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Unit 1 Plan Math 2 Key Learning(s): Analyzes the graphs of and solves quadratic equations and inequalities by factoring, taking square roots, and using the quadratic formula. Topic: Quadratics and Complex Numbers Unit Essential Question(s): How do I determine characteristics of a quadratic function algebraically and graphically? Concept 1 Imaginary and Complex Numbers Concept 2 Horizontal Shifts of Quadratic Functions Days: 3 Days: 1 Essential Question: How do I represent the square root of a negative number? How do I simplify and perform operations using complex numbers? Vocabulary: Vertex, Vertex form, Horizontal Shift Grade: 10 Optional Instructional Tools: Graphing calculator, graph paper, learning tasks, and graphic organizers Concept 3 Converting from Standard to Vertex Form Concept 4 Solving Quadratic Equations by Factoring Concept 5 Quadratic Formula and the Discriminant Days: 2 Days: 1 Essential Question: How do I graph transformations of quadratic functions? How do I know when to shift a parabola from left to right based on the equation? Essential Question: How do I convert a quadratic equation from standard to vertex form? Essential Question: How do I solve quadratic equations by factoring when the leading coefficient is not 1? Essential Question: How do I solve quadratic equations using the quadratic formula? How do I use the discriminant to determine the nature of roots? Vocabulary: Vertex, Horizontal Shift Vocabulary: Vertex Form Vocabulary: Vocabulary: Discriminant, Quadratic Formula, Nature of Roots Days: 2 Unit 1 Plan Math 2 (Pg. 2) Key Learning(s): Analyzes the graphs of and solves quadratic equations and inequalities by factoring, taking square roots, and using the quadratic formula. Topic: Quadratics and Complex Numbers Unit Essential Question(s): How do I determine characteristics of a quadratic function algebraically and graphically? Concept 6 Partial Sums of Arithmetic Series Concept 7 Solving Quadratic Inequalities Days: 1 Days: 1 Essential Question: How can arithmetic sequences be expressed and manipulated as functions? Essential Question: How do I solve quadratic inequalities algebraically and by using a graphing calculator? Vocabulary: Vocabulary: Grade: 10 Optional Instructional Tools: Graphing calculator, graph paper Unit 2 Plan Math 2 Key Learning(s): Students will learn how to: Determine side lengths of special right triangles and apply trigonometric ratios to right triangles. Concept 1 Constant ratios in similar right triangles Days: 1.5 Topic: Right Triangle Trigonometry Grade: 10 Optional Instructional Tools: Unit Essential Question(s): How do I determine side lengths of special right triangles? How do I apply sine, cosine, and tangent to solve problems involving right triangles? Concept 2 Special right triangles Days: 3 Graph paper, graphic organizers, graphing calculators or utility Concept 3 Defining and using trigonometric ratios Concept 4 Using trigonometric functions for complementary angles Concept 5 Introduction to inverse trigonometric functions Days: 3 Days: 3 Days: 1 Evaluation: 1.5 Essential Question: How do I use constant ratios to solve similar right triangles? Essential Question: How do I determine side lengths of 30°60°- 90° triangles and 45°- 45°- 90° triangles? Essential Question: How do I use sine, cosine, and tangent to find missing information in right triangles? Essential Question: How do I use the relationship between trigonometric functions and complementary angles? Essential Question: How do I use the inverse trigonometric functions on my graphing calculator to find angles given their sines, cosines, or tangents? Vocabulary: Similar right triangles, Ratios Vocabulary: 30°- 60°- 90° triangles, 45°- 45°90° triangles Vocabulary: Sine, cosine, tangent, trigonometric ratio, trigonometric function Vocabulary: Complementary Vocabulary: Unit 3 Plan Math 2 Key Learning(s): • • • • • Parts of a circle Angle measures in a circle Chords, tangents, and secants Arc lengths and areas of sectors Volume and surface area of spheres Concept 1 Parts of a Circle Topic: Circles and Spheres Grade: 10 Optional Instructional Tools: Unit Essential Question(s): How do I find the measures of special segments and angles of a circle? How do I use and apply properties of circles to solve various problems? Concept 2 Angle Measures in a Circle Concept 3 Segments of Circles Graphic organizers, calculators, random stuff ; ) Concept 4 Arc Length and Area of a Sector Concept 5 Volume and Surface Area of a Sphere Days: 4 Days: 1.5 Days: 2 Days: 2 Days: 3.5 Essential Question: Essential Question: Essential Question: Essential Question: Essential Question: How do I distinguish among the special segments and angles associated with a circle? How do I find the measures of various angles formed by intersecting segments inside or tangent to a circle? How do I use triangle similarity to understand properties of intersecting chords, tangents, and secants of circles? How do I use the properties of circles to solve problems involving the length of an arc and the area of a sector? How do I use and apply surface area and volume of a sphere? How do I determine the effect on surface area and volume of changing the radius and diameter of a sphere? Vocabulary: Vocabulary: Vocabulary: Vocabulary: Vocabulary: Central angle, inscribed angle, vertex, intercepted arc Chord, secant, tangent, point of tangency, central angle, inscribed angle, intercepted arc, similar triangles, AA similarity Arc length, circumference, area of a circle, area of a sector, exact values, approximate values Radius, diameter, sphere, surface area, volume, circumference Center, diameter, radius, secant, chord, tangent, point of tangency, central angle, inscribed angle, arc, major arc, minor arc, semicircle Evaluation of Unit: 1.5 days Unit 4 Plan Math 2 Topic: Statistics Key Learning(s): Unit Essential Question(s): Analyzing data by looking at standard deviation, normal distribution, and sample and population distributions Concept 1 Means, Variances, and Standard Deviations How do I use measures of variability and normal distributions to analyze data? Concept 2 The Empirical Rule Grade: 10 Optional Instructional Tools: Graphing calculator, Graph paper, and Learning tasks Concept 3 The Golden Ratio Days: 3.5 Days: 1.5 Days: 2.5 Essential Question: How do we calculate and interpret the relationship among mean, variance, and standard deviation in problem solving? Essential Question: How do I determine when and how to use empirical rule to interpret the mean and standard deviation given a distribution of data values? Essential Question: How do I make inferences on populations and their samples using mean and standard deviation? Vocabulary: Mean, Mean deviation, Standard deviation, Variance, Frequency , Frequency distribution Vocabulary: Empirical rule, Normal distribution, Standard deviation, Mean, Dotplot, Outlier, Center, Shape, Skewedness, Symmetrical, Spread Vocabulary: Golden ratio, Standard deviation, Mean, Dotplot, Sample, Population, Random sample, Probability Unit 4 Plan Math 2 (Pg.2) Key Learning(s): Analyzing data by looking at standard deviation, normal distribution, and sample and population distributions Concept 4 Comparing Population Means and Standard Deviations Days: 6 Topic: Statistics Grade: 10 Optional Instructional Tools: Unit Essential Question(s): How do I use measures of variability and normal distributions to analyze data? Concept 5 Comparing Sample and Population Distributions Days: 6 Graphing calculator, Graph paper, and Learning tasks Concept 6 Non-Normal Distributions Days: 6 Evaluation of Unit: 2 Essential Question: How do I make conclusions about data using the comparison of mean and standard deviation? Essential Question: How do I make conclusions about data based on comparing the sample versus the population mean and the sample versus the population distribution? Essential Question: How do I determine if data has a nonnormal distribution and how do I use this information to make conclusions about the data? Vocabulary: Scatterplot, Mean, Population, Stem-and-leaf plot, Standard deviation, Least squares regression line, Correlation coefficient Vocabulary: Mean, Population, Random Sample, Scatterplot, Standard deviation, Stem and leaf plot Vocabulary: Normal distribution, Non-normal distribution, Dotplot, Mean, Median, Standard deviation, Interquartile range, Outliers Unit 5 Plan Math 2 Key Learning(s): Students will learn how to: Identify and graph piecewise, inverse, and exponential functions. Solve exponential equations and inequalities. Topic: Piecewise, Inverse, and Exponential Functions Unit Essential Question(s): How do I describe and use piecewise, inverse, and exponential functions? Grade: 10 Optional Instructional Tools: Graphing calculator, Graph paper, Learning tasks, Graphic organizers Concept 1 Piecewise Functions Concept 2 Points of Discontinuity Concept 3 Floor Functions Concept 4 Ceiling Functions Concept 5 Solving Exponential Equations and Inequalities Days: 2 Days: 1 Days: 1 Days: 2 Days: 2 Essential Question: How do I identify, describe, and graph piecewise functions? Essential Question: How do I identify points of discontinuity in piecewise functions? Essential Question: How do I graph a greatest integer function? How do I determine if a piecewise function is a floor function? Essential Question: How do I determine if a piecewise function is a ceiling function? Essential Question: How do I use properties of exponents to simplify algebraic expressions and solve exponential equations and inequalities? Vocabulary: Piecewise function Vocabulary: Point of discontinuity Vocabulary: Step function, Floor function, Greatest integer function Vocabulary: Step function, Ceiling function Vocabulary: Unit 5 Plan Math 2 (Pg. 2) Key Learning(s): Topic: Piecewise, Inverse, and Exponential Functions Unit Essential Question(s): Students will learn how to: Identify and graph piecewise, inverse, and exponential functions. Solve exponential equations and inequalities. How do I describe and use piecewise, inverse, and exponential functions? Grade: 10 Optional Instructional Tools: Graphing calculator, Graph paper, Learning tasks, Graphic organizers Concept 6 Transformations of Exponential Functions Concept 7 Geometric Sequences Concept 8 Inverse Functions Concept 9 Composition of Functions Days: 2 Days: 2 Days: 5 Days: 2 Evaluation of Unit: 2 days Essential Question: How do I graph transformations of exponential functions? Essential Question: How do I use the common ratio in a geometric sequence with exponential functions? Essential Question: How do I determine the inverses of linear, quadratic, and power functions? How do I describe the graphs of inverse functions? Essential Question: How do I use composition of functions to verify that functions are inverses of each other? Vocabulary: Vocabulary: Common Ratio, Geometric Sequence Vocabulary: Inverse function, Oneto-oneness Vocabulary: Composition of functions Unit 6 Plan Math 2 Topic: Finding the Best Model Key Learning(s): Unit Essential Question(s): Analyzing data and finding a model that best fits the data Solving Absolute value equations and inequalities How do I find a model that best fits a set of data? How do I solve absolute value equations and inequalities? How do I describe relationships using causation and correlation? Grade: 10 Optional Instructional Tools: Graphing calculator, Graph paper, Learning tasks, and Graphic organizers Concept 1 Solving Absolute Value Equations and Inequalities Concept 2 Choosing Appropriate Models for a Set of Data Concept 3 Correlation and Causation Days: 3 Days: 5 Days: 3.5 Essential Question: How do I solve absolute value equations and inequalities both algebraically and graphically? Essential Question: How do I determine the best fitting model for a set of data using visual approximation, median-median line, and least squares regression? Essential Question: How do I use the correlation coefficient to determine the strength and direction of a linear relationship? How do I distinguish between correlation and the causation between two quantitative variables? Vocabulary: Vocabulary: Extrapolation, Interpolation, Linear regression line, Least Squares Regression line, Median-median line, Method of finite differences, Quadratic regression, Regression curve Vocabulary: Correlation coefficient, Correlation, Causation