, and solve (ASSE.3) 5.8.a Rearrange formulas to solve for a given variable or a given situation (A.CED.4) 5.8.b Quadratic expressions equal to zero (ASSE.3.a) 5.8.c Complete square to find max/min value (ASSE.3.b) 5.8.d Use properties of exponents to transform and solve exponential expressions (ASSE.3.c) 5.8.e Mortgage payment problems (sum of a finite geometric series) (ASSE.MA.4) Build a function that models a relationship between two quantities. 5.9 F.BF.1 Write a function that describes a relationship between two quantities. 5.9.a Determine an explicit expression, a recursive process, or steps for calculation from a context. 5.9.b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Vocabulary Critical Terms: Quadratic Parabola Translation Transformation Residual Supplemental Terms: Rational models System Correlation Coefficient Completing the Square Quadratic Formula Standard form Vertex form Intercepts Intervals relative maximums relative minimums symmetries end behavior periodicity March
/April
UNIT 6 – Right Triangle Trigonometry Essential Questions: How does similarity give rise to the trigonometric ratios? How do the trigonometric ratios of complementary angles relate to one another? G.SRT.6 G.SRT.7 G.SRT.8 MP.1 MP.2 MP.5 MP.6 Students will be able to… Define trigonometric ratios and solve problems involving right triangles 6.1 Side ratios in right triangles leading to all six definitions of trigonometric ratios for acute angles 6.2 Relationship between sine and cosine of complementary angles • Parabolic Paths • Quadratic Functions and Stopping Distances • Maximizing Area of a Garden • Linear Systems and Calories • Applications of Linear Systems • Maximizing Your Efforts • Linear-­‐Quadratic Inequalities Graphing Calculator: • 2nd Calc Max/Min • 2nd Calc Zero or Intersect with Y2=0 • ^3, ^4, etc. • 2nd List-­‐ Seq or cum Sum
Formative/Summative: ● Written section assessments ● Review games ● Practice exercises ● White board demonstrations ● Lab activities How can the Pythagorean Theorem be used to solve problems involving triangles? Prerequisite Concepts: Students should already be able to: Grade 9 Integrated Geometry, UNIT 7: • Understand similarity in terms of similarity transformations. • Dilations with Scale Factor (G.SRT.1) • Definition of similarity in terms of similarity transformations • Explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. (G.SRT.2) • Properties of similarity transformations to establish the AA criterion (G.SRT.3) • Prove theorems involving similarity: Triangles • Prove the Pythagorean Theorem using triangle similarity. (G.SRT.4) • Congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. (G.SRT.5) • Dilation of a line segment in the ratio given by the scale factor. • Use the Pythagorean Theorem to solve for a missing side of a right triangle with integer-­‐valued sides Unit 6 Concepts: • The trigonometric function definitions of sine, cosine, and tangent as ratios of the sides of a MP.7 MP.8 6.3 Apply trigonometric ratios to right triangle problem solving situations Translate between the geometric description and the equation for a conic section 6.4 Derive the equation of a circle given a center and a radius by using the Pythagorean Theorem and completing the square method Vocabulary Critical Terms: Hypotenuse Opposite side Adjacent side Sine Cosine Tangent Similarity Transformations Trigonometry Supplemental Terms: Pythagorean triple "solve" a triangle Complementary angles Special right triangles (30-­‐60-­‐90, 45-­‐45-­‐90) ●
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Ticket to Leave Unit 6 Common assessment Technology assessments Quick Quizzes Graded Classwork Flipped Classroom Instruction Text/Resources McDougal Larson Algebra 2 Common Core Edition 2012 Chapter 9 (9.1, 9.3, 9.4, 9.5, 9.6) Technology TI Nspire Labs: • Exploring the Pythagorean Theorem • Trig Ratios Graphing Calculator • Radian Mode • Sin, Cos, Tan • Square Root
right triangle • Use the trigonometric ratios and knowledge of special right triangles to determine the sine, cosine, and tangent values of 30º, 45º, and 60º without the assistance of technology. • Apply the Pythagorean Theorem to problems involving right triangles. • Solve for the angles in a right triangle, given at least two sides. • Solve for the missing sides of a right triangle, given either two sides or one acute angle and one side UNIT 7-­‐ Statistics and Probability April/
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Essential Questions: How can an event be described as a subset of outcomes using correct set notation? How are probabilities, including joint probabilities, of independent events calculated? How are probabilities of independent events compared to their joint probability? How does conditional probability apply to real-­‐life events? How are two-­‐way frequency tables used to model real-­‐life data? How are conditional probabilities and independence interpreted in relation to a situation? What is the difference between compound and conditional probabilities? S.CP.1 S.CP.2 S.CP.3 S.CP.4 S.CP.5 S.CP.6 S.CP.7 MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 Students will be able to… Utilize Combinatorials 7.1 Correctly denote, formulate and calculate permutations and combinations in an experimental setting« Conditional Probability 7.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities. Use this to prove they are independent.« 7.3 Understand conditional probability and interpret independence of A and B« 7.4 Denote and calculate the probability of two dependent events. Model conditional probability with two stages by using a probability tree. • Investigate calculating a sample variance using both n and n-­‐1 as the divisor for samples drawn with and without replacement • Examine distributions of sample means of random samples of size n from four different populations. • investigate the relationship between the standard deviation of a population, the area of a Formative/Summative: ● Written section assessments ● Review games ● Practice exercises ● White board demonstrations ● Lab activities ● Ticket to Leave ● Unit 7 Common assessment ● Technology assessments ● Quick Quizzes ● Graded Classwork ● Flipped Classroom Instruction Text/Resources McDougal Larson Algebra 2 Common Core Edition 2012 Chapter 6 (6.1, 6.2) IMP Activity: 1. What are the Chances? Year One; p.92 ●
How is the probability of event (A or B) found? set of rectangles, and the standard deviation of the sampling distribution of sample mean areas of the rectangles. Vocabulary Critical Terms: ● Joint probability ● Event ● Independent events ● Conditional ● Conditional probability ● Independence ● Marginal probability ● Random variable Supplemental Terms: ● Sample space ● Subset ● Outcome ● Union ● Intersection ● Complement ● Set notation Prerequisite Concepts: Students should already be able to: • Represent sample spaces. • Apply basic properties of probability. • Use Venn diagrams and two-­‐way frequency tables. Unit 7 Concepts: • Establish events as subsets of sample space based on the union, intersection, and/or complement of other events. • Calculate the probability of an event. • Determine if two events are independent with justification. • Calculate the conditional probability of A given B. • Use the concept of conditional probability and independence using real life examples. • Calculate the probability of the intersection of two events. • Calculate the conditional probability of A given B. • Determine the probability of the union of two events using the Addition Rule. May/ June UNIT 8-­‐ Circles Essential Questions: What are the different relationships among inscribed angles, radii, and chords of a circle, and of the angles of a A.SSE.2 G.C.1 G.C.2 G.C.3 G.C.5 Students will be able to… Understand and apply theorems about circles. 8.1 Prove that all circles are similar. (G.C.1) 8.2 Identify and describe relationships among inscribed angles, radii, and chords. 2. Rug Games Year One; p.97 3. Portraits of Probabilities Year One; p.98 4. Mystery Rugs Year One; p.102 5. Spinner Give and Take Year One; p. 109 6. Martian Basketball Year One; p.123 7. One-­‐and-­‐One Year One; ps.115-­‐117 8. Samples and Populations Year Two; p.193 9. A Difference Investigation Year Two; p.237 10. Quality of Investigation Year Two; p.p.197 11. Who gets A’s and Measles? Year Two; p.196 Technology TI Nspire Labs: • Two-­‐way Tables and Association • Probability Distributions • Tossing Dice • Tossing Coins • Binomial PDF-­‐ Eye Color • Conditional Probability Graphing Calculator: • Stat-­‐ Tests • 2nd Distr • 2nd List-­‐Math • Math-­‐ Prb Formative/Summative: ● Written section assessments ● Review games ● Practice exercises ● White board quadrilateral inscribed in a circle? What is the relationship between the length of the arc of a circle, the central angle of the circle that intercepts this arc, and the radius of the circle? What is the area of a sector of a circle? Given the coordinates of the center of the circle and the radius of that circle, what is the equation of the circle? Given an equation for a circle drawn in the coordinate plane, what are the coordinates of the center of the circle and the radius of the circle? Prerequisite Concepts: • Apply the Pythagorean Theorem to find distances between points on the coordinate plane Unit 8 Concepts: • Recognize if one geometric object can be transformed to another through a sequence of rigid motions combined with a dilation. • Sketch a figure that represents specific given information. • Construct a conditional statement that represents a given conjecture. • Determine the area of a sector of a circle from the radius of the circle and the measure of the central angle of the sector. • Use the method of completing G.GPE.1 G.GMD.1 A.SSE MP.1 MP.2 MP.3 MP.5 MP.6 MP.7 Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. (G.C.2) 8.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Construction: Construct the inscribed and circumscribed circle of a triangle (G.C.3) Find arc lengths and areas of sectors of circles. 8.4 Derive using similarity the fact that the length of the arch intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant or proportionality; derive the formula for the area of a sector. (G.C.5) Translate between the geometric description and the equation for a conic section. 8.5 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. (G.GPE.1) Area Technique: Find the area of a circle and a sector. Algebra Technique: Simplify and perform operations on expressions involving pi. Vocabulary Critical Terms: ● Circle ● Radius ● Diameter ●
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demonstrations Lab activities Ticket to Leave Unit 8 Common assessment Technology assessments Quick Quizzes Graded Classwork Flipped Classroom Instruction Text/Resources McDougal Larson Algebra 2 Common Core Edition 2012 Chapter 8 (8.1, 8.3) IMP Activity: 1. Inscribed Angles Year Three; p. 73 2. More Inscribed Angles Year Three; p. 74 3. Proving with Distance, Part II Year Three; p. 32 4. Daphne’s Dance Floor Year Three; p. 48 – 49 5. What a Mess! Year Four; p. 232 Technology TI Nspire Labs: • Circles-­‐ Angles and Arcs • Chords of a Circle • Exploring the Equation of a Circle Graphing calculator: • Graph Circle as Two Functions • 2nd Calc Intersect the square to determine the coordinates of the center of the circle and the radius of the circle, given the equation of the circle. • Use the structure of an expression to identify ways to rewrite it. • Factor a quadratic expression to reveal the zeros of the function it defines. • Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. • Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. ● Arc ● Chord ● Tangent ● Central angles ● Inscribed angle ● Circumscribed angle ● Intercepted arc ● Radian ● Sector of a circle ● Coordinate plane Supplemental Terms: ● Conditional statement ● Hypothesis ● Conclusion ● Proof ● Necessary Conditions ● Sufficient Conditions ● Postulate ● Theorem ● Length ● Angle measure ● Degree Geometer's Sketchpad Labs: Exploring Geometry; ps. 121, 123, 124, 125