Curriculum Map for Accelerated Probability, Statistics, Trigonometry

Transcription

1 Curriculum Map for Accelerated Probability, Statistics, Trigonometry Statistics Chapter Two September / October Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, S-ID.1, S-ID.2, S-ID.3, S-IC.1, S-IC.2, S-IC.3, S-IC.6 Different Types of Averages, Standard Deviation, Quartiles, Percentiles Essential Questions: What are the Types of Averages and when is each is most useful? What are the ways we measure Dispersion of Data Mean Median Mode Standard Deviation Variance Outliers Bar Graphs Box Plots Five Number Summary Quartiles Percentiles Usual and Unusual Values Calculate Mean, Median and Mode with and without a Calculator and when each is best to use. Calculate Standard Deviation and Variance with and without a Calculator. Identify Outliers Identify Usual and Unusual Values Calculate Usual and Unusual Values Calculate Quartile and/or Percentile of a Given Data Point. Use of Graphing Calculator will be Demonstrated using Overhead Projector and Emulator Software.

2 When given a Percentile or Quartile, Identify the Data Point How to Normalize Test Results. Draw Boxplots using the Five Number Summary Graphing Calculator Emulator Data Sets from the Textbook Loaded into the Graphing Calculator.

3 Statistics Chapter Three October / November Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, S-CP.1, S-CP.2, S-CP.3, S-CP.5, S-CP.6,S-CP.7, S-CP.8,S-CP.9, S-MD.3 Probability, Counting Techniques, Permutations, Combinations, Factorials Essential Questions: How to Calculate Probability, And and Or types of Combined Probability. The Difference between Combinations and Permutations. Dependent and Independent Events. Definition of Probability Factorials Permutations Combinations Dependent Events Independent Events Complementary Events Probability Trees Bayles Theorem Calculation of Simple Probability Calculation of Factorials, Permutations and Combinations with and without a Calculator. Identify Independent and Dependent Combined Probability Events and when to use Or and And, Addition and Multiplication Calculate Probabilities using the Complement. Calculate Probabilities using Trees and Bayles Theorem. Use of Graphing Calculator will be Demonstrated using Overhead Projector and Emulator Software. Use of Dice and Coins to Calculate Probabilities. Survey of Classes for the Birthday Problem. on First Six Sections Quest for the Last Section

4 Graphing Calculator Emulator Data Sets from the Textbook Loaded into the Graphing Calculator.

5 Statistics Chapter Four November Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, S-CP.1, S-CP.2, S-CP.3, S-CP.5, S-CP.6,S-CP.7, S-CP.8, S-CP.9, S-MD.1, S-MD.2, S-MD.3, S-MD.4, S-MD.5, S-CMD.6, S-MD.7 Binomial Probability Distribution, Poisson Probability Distribution Essential Questions: What is a Binomial Probability Distribution? What is a Poisson Probability Distribution? What is Expected Value and what is the Connection to the Mean of the Distribution How to set up a Binomial Distribution How to Calculate a Binomial Probability Distribution The Connection between the Mean of a Binomial Probability Distribution and Expected Value How to Calculate a Poisson Probability Distribution Differences between the Two Types of Distributions Calculate Binomial Distributions by 1) Using the Definition Formula Involving Combinations 2) Using a Table 3) Using a Calculator Calculate Cumulative Binomial Probabilities using the Calculator Calculate Poisson Probabilities using the Calculator Students will do Extensive Work on Probabilities of Getting a Certain Number Questions Correct on a Defined Multiple Choice Tests Lottery Examples will be Used to Demonstrate Expected Value Insurance Examples will be Used to Demonstrate Expected Value

6 Graphing Calculator Emulator Data Sets from the Textbook Loaded into the Graphing Calculator.

7 Statistics Chapter Nine November / December Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, A-CED.1, A-CED.2, A-CED.3, A-REI.3, F-LE.1, F-LE.3, S-ID.5, S-ID.6, S-ID.7, S-ID.8, S-ID.9, S- IC.1, S-IC.2, S-IC.3, S-IC.6 Regression Analysis for Curve Fitting Correlation Best Fit Modeling Essential Questions: How Can Collected Data Lead to an Equation of Best Fit. How this Model Lead to Predictions Using Interpolation and Extrapolation Least Squares Fit and How it is Calculated Residuals Scatterplots Correlation Correlation Coefficient (r) What the Meaning is of r 2 and how it is Calculated The Shape of Various Types of Curves Interpolation and Extrapolation and Looking at a Scatterplot, Determine the Probable Best Type of Regression. How to do a Least Squares Fit on the Calculator Calculate Residuals from a Least Squares Fit Use the r Value to Determine if there is a Linear Correlation Use the r 2 Value to Determine Best Fits of Non Linear Correlations will be done from Data Sets Contained in the Textbook and Loaded on the Calculator Actual Scientific Studies Will be Used an Examples An Example Using the TI Nspire Calculator using Regression Analysis will be used to Calculate the Formula for the Area of a Circle.

8 the Dangers of Relying on Extrapolation Correlation How to do Scatterplots and Regressions on the Calculator Graphing Calculator Emulator Data Sets from the Textbook Loaded into the Graphing Calculator. Statistics Chapter Five November Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, A-CED.1, A-REI.3, S-ID.1, S-ID.2, S-ID.3, S-ID.4, S-IC.1, S-IC.2, S-IC.3, S-IC.6 The Normal Distribution, The Central Limit Theorem Essential Questions: What is the Theory Behind the Normal Distribution? When and How is it Used? What is the Central Limit Theorem? The Connection between the Area Under a Density Curve and Probability Calculate z Scores and their Meaning How to Calculate the Probability of Events that are Normally Distributed Calculate Probabilities of a Normal Distribution using z Scores and Tables Given a Probability of a Normal Distribution, Calculate a z Score How to Normalize a Test. How SAT Scores are Calculated How Manufacturers Decide on Sizes of Items that are Made and Sold Normalizing Test Results

9 Using a Table How to Normalize Tests The Significance of the Central Limit Theorem and How to Use it. Graphing Calculator Emulator Data Sets from the Textbook Loaded into the Graphing Calculator.

10 Trigonometric Functions Chapter One February / March Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, A-REI.3, G-SRT.2, G-SRT.3, G-SRT.6, G-SRT.7, G-SRT.8, G-CO.1 Angles as Rotations, Similar Triangles, Definition of Trigonometric Functions Essential Questions: What is an Angle, How are Similar Triangles Used in Applications, Definition of Trigonometric Functions using Coordinate Geometry and Circles Definition of Angles using Rotations Co Terminal Angles Negative Angles Application of Similar Triangles Definition of Sine, Cosine, Tangent, Cosecant, Secant and Cotangent Determine Quadrant of Angles No Matter What Kind of Number is used for Degrees How Similar Triangles are used in Geometry and Science How to Compute any Trigonometric Function Given: a) Position of an Angle b) One Trig Function and the Quadrant Graphing Calculator Emulator Connections with Science and Geometry will be used in Examples

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12 Right Triangle Trigonometry Chapter Two March Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, A-REI.3, G-SRT.2, G-SRT.3, G-SRT.6, G-SRT.7, G-SRT.8, G-CO.1 Solving Right Triangles Essential Questions: How are Right Triangles Solved and what are the Applications Definition of Sine, Cosine and Tangent as Applied to Right Triangles Angles of Elevation and Depression Solve Right Triangles Using the Graphing Calculator Apply Angle of Elevation and Depression to Real Life Problems Graphing Calculator Emulator Students will use Angle of Elevation and Depression to Problems in Science and to Problems that will be used in Physics and Calculus

13 Right Triangle Trigonometry Chapter Three March / April Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, A-REI.3, G-SRT.2, G-SRT.3, G-SRT.6, G-SRT.7, G-SRT.8, G-CO.1, G-C.5, F-T.1, F-T.2, F-T.3, F- T.4 Construction of the Unit Circle, Applications to Physics Essential Questions: What is the Unit Circle and How is it used in Trigonometry. What is Radian Measure as applied to measurement of angles. What is meant by Linear and Angular Velocity and how is it applied to Circular Motion in Physics Values of the Unit Circle Radians Degrees Reference Angles Linear Velocity Angular Velocity Translate between Radian and Degree Measure of Angles Calculate Trigonometric Values of Special Angles without a Calculator How to Work with Reference Angles Know the Difference between Linear and Angular Velocity How to Translate from One to the Other. How Each is Applied to Circular Construction of the Unit Circle using Triangle and Triangle from Geometry Calculate Linear and Angular Velocities using Pulley Systems from Physics Calculate the Linear Velocity of any Point on Earth Given the Latitude. How this Calculation is Used to Aim Telescopes so that they always face the same portion of the sky.

14 Motion in Physics Graphing Calculator Emulator

15 Right Triangle Trigonometry Chapter Four April Targeted Standard(s): F-T.1, F-T.2, F-T.3, F-T.4, F-T.5, F-T.6 Trigonometric Function Graphs, the Meaning of Periodic Functions Essential Questions: How are Trigonometric Functions are Affected by Different Parameters, How are Graphs Applied to Non Trigonometric Applications What a Periodic Function is The Shapes of Basic Sine and Cosine Functions How are these Functions are affected by Changing Parameters Graph a Trigonometric Function Given a Trigonometric Function Graph, Construct a Equation Apply these Graphs and Equations to Real Life Applications Use the Wrapping Function as Demonstrated in the Geometer Sketchpad Program to Construct Basic Sine and Cosine Graphs Use the Geometer Sketchpad Program to Demonstrate how Changes in Parameters Change Graphs. Use Graphs to Construct Tide Tables and Hours of Daylight Applications

16 Graphing Calculator Emulator Geometer Sketchpad Program

17 Targeted Standard(s): F-T.8, F-T.9 Right Triangle Trigonometry Chapter Five April / May Using Trigonometric Identities to Simplify Expressions and Solve Proofs Essential Questions: How are Trigonometric Expressions Simplified and How are Proofs Done. What are the Later Connections to Solving Trigonometric Equations and Calculus Reciprocal Identities Pythagorean Identities Negative Angle Identities Co Function Identities Double Angle Identities Half Angle Identities Simplify Trigonometric Expressions Solve Trigonometric Proofs Graphing Calculator Emulator Examples of using each Type of Identity Review of Algebra Techniques to Help with Simplification and Proofs Checking Results using Graphs on the Graphing Calculator

18 Right Triangle Trigonometry Chapter Six May / June Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, A-SSE.3, A-CED.3, A-REI.2, A-REI.4,F-TF.1, F-TF.2, F-TF.3, F-TF.8 Using Trigonometric Identities to Solve More Difficult, Complicated Trigonometric Equations Essential Questions: How to use the Techniques of the Last Chapter to Solve Complicated Trigonometric Equations How to Solve Difficult, Complicated Trigonometric Equations How to Solve Trigonometric Equations using Factoring, Quadratics Methods and Trigonometric Identities How to Solve Equations Involving Half Angle and Multiple Angles Graphing Calculator Emulator Review of Algebra Techniques as Applied to Solving Trigonometric Equations

19 Right Triangle Trigonometry Chapter Seven June Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, G-SRT.9, G-SRT.10, G-SRT.11 Solving Oblique (Non Right) Triangles, Finding Areas of Triangles that are SAS or SSS Essential Questions: How to Solve Triangles that cannot use SOHCAHTOA Rules that Applied to Right Triangles The Law of Sines The Ambigious Case and the Law of Sines The Law of Cosines Area Formula for Triangles when Given Two Sides and the Included Angle (SAS) Heron s Formula for the Area of a Triangle when given All Three Sides (SSS) Solve any Triangle, Right or Oblique Be able to Determine when a Triangle may not have a Unique Solution or No Solution at All. Be able to Obtain All Solutions when there is Not a Unique Solution. Find Areas of Triangles that Have Given Two Sides and the Included Angle (SAS) or All Sides (SSS) Connections will be made to Physics, Surveying and Navigation

20 Graphing Calculator Emulator Geometer Sketchpad