Total days including assessments 169

Transcription

1 Unit Unit Title Days Month plus review 1 Number and Polynomial Operations 12 Sept 6 to Sept 23 2 Rational Numbers and Expressions 11 Sept 24 to Oct 8 3 Real Numbers and Radicals 11 Oct 7 to Oct 24 4 Relations and 9 Oct 25 to Nov 6 Quarterly Assessment 1 3 November Quadratic and Complex 21 Nov 14 to Dec 16 Numbers 6 Sequences and Series 9 Dec 17 to Jan 8 7 Exponential 12 Jan 9 to Jan 27 Quarterly Assessment 2 4 Jan Logarithmic 14 Feb 3 to Feb 24 9 Trigonometric 13 Feb 25 to Mar More Trigonometric 7 Mar 14 to Mar Graphs of Trigonometric 10 Mar 25 to Apr 7 Quarterly Assessment 3 4 Apr Statistics 16 Apr 28 to May Probability and the Binomial Theorem 13 May 20 to June 6 Total days including assessments 169 While reviewing for the final exam, teachers should focus on areas of weakness as shown on the quarterly exams and common assessments. Cumulative review for the final will be during the week of June 9 13

2 Unit 1: X Whole Numbers, Integers, and the Number Line X A.APR.1 Writing and Solving Number Sentences Adding Polynomials What is the set of real numbers (Set r) and its subsets? What are the properties of real number (Set R) and how are they applied in the operations with real numbers? What are the properties of equality/inequality and how are they applied? How do we add polynomials? Set, set symbol, set R and its subsets, properties of real numbers (commutative, identity, inverse, associative, distributive), roster method, descriptive method of describing a set. Properties of equality, equation, reflexive, symmetric, multiplicative and additive properties, transitive; inequality, order relations symbols (<, >,, ) Constant, coefficient, base, exponent, like/similar terms, unlike or dissimilar terms X A.APR.1 Solving Absolute Value Equations and Inequalities Multiplying Polynomials A.APR.1 Factoring Polynomials A.CED.1 A.REI.4 Quadratic Equations with Integral Roots A.CED.1 Quadratic Inequalities How do we solve an absolute value equation or inequality? How do we multiply polynomials? How do we factor polynomials? How do we find the integral roots of quadratic equations? How do we find the solution of a quadratic inequality? COMMON ASSESSMENT #1 Absolute value, solution, solution set Term, power, monomial, binomial, trinomial, polynomial factor, greatest common factor, common monomial factor, common binomial factor, binomial factors, special products, special factors, prime polynomial Quadratic equation, standard form, degree. Quadratic inequality

3 Unit 2 A.APR.8 N.RN.1 A.APR.8 N.RN.3 Rational Numbers What differentiates a rational from irrational number as subsets of set R? How are the properties of Set R applied to the set of Rational and irrational numbers, reciprocal, decimal number, terminating decimal, nonterminating repeating decimal, repeating decimal rational numbers? Simplifying Rational Expressions How do you simplify rational expressions? Rational expression, simplest form or lowest terms, canceling, numerator, denominator, product, reduction to lowest terms A.APR.8 Multiplying and Dividing Rational Expressions A.APR.8 X A.APR.8 Adding and Subtracting Rational Expressions A.REI.2 Solving Rational Equations How do you multiply rational expressions? How do you divide rational expressions? How do you add/subtract rational expressions? Ratio and Proportion In a proportion, how do you find a missing mean or extreme? Complex Rational How do you simplify a Expressions complex fraction? How do you find the solution of a rational equation? Factors, multiplier, multiplicand, product, quotient, dividend, divisor Addend, sum, subtrahend, minuend, difference, least common denominator Ratio, proportion, means, extremes, ratio symbols. Complex fraction, complex rational expression, least common multiple, least common denominator, Rational equation, extraneous root Assessment #2

4 Unit 3 8-NS.1 Real numbers, irrational and rational numbers, absolute value, interval notation, absolute value inequality N.RN.3 Roots and Radicals How do we perform operations on irrational numbers and find its nth root? Square root, cube root, nth root, radicand, index, principal root, radical N.NR.3 N.RN.3 N.RN.3 Coefficient, index, radicant Like radicals, unlike radicals, reducible radicals Product of radicals, sum containing radicals, coefficient of a radical N.RN.3 Dividing Radicals How do you divide radicals? Radical numerator, radical denominator N.RN.3 Rationalizing a Denominator A.REI.2 The Real Numbers and Absolute Value radicands Adding and Subtracting How do we add or subtract Radicals radicals with both like or unlike radicands? Multiplying Radicals How do we multiply radicals? Solving Radical Equations What are real, irrational and rational numbers and how are they arranged in a number line which can be described using an inequality? Simplifying Radicals How do we simplify radical expressions with positive integral How do you rationalize a radical denominator to simplify the fraction? How do we solve radical equations? COMMON ASSESSMENT #3 Conjugate, conjugate pair, rationalizing the denominator Roots, radical equation,

5 Unit 4 F.IF.1 Relations and #27: How do we determine when a relation is a function? Function, relation, one-to-one correspondence, domain, range, dependent variable, independent variable, onto, vertical line test F.IF.2 F.IF.1 F.IF.7 F.IF.7 F.IF.2 F.IF.2 Function Notation Linear and Direct Variation Absolute Value Polynomial The Algebra of Composition of How do we use functional notation and find the image when the pre-image is given under f? How do we determine whether a function in linear and whether onto or one-toone How do you graph an absolute value function? How do we find the roots of a polynomial function and how are they linked with the graph of the function? How do we perform operations with functions What is the domain of a composition function and how is it formed? Functional notation forms, rule of pairing Linear function, one-to-one function, horizontal line test, Absolute value function, manytoone function, Polynomial function, degree, parabola, turning point, vertex, axis of symmetry, direction of infinite extent, roots of polynomial function, double roots Sum, difference, product, and quotient of functions Composition of functions, composite function, F.BF.4 Inverse How are inverse functions related to the identity function? Identity function, inverse functions, absolute value function and its inverse, inverse of a quadratic function Assessment #4

6 Unit 5 A.REI.4 A.REI.4 Aim Real Roots of a Quadratic Equation The Quadratic Formula How do we find roots using completing the square method? How do we derive the quadratic formula and use it to find roots of quadratic equations? A.REI.4 The Discriminant : How do we use the discriminant to determine the roots of a quadratic equation? N.CN.1 The Complex Numbers What are complex numbers and their subsets? What is i and the powers of i? Perfect squares, completing the square Quadratic formula, standard form Coefficients, discriminant Complex number plane, i, complex numbers, points in the complex number plane, N.CN.3 N.CN.4 A.REI.4 N.CN.8 A.REI.4 A.REI.4 A.REI.6 Operations with Complex Numbers Complex Roots of a Quadratic Equation Sum and Product of the Roots of a Quadratic Equation Solving Higher Degree Polynomial Equations Solutions of Systems of Equations and Inequalities How do we change the square root of a negative number and use algebraic properties to perform operations on this group of numbers? How do we find complex roots of quadratic equations? How do we get the sum and product of roots of a quadratic equation to confirm that the roots found are correct? How do we find the roots of higher degree polynomials? How do we find the solutions of systems of equations? conjugate pair Square roots of negative radicands, sum, difference, product, and quotient of complex numbers Complex roots, negative discriminant Sum of roots, product of roots Higher degree polynomials Systems of equations, systems of inequalities How do we find the solutions of systems of inequalities? Systems of equations, systems of inequalities Assessment #5

7 Unit 6 F.IF.3 F.BF.2 Topic/Lesson Sequences Essential Question How can we specify the terms of a sequence, given its recursive definition? Vocabulary Sequence, finite and infinite sequence, recursive definition Date F.IF.3 F.BF.2 Arithmetic Sequences How do we identify an arithmetic or geometric sequence and find its nth term? Arithmetic sequence, geometric sequence, nth term, common difference, common factor, arithmetic mean X Sigma Notation How do we find a sum using the sigma notation? Sigma, series, sigma notation, finite series, infinite series X Arithmetic Series How do we find the sum of Arithmetic series F.BF.2 Geometric Sequences How do we generate a geometric sequence and Geometric sequence, first term, common factor/ratio find the sum of a geometric series, find its nth A.SSE.4 Geometric Series How do we find the sum of Geometric series X Infinite Series How do we determine that Limit, without limit, an approaches a limit arithmetic series increases without limit, decreases without limit, or approaches a limit? Assessment #6

8 Unit 7 Algebra I Laws of Exponents How do we write and use the laws of exponents in simplifying expressions? Algebra I Zero and Negative Exponents How do we simplify expressions with negative exponents? Algebra I Fractional Exponents How are expressions with fractional exponents simplified? Factor, base, exponent exponential form, standard form Zero exponent, negative exponent Fractional exponent, coefficient of a radical Algebra I Exponential and Their Graphs Algebra I Solving Equations Involving Exponents How are exponential functions graphed manually and using the graphing calculator? How do we find their solution of equations involving exponents? Exponential function, Cartesian Plane, ordered pair, plotting of points Equations with exponents Algebra I A.SSE.2 A.CED.1 Algebra I A.SSE.2 A.CED.1 Solving Exponential Equations Applications of Exponential How are exponential equations solved? How do we solve the different kinds of exponential equation problems? Exponential equations, base, exponent, power Exponential equations, base, exponent, power, solutions, extraneous roots Assessment #7

9 Unit 8 F.IF.7e Inverse of an Exponential Function How do we show the inverse of an exponential function and its graph? Exponential function, inverse of exponential function, logarithm F.LE.4 Logarithmic Form of an Exponential Equation How do we compare logarithmic form from exponential form and convert one form to the other? Logarithmic form, exponential form F.LE.4 Logarithmic Relationships What are the properties of logarithms and how are they applied? Properties of logarithms F.LE.4 Logarithms How numbers in standard form converted to common logarithmic forms? F.LE.4 Natural Logarithms How do we simplify powers using natural logarithms? A.SSE.2 Exponential Equations How do we solve exponential A.CED.1 equations using logarithmic method? A.IF.8b F.LE.4 A.IF.8b F.LE.4 Logarithmic Equations How do we find the solution of logarithmic equations? Assessment #8 logarithm Natural logarithm Properties of logarithms; properties of equality; properties of real numbers Properties of logarithms; properties of equality; properties of real numbers

10 Unit 9 Geometry Geometry F.TF.2 F.TF.2 Trigonometry of the Right Triangle Angles and Arcs as Rotations The Unit Circle, Sine, and Cosine How do we find the parts of a right triangle using the sine, cosine, or tangent function? How do we determine that angles are coterminal, quadrantal, or both? How do we use the unit circle to find the sine, cosine, and coordinates of the terminal side of an angle in standard position? Hypotenuse, legs, similar triangles, sine, cosine, tangent, acute angle, right angle. Angle, initial side, terminal side, angle in standard position, angular speed, quadradrantal angles, coterminal angles Unit circle, sine function, cosine function Geometry The Tangent Function How can we use the tangent Tangent function function to solve any right triangle when the sine and cosine are Geometry The Reciprocal How can we solve a right Secant, cosecant, cotangent Trigonometric triangle when the reciprocal of the sine, cosine or tangent are Geometry Geometry Geometry Function Values of Special Angles Function Values from the Calculator Reference Angles and the Calculator known? How do we find the six trigonometric functions of special angles? How do we use the calculator to determine the measure of an angle using degree or radian unit of angular measure? How do we express function values of angles greater than 90 degrees as function values of positive acute angles? Assessment #9 Special angles, isosceles triangle, degree right triangle Degree, radian, central angle, arc, radius, sector Reference angle, negative angle, positive angle, first/second/third/fourth quadrant angle

11 Unit 10 F.TF.1 Radian Measure How do we convert radian measure to degree measure and vise- versa? Radian measure, degree measure, Pi, F.TF.2 Trigonometric Function Values and Radian Measure How do we use radian measure to find exact values of trigonometric functions? Pi-radian/degree equivalents, arc, central angle F.TF.8 Pythagorean Identities Given a trigonometric function of an angle, how do we find the other trigonometric functions using any of the Pythagorean identities? Pythagorean identities F.TF.2 Domain and Range of Trigonometric How do we find the domain and range of any given trigonometric function? Assessment #10 Domain and range of a trigonometric function

12 Unit 11 Geometry Graph of the Sine Function How do we graph the sine function Sine graph F.IF.7e and describe its cycle and period? Geometry F.IF.7e Graph of the Cosine Function How do we graph the cosine function and determine its amplitude, period, phase shift, and frequency? Cosine curve F.IF.7e F.TF.5 F.IF.7e F.IF.7e F.IF.7e F.TF.5 Amplitude, Period, and Phase Shift Writing the Equation of a Sine or Cosine Graph Graph of the Tangent Function Graphs of the Reciprocal How do we determine the amplitude, period, and phase shift of a sine or cosine graph? How do we write the equation of a sine or cosine graph? How do we graph the tangent function and describe its amplitude, period, domain and range? How do we graph the reciprocal functions of sine, cosine, and tangent? Assessment #11 Cycle, period, amplitude, phase shift, frequency Y=a sin (bx+c) Y= a cos (bx+c) Cycle, period, amplitude, phase shift, frequency Reciprocal functions

13 Unit 12 7th Grade Gathering Data How do we show data Statistics, data, inivariate using a stemand-leaf diagram, frequency census, survey, statistics, distribution, and histogram? controlled experiment, observational studies, population, sample, stemand-leaf, frequency distribution table, tally 7th Grade Measures of Central Tendency How do we find the measures of central tendency in a set of data? Measure of central tendency, mean, arithmetic mean, average, median, mode, quartiles, first/lower quartile, second quartile/median, third/upper quartile, statistical summary, boxand- whisker plot S.ID.2 Measures of Central Tendency for Grouped Data Measures of Dispersion S.ID.4 Variance and Standard Deviation S.ID.4 Normal Distribution S.ID.6c Bivariate Statistics S.ID.8 Correlation Coefficient S.IC.1 Non-Linear Regression Interpolation and Extrapolation Assessment #12 How do we find the measures of central tendency for grouped data? How do we find the measure of dispersion to show the spread of individual data on both sides of the mean? How do we calculate the variance and standard deviation of a set of data? How does the standard deviation in a normal curve describe the spread of the data How do we show a bivariate statistics in a scatter plot and produce a line of best fit? How do we find and use correlation coefficients? How do we determine and use regression functions? When do we use interpolation and extrapolation process? Frequency distribution table, cumulative frequency, percentile, Measure of dispersion, range, interquartile range, outlier Variance, standard deviation Normal curve, Gaussian or normal distribution, z-score, empirical rule, probability density function, frequency curve, Bivariate statistics, scatter plot, correlation, line of best fit, regression line Correlation, positive/negative correlation, Pearson correlation coefficient Independent variable, dependent variable, regression models Interpolation, extrapolation

14 Unit 13 S.CP.9 The Counting Principle Permutations and Combinations How do you use the counting principle to determine the number of outcomes occur in two given activities? How do we find permutations of a given sample space? How do we find the number of combinations from a given sample space? Sample space, event, outcome, dependent event, independent event, counting principle Arrangement, factorial, permutation, combination Probability Probability with Two Outcomes Binomial Probability and the Normal Curve The Binomial Theorem How is theoretical probability found? How is empirical probability calculated? How do we use the binomial probability formula to make predictions? How do we find binomial probabilities defined by restrictions like at least or at most? How do you apply the binomial theorem to expand a binomial raised to a power n? COMMON ASSESSMENT #13 Theoretical probability, random variable, empirical probability. Distribution, complement Bernoulli or binomial experiment, binomial probability formula At least, at most Pascal s triangle, binomial theorem