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Curriculum Overview Map Detroit Public Safety Academy 2015-2016 Course/Subject: ALGEBRA II Grade: 11 Quarter: 1st Essential Questions-Units-Chapters-Concepts UNIT 1 LINEAR FUNCTIONS AND EQUATIONS: How do variables help you model real-world situations? How can you use the properties for real numbers to simplify algebraic expressions? How do you solve an equation or inequality? How are patterns represented using variables? How can you represent mathematical phrases and real-world quantities using algebraic expressions? What are sets and subsets of numbers and how are real numbers related in specific ways? How do properties of real numbers allow you to solve equations and inequalities? UNIT 2 UNIVARIATE DATA AND DISTRUBUTIONS: How can visual displays and statistical calculations be used to organize, analyze, and evaluate data sets? How is data collected (types of samples)? What are some possible sources of bias that occur in collecting data? What are some methods of reducing bias? What is the different between observational studies, randomized experiments, and sample surveys? What conclusions can be drawn from each? Given a frequency distribution graph, what is the relationship between the median and the mean in a distribution that is skewed to the left? Skewed to the right? Explain why this relationship exists. How can you use mean and standard deviation of a normal distribution to compare two pieces of data? UNIT 3 USING TOOLS TO MODEL AND SOLVE MATRICES & VECTORS: How can matrices and vectors be used to solve problems in mathematics and other related fields? How can you tell whether two matrices can be multiplied together? What process is used to solve a system of linear equations using matrices? Resources (include websites) Atlas Rubicon Oakland Schools (2015). https://oaklandk12public.rubiconatlas.org/Atlas/Browse/Vie w/Calendars Pearson Education(2015). www.pearsonsuccess.net (2012). Algebra 2 Curriculum Crafterhttps://curriculumcrafter.org/login.aspx Sims. (2015). Algebra Housewww.algebrahouse.com Kuta Software (2015). https://www.kutasoftware.com/freeia2.ht ml Khan Academy, 2015. https://www.khanacademy.org/ Teacher Tube, 2015 www.teachertube.com Learning Focused, 2013. Higher Order Thinking Learning Focused Lessons http://www.learningfocused.com/index.p hp/page/lfs-engaged Standards-CCSS/GLCEs/HSCEs-KC4 Unit 1: A.REI.1, A.REI.2, A.REI.7, A.REI.11 F.IF.4, F.IF.6, F.BF.1, F.BF.2, F.LE.5 Unit 2: N.Q.A.2, N.Q.A.3, S.ID.A.1, S.ID.A.2, S.ID.A.3, S.ID.A.4, S.IC.A.1, S.IC.A.2, S.IC.B.3 Unit 3: N.VM.A.1, N.VM.A.2, N.VM.A.3, N.VM.B.4, N.VM.C.7, N.VM.C.8, N.VM.C.9, A.REI.C.8, A.REI.C.9, N.Q.A.2, N.Q.A.3 Vocabulary/Key Concepts Unit 1: Variable, Numerical Expression, Algebraic Expression, Properties of Real Numbers, Evaluate, term, coefficient, constant term, like terms, Properties of Algebraic Expressions, Properties of Equality, equation, inverse operations, identity, literal equation, Properties of Inequalities, Compound Inequalities, Extraneous Solutions, Absolute Value Assessments/Projects Standard Based Assessment: Interpreting Data through charts, tables and graphs. (Pre/Post x 2) Unit 1, 2, & 3 Assessments (pre/post) STEM Cross Curricular Projects Unit 2: Dot plots, relative frequency histograms, bar graphs, box plots, skewed distribution, symmetric distribution, outlier, M-STEP & SAT Prep measures of center (mean, median, mode), Measure of variation (percentiles, quartiles, range, IQR, variance, standard deviation), normal distribution, margin of error, simulation, sample, census, bias, sampling methods, observational study, experimental study Unit 3: Associative Property, Commutative Property, Cramer’s Rule, Determinant, dimension, element, identity matrix, inverse matrix, linear programming, matrix operations, multiplication by a scalar, solving systems of equations, transformation matrices, vector , components, magnitude, direction, initial point, terminal point, add and subtract vectors, resultant, parallelogram rule, scalar, scalar multiplication Curriculum Overview Map Detroit Public Safety Academy 2015-2016 Course/Subject: ALGEBRA II Grade: 11 Essential Questions-Units-Chapters-Concepts UNIT 3 USING TOOLS TO MODEL AND SOLVE MATRICES & VECTORS: How can matrices and vectors be used to solve problems in mathematics and other related fields? How can you tell whether two matrices can be multiplied together? How can two vectors be added together? How do you represent a vector by using a matrix? UNIT 4 EXPONENTIAL & LOG FUNCTIONS: What is the connection between exponential and logarithmic functions? What patterns of change are modeled by logarithmic functions as seen in real-world situations, and the tables, graphs, and function rules that represent these situations? How can the properties of logarithms be used to write algebraic expression inequivalent forms? What types of real world relationships are best described using a logarithmic scale? Why? What relationships- graphical, algebraic, numeric- exist between a function and its inverse? Why can’t a logarithm have an argument of zero or a negative number? What are the similarities and differences between exponential and logarithmic functions? UNIT 5 RATIONAL EXPRESSIONS AND FUNCTIONS: How does understanding polynomial functions (and other function families) aid in making sense of rational functions? How can equations and tables of values for rational functions help reveal key features in their graphs? How can the key features of graphs of rational functions be used to create an algebraic model? How do different forms of rational functions highlight structures where polynomial functions and transformations can aid in making sense of rational functions? How does understanding operations with rational numbers inform operations with rational expressions? Quarter: 2nd Resources (include websites) Atlas Rubicon Oakland Schools- https://oaklandk12public.rubiconatlas.org/Atlas/Browse/View/Calendars Pearson- www.pearsonsuccess.net Curriculum Crafterhttps://curriculumcrafter.org/login.aspx Pearson. (2012). Algebra 2 Sims. (2015). Algebra Housewww.algebrahouse.com Kuta Software (2015). https://www.kutasoftware.com/freeia2.html Khan Academy, 2015. https://www.khanacademy.org/ Teacher Tube, 2015 www.teachertube.com Learning Focused, 2013. Higher Order Thinking Learning Focused Lessons http://www.learningfocused.com/index.php/page/lfsengaged Standards-CCSS/GLCEs/HSCEs-KC4 Unit 3: N.VM.A.1, N.VM.A.2, N.VM.A.3, N.VM.B.4, N.VM.C.7, N.VM.C.8, N.VM.C.9 Unit 4: F.IF.C.7e, IF.C.8b, IF.C.9, F.BF.A.1c, F.BF.B.4b, F.BF.B.5, F.LE.A.2, F.LE.A.4 Unit 5: A.APR.B.2, A.APR.D.6, A.APR.D.7, F.IF.C.7d, F.BF.B.3 Vocabulary/Key Concepts Unit 3: Associative Property, Commutative Property, Cramer’s Rule, Determinant, dimension, element, identity matrix, inverse matrix, linear programming, matrix operations, multiplication by a scalar, solving systems of equations, transformation matrices, vector , components, magnitude, direction, initial point, terminal point, add and subtract vectors, resultant, parallelogram rule, scalar, scalar multiplication Assessments/Projects Standard Based Assessment: Interpreting Data through charts, tables and graphs. (Pre/Post x 2) Unit 3, 4, & 5 Assessments (pre/post) STEM Cross Curricular Projects Unit 4: Asymptote, base of a logarithm, base ten logarithms M-STEP & SAT Prep (common logarithms), composition of functions, domain, e, end behavior, exponential functions, exponential models (compound Final Exam Semester 1 interest, populations, radioactivity), f(x)= - e^x, f(x)= ab^x, inverse function, logarithmic function, logarithmic scales (Richter scale for earthquakes, decibel for acoustic power, entropy, pH for acidity, stellar magnitude scale for brightness of stars), log b x=y, natural logarithms, properties of exponents, range, transformation of functions Unit 5: Asymptote (horizontal, vertical, slant), continuity (continuous, discontinuous, holes/undefined points), domain and range, end behavior, rational function, solutions to rational equations (extraneous solutions and solutions), intercepts (xintercept, y-intercept) Curriculum Overview Map Detroit Public Safety Academy 2015-2016 Course/Subject: ALGEBRA II Grade: 11 Quarter: 3rd Essential Questions-Units-Chapters-Concepts UNIT 6 SEQUENCES AND SERIES: What connections exist between arithmetic and geometric sequences and linear and exponential functions? Given a sequence of numbers, how can you determine if it is arithmetic, geometric, or neither? Find the recursive and explicit formulas for a given arithmetic or geometric sequence. Translate between sigma notation and expanded form. What are the strategies for finding an arithmetic or geometric series? Given an arithmetic or geometric sequence, what information is needed to find the nth term? UNIT 7 QUADRATIC RELATIONS AND CONIC SECTIONS: How can algebraic and geometric ideas be used to explore and connect representations of quadratic relations from the conic sections? What shapes result from passing a plane though a cone? How are the equation and the properties of a circle and ellipse similar and different? Given the equation of a conic section, how can you identify whether the graph will be a circle, ellipse, parabola, or hyperbola? How can you use a line for the directrix and a point for the focus to sketch a resulting parabola? What methods are available to convert an equation in the general conic from into a form more suitable for graphing? Resources (include websites) Atlas Rubicon Oakland Schoolshttps://oaklandk12public.rubiconatlas.org/Atlas/Browse/View /Calendars Pearson- www.pearsonsuccess.net Curriculum Crafterhttps://curriculumcrafter.org/login.aspx Pearson. (2012). Algebra 2 Sims. (2015). Algebra Housewww.algebrahouse.com Kuta Software (2015). https://www.kutasoftware.com/freeia2.htm l Khan Academy, 2015. https://www.khanacademy.org/ Teacher Tube, 2015 www.teachertube.com Learning Focused, 2013. Higher Order Thinking Learning Focused Lessons http://www.learningfocused.com/index.ph p/page/lfs-engaged Standards-CCSS/GLCEs/HSCEs-KC4 Unit 6: A.SSE.B.4, IF.A.3, F.BF.A.2, F.LE.A.1b, F.LE.A.1c, F.LE.A.2 Unit 7: N.CN.A.1, N.CN.A.2, N.CN.A.3, N.CN.C.7, N.CN.C.8, N.CN.C.9, A.SSE.B.3, A.SSE.B.3a, A.SSE.B.3b, A.CED.A.1, A.CED.A.2, A.REI.B.4a, A.REI.B.4b, A.REI.C.7, A.REI.D.10, F.IF.A.1, F.IF.B.4, F.IF.B.5, F.IF.B.6, F.IF.C.7, F.IF.C.7a, F.IF.C.7d, F.IF.C.8, F.IF.C.8a, F.IF.C.9, F.BE.A.1, F.BF.A.1a, F.BF.A.1b, F.BF.B.3, G.GPE.A.1, G.GPE.A.2, G.GPE.A.3, G.GMD.B.4 Vocabulary/Key Concepts Unit 6: Arithmetic sequence, arithmetic series, convergence, divergence, explicit formulas, finite series, geometric series, infinite series, nth term, recursive formulas, subscripted notation, sum of a series, summation/sigma notation Unit 7: Relationship of (circles, ellipses, and hyperbolas to cones), circle, ellipse, parabola, hyperbola, locus of points, completing the square, discriminant, symmetry (lines and axes of graphs of conic sections), major axis and minor axis, transverse axis and conjugate axis, asymptotes, focus, foci, vertex, vertices Assessments/Projects Standard Based Assessment: Interpreting Data through charts, tables and graphs. (Pre/Post x 2) Unit 6 & 7 Assessments (pre/post) STEM Cross Curricular Projects M-STEP & SAT Curriculum Overview Map Detroit Public Safety Academy 2015-2016 Course/Subject: ALGEBRA II Grade: 11 Quarter: 4th Essential Questions-Units-Chapters-Concepts UNIT 8 TRIGONOMETRIC FUNCTIONS: How can the unit circle be used to develop a circular definition of trigonometric functions? What is the relationship between degree and radian measures of angles? Why or when would you use degree or radian? How can the effect of transformations on the sine and cosine curves be seen in the graphs and tables of these functions? How can the unit circle be used to generate the sine and cosine graphs? Why are the trigonometric functions periodic? How do you know if a function is periodic? UNIT 9 PROBABILITY: How can the ideas of independence and conditional probability, along with expected value, be used to evaluate the outcomes of decision in a variety of contexts? How can you generate the numerical values of Pascal’s Triangle? How do you recognize when to use conditional probability rules? What is the difference between permutations and combinations? Give an example of a situation where each would be used. If the probability of an event occurring is p, what is the probability of that event not occurring? Explain why your answer makes sense. What is the meaning of expected value? Resources (include websites) Atlas Rubicon Oakland Schoolshttps://oaklandk12public.rubiconatlas.org/Atlas/Browse/ View/Calendars Pearson- www.pearsonsuccess.net Curriculum Crafterhttps://curriculumcrafter.org/login.asp x Pearson. (2012). Algebra 2 Sims. (2015). Algebra Housewww.algebrahouse.com Kuta Software (2015). https://www.kutasoftware.com/freeia2. html Khan Academy, 2015. https://www.khanacademy.org/ Teacher Tube, 2015 www.teachertube.com Learning Focused, 2013. Higher Order Thinking Learning Focused Lessons http://www.learningfocused.com/index .php/page/lfs-engaged Standards-CCSS/GLCEs/HSCEs-KC4 Unit 8: N.Q.A.2, N.Q.A.3, F.IF.A.2, F.BF.A.1, F.BF.A.1b, F.BF.B.4, F.BF.B.4a, F.BF.B.4c, F.BF.B.4d, A.TF.A.1, A.TF.A.2, F.TF.A.3, F.TF.A.4, F.TF.B.5, F.TF.B.6, F.TF.B.7, F.TF.C.8, F.TF.C.9 Unit 9: F.IF.A.1, F.IF.B.4, F.IF.B.5, F.IF.C.7, F.BF.A.1, F.BF.A.1a, F.BF.B.3, S.CP.A.1, S.CP.A.2, S.CP.A.3, S.CP.A.4, S.CP.A.5, S.CP.B.6, S.CP.B.7, S.CP.B.8, S.CP.B.9, S.MD.A.1, S.MD.A.2, S.MD.A.3, S.MD.A.4, S.MD.B.5, S.MD.B.5b, S.MD.B.6, S.MD.B.7 Vocabulary/Key Concepts Unit 8: Amplitude, asymptote, cosecant, cosine, cotangent, degree and radian relationship and conversion, domain, maxima, minima, period, phase shift, range, relate graphs of trigonometric functions to their inverses, secant, sine, tangent, transformations of trig functions form the parent functions, unit circle Assessments/Projects Standard Based Assessment: Interpreting Data through charts, tables and graphs. (Pre/Post x 2) Unit 8 & 9 Assessments (pre/post) Unit 9: Pascal’s Triangle and its connections to combinations, STEM Cross Curricular Projects Permutation P(n,k)=n!/(n-k)!, Combination C(n,k)=n!/[(n-k)!k!], Fundamental principle of Counting, Tree diagram, Sample space, Final Exam Semester 2 Probability Distribution, Independent vents, Addition Rules for Mutually Exclusive Events, Compound events, Complementary events, Conditional Probability P(A│B)=P(A and B)/P(B), Applications of probability to real-world situations, Simulation, Law of Large Numbers, Expected Value, Two-way Frequency Table