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Transcript
Pre-Calculus Pacing Guide Suggested Book List 1st Grade All Sorts of Numbers – counting * Henry the Fourth – ordinal numbers * 3 Little Firefighters – sorting * It’s About Time! * Bug Dance * The Best Vacation Ever – data collecting, problem solving skills * Count on Clifford 2nd Grade Amanda Bean’s Amazing Dream – multiplication * Clocks and More Clocks - time * Much Bigger than Martin – size “Slowly, Slowly, Slowly” said the Sloth * Lemonade for Sale - money * 100 Days of School – counting to 100 * Biggest Bed in the World – size * Give Me Half – halves 3rd Grade Sir Cumference and the Dragon Pi * Grandfather’s Tang Story - changing shape * Chicken Soup with Rice – months * Counting on Frank – size comparison, math facts, counting * Hershey’s Milk Chocolate Bar Fraction * How Much is a Million Mummy Math: An Adventure in Geometry * Millions of Cats * Three Days on a River in a Red Canoe 4th Grade Carry On, Mr. Bowditch Sir Cumference and the Great Knight of Angle Land – acute, obtuse, straight angles Sir Cumference and the Sword in the Cone – cubes, pyramids, prisms Sir Cumference and the First Round Table – measurement * A Million Fish…More or Less Dear Mr. Henshaw A Higher Geometry * The Village of Round and Square Houses - shape 5th Grade * How the Second Grade Got $8205.50 to Visit the Statue of Liberty – money Hannah, Divided The Secret Life of Amanda K. Woods – probability Tuck Everlasting – calculate population Gulliver’s Travel – geometry Jayden’s Rescue – problem solving The Curious Incident of the Dog in the Night – time, probability The Heroic of Hercules Amsterdam – counting 6th Grade The Da Vinci Code – Fibonacci Sequence The Twenty-one Balloons – mathematical reasoning Journey to Topaz – measurement 7th Grade The Sand-Reckoner – problem solving The Pearl – currency calculation Middle – High School Imaginary Numbers Mathematics in the Time of Pharaohs Medieval Chinese Innovations Math Talk: Mathematical Ideas in Poems for Two Voices High School Against the Odds – number theory Five Equations that Changed the World The Man Who Loved Only Numbers Math Equals: Biographies of Women Mathematical Scandels Archimede’s Revenge – application of math Calculus and Pizza * denotes AR books …………………………………………………………………………. Pre-Calculus Pacing Guide Alabama COS Standards 1 ST Textbook Correlation Pacing Guide Big Ideas / Essential Question AMSTI Essential Vocabulary AHSGE & NAEP Correlations / ARMT Blueprint Nine Weeks Review Algebra II (Refer to COS) P.1-P.6 1 Week 12. Determine the equation of a curve of best fit from a set of data by using exponential, quadratic, or logarithmic functions. 1.1-1.6 3 Weeks 4. Analyze the graphs of rational, logarithmic, exponential, trigonometric, and piecewise-defined functions by determining the domain and range; identifying any vertical, horizontal, or oblique asymptotes; and classifying the function as increasing or decreasing, continuous or discontinuous, and noting the type of discontinuity if one exists. Approximating rates of change using the difference quotient 2.1-2.9 3 Weeks “High Drive” Ferris Wheel Day 23 Quad. Equation (Chapter P) “High Drive” Ferris Wheel Day 23 Quad. Equation (Chapter P) Page 2 of 8 Range, domain, discontinuity, continuous, bounded, maximum, minimum, relative extrema, horizontal asymptote, piecewise, rational functional, asymptote, x-intercepts, yintercepts Technology Based Lessons / Links Pre-Calculus Pacing Guide Alabama COS Standards Textbook Correlation Pacing Guide Big Ideas / Essential Question AMSTI 2ND Nine Weeks 5. Analyze the effects of parameter changes on the graphs of trigonometric, logarithmic, and exponential functions. Example: explaining the relationship of the graph of y = ex -2 to the graph of y = ex 3.1-3.6 1 Week “High Dive” Sine function Day 4 Day 5 (Chapter 3) Determining the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses 1 Week ACT Review 5. Analyze the effects of parameter changes on the graphs of trigonometric, logarithmic, and exponential functions. Example: explaining the relationship of the graph of y = ex -2 to the graph of y = ex 3.1-3.6 2 Weeks Determining the amplitude, period, Page 3 of 8 Essential Vocabulary AHSGE & NAEP Correlations / ARMT Blueprint Technology Based Lessons / Links phase shift, domain, and range of trigonometric functions and their inverses 6. Apply the laws of logarithms to simplify expressions and to solve equations using common logarithms, natural logarithms, and logarithms with other bases. 4.1-4.8 4 Weeks Exponential function, base, growth factor, decay factor, limit to growth, logarithmic function, common logarithmic , natural logarithmic , sinusoid, amplitude, frequency, phase shift Page 4 of 8 Pre-Calculus Pacing Guide Alabama COS Standards Textbook Correlation Pacing Guide AMSTI Big Ideas / Essential Question Essential Vocabulary 3RD Nine Weeks 7. Solve trigonometric equations and inequalities using sum, difference, and half- and double-angle identities. Verifying trigonometric identities 5.1 – 5.4 2 weeks 1. Perform the vector operations of addition, scalar multiplication, and absolute value. Determining coincidence, parallelism, collinearity, or perpendicularity of vectors Using vectors to model real life and mathematical situations 6.1, 6.2 3 weeks for 6.1–6.5 8. Use parametric equations to represent real-life and mathematical situations. 6.3 Reduction formula High Dive – day 9 and 17 Scalar, initial point, terminal point, vector, magnitude, standard position, component form, velocity, dot product, orthogonal, vector projection Parametric curve, parametric equations, parameter, parameter interval Page 5 of 8 AHSGE & NAEP Correlations / ARMT Blueprint Technology Based Lessons / Links Pre-Calculus Pacing Guide Textbook Correlation Pacing Guide Alabama COS Standards 11. Convert coordinates, equations, 6.4, 6.5 and complex numbers in Cartesian form 6.5 (graph to polar form and from polar form to only) Cartesian form. Graphing simple polar equations in the polar coordinate plane AMSTI Big Ideas / Essential Question Polar coordinate system, polar axis, polar coordinates, directed distance, directed angle, maximum r value Example: graphing r = 2 + 2 cosф or r = 2 + sin 3ф Graphing polar coordinates and complex numbers 3. Graph conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. 8.1-8.4 Essential Vocabulary 3 weeks Conic section, vertex, degenerate conic sections, parabola, focus (foci), directrix, axis, chord, ellipse, minor axis, major axis, hyperbola, transverse axis, conjugate axis Example: graphing x2 – 6x + y2 – 12y + 41 = 0 or y2 – 4x + 2y + 5=0 Formulating equations of conic sections from their determining characteristics Example: writing the equation of an ellipse with center (5, -3), horizontal major axis of length 10, and minor axis of length 4. Page 6 of 8 AHSGE & NAEP Correlations / ARMT Blueprint Technology Based Lessons / Links Pre-Calculus Pacing Guide Alabama COS Standards Textbook Correlation Pacing Guide AMSTI Big Ideas / Essential Question Essential Vocabulary 4th Nine Weeks 12. Determine the equation of curve of best fit form from a set of data by using exponential, quadratic, or logarithmic functions. 9.1, 9.2 9. Solve applied problems involving sequences with recurrence relations. Determining characteristics of arithmetic and geometric sequences and series, including those defined with recurrence relations, first terms, common differences or ratios, nth terms, limits, or statements of convergence or divergence. Expanding binomials raised to a whole number power using the Binomial Theorem. 9.4, 9.5 3 weeks for 9.1, 9.2, 9.4, 9.5 Sequence, finite sequence, infinite sequence, recursively, arithmetic sequence, geometric sequence, common difference, common ratio, summation notation, index of summation, infinite series, partial sums, converges, diverges Page 7 of 8 AHSGE & NAEP Correlations / ARMT Blueprint Technology Based Lessons / Links Pre-Calculus Pacing Guide Alabama COS Standards 2. Define e using the limit forms of sigma notation lim(1 + 1/n)n, and lim(1 + n)1/n. 10. Find limits of functions at specific values and at infinity numerically, algebraically, and graphically. Applying limits in problems involving convergence and divergence. Textbook Correlation Pacing Guide 10.1–10.3 3 weeks 10.1-10.3 5 weeks AMSTI Big Ideas / Essential Question Essential Vocabulary Left hand limit, right hand limit, two sided limit Page 8 of 8 AHSGE & NAEP Correlations / ARMT Blueprint Technology Based Lessons / Links