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# Math Appendix A

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### Math Appendix A

1. 1. common core state stanDarDs Formathematicsappendix a:Designing High schoolmathematics coursesBased on the commoncore state standards
6. 6. Common Core State StandardS for matHematICS How to read the Pathways: Each pathway consists of two parts. The first is a chart that shows an overview of the pathway. Organized by course and by conceptual category (algebra, functions, geometry, etc…), these charts show which clusters and standards appear in which course (see page 5 of the CCSS for definitions of clusters and standards). For example, in the chart below, the three standards (N.Q.1, 2, 3) associated with the cluster “Reason quantitatively and use units to solve problems,” are found in Course 1. This cluster is found under the domain “Quantities” in the “Number and Quantity” conceptual category. All high school standards in the CCSS are located in at least one of the courses in this chart. courses Domain appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | clusters, notes, and standardsconceptualcategory 6
7. 7. Common Core State StandardS for matHematICS The second part of the pathways shows the clusters and standards as they appear in the courses. Each course contains the following components: • An introduction to the course and a list of the units in the course • Unit titles and unit overviews (see below) • Units that show the cluster titles, associated standards, and instructional notes (below) It is important to note that the units (or critical areas) are intended to convey coherent groupings of content. The clusters and standards within units are ordered as they are in the Common Core State Standards, and are not intended to convey an instructional order. Considerations regarding constraints, extensions, and connections are found in the instructional notes. The instructional notes are a critical attribute of the courses and should not be overlooked. For example, one will see that standards such as A.CED.1 and A.CED.2 are repeated in multiple courses, yet their emphases change from one course to the next. These changes are seen only in the instructional notes, making the notes an indispensable component of the pathways. Unit title and appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | overview standards associated with clustercluster Instructional note 7
8. 8. Common Core State StandardS for matHematICSoverview of the traditional Pathway forthe common core state mathematics standardsThis table shows the domains and clusters in each course in the Traditional Pathway. The standards from each cluster includedin that course are listed below each cluster. For each course, limits and focus for the clusters are shown in italics. Domains High School Algebra I Geometry Algebra II Fourth Courses * • xtend the properties E of exponents to rational exponents. The Real N.RN.1, 2 Number System • se properties of U rational and irrational numbers. appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | N.RN.3 • eason quantitatively R and use units to solve problems. Quantities Foundation for work with expressions, equations and functions N.Q.1, 2, 3 • erform arithmetic P • erform arithmetic P Number and Quantity operations with operations with complex numbers. complex numbers. N.CN.1, 2 (+) N.CN.3 The Complex Number • se complex numbers U • epresent complex R System in polynomial identities numbers and their and equations. operations on the complex plane. Polynomials with real coefficients (+) N.CN.4, 5, 6 N.CN.7, (+) 8, (+) 9 • epresent and model R with vector quantities. (+) N.VM.1, 2, 3 • Perform operations on vectors. Vector (+) N.VM.4a, 4b, 4c, 5a, Quantities and 5b Matrices • Perform operations on matrices and use matrices in applications. (+) N.VM.6, 7, 8, 9, 10, 11, 12*The (+) standards in this column are those in the Common Core State Standards that are not included in any of the Traditional Pathway courses.They would be used in additional courses developed to follow Algebra II. 8
9. 9. Common Core State StandardS for matHematICS Domains High School Algebra I Geometry Algebra II Fourth Courses • nterpret the structure I • nterpret the structure I of expressions. of expressions. Linear, exponential, Polynomial and rational quadratic A.SSE.1a, 1b, 2 A.SSE.1a, 1b, 2 Seeing • rite expressions in W Structure in equivalent forms to • rite expressions in W Expressions solve problems. equivalent forms to solve problems. A.SSE.4 Quadratic and exponential A.SSE.3a, 3b, 3c • erform arithmetic P • erform arithmetic P operations on operations on polynomials. polynomials. appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | Linear and quadratic Beyond quadratic A.APR.1 A.APR.1 • nderstand the U relationship betweenAlgebra zeros and factors of Arithmetic polynomials. with A.APR.2, 3 Polynomials and Rational • se polynomial U Expressions identities to solve problems. A.APR.4, (+) 5 • ewrite rational R expressions. Linear and quadratic denominators A.APR.6, (+) 7 • reate equations that C • reate equations that C describe numbers or describe numbers or relationships. relationships. Creating Linear, quadratic, and Equations using all Equations exponential (integer available types of inputs only); for A.CED.3 expressions, including linear only simple root functions A.CED.1, 2, 3, 4 A.CED.1, 2, 3, 4 9
10. 10. Common Core State StandardS for matHematICS Domains High School Algebra I Geometry Algebra II Fourth Courses • nderstand solving U • nderstand solving U • olve systems of S equations as a process equations as a process equations. of reasoning and of reasoning and (+) A.REI.8, 9 explain the reasoning. explain the reasoning. Master linear; learn as Simple radical and general principle rational A.REI.1 A.REI.2 • olve equations and S • epresent and R inequalities in one solve equations and variable. inequalities graphically. Linear inequalities; Combine polynomial, literal that are linear rational, radical, in the variables being absolute value, and ReasoningAlgebra solved for; quadratics exponential functions with with real solutions appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | Equations and A.REI.11 Inequalities A.REI.3, 4a, 4b • olve systems of S equations. Linear-linear and linear- quadratic A.REI.5, 6, 7 • epresent and R solve equations and inequalities graphically. Linear and exponential; learn as general principle A.REI.10, 11, 12 • nderstand the U • nterpret functions that • nalyze functions I A concept of a function arise in applications in using different and use function terms of a context. representations. notation. Emphasize selection of Logarithmic and Learn as general appropriate models trigonometric functions principle; focus on F.IF.4, 5, 6 (+) F.IF.7d linear and exponential and on arithmetic and • nalyze functions A geometric sequences using different F.IF.1, 2, 3 representations. Focus on using key • nterpret functions that IFunctions features to guide arise in applications in Interpreting selection of appropriate terms of a context. Functions type of model function Linear, exponential, and F.IF.7b, 7c, 7e, 8, 9 quadratic F.IF.4, 5, 6 • nalyze functions A using different representations. Linear, exponential, quadratic, absolute value, step, piecewise- defined F.IF.7a, 7b, 7e, 8a, 8b, 9 10
11. 11. Common Core State StandardS for matHematICS Domains High School Algebra I Geometry Algebra II Fourth Courses • uild a function that B • uild a function that B • uild a function that B models a relationship models a relationship models a relationship between two between two between two quantities. quantities. quantities. For F.BF.1, 2, linear, Include all types of (+) F.BF.1c exponential, and functions studied quadratic • uild new functions B F.BF.1b from existing F.BF.1a, 1b, 2 functions. • uild new functions B Building • uild new functions B from existing (+) F.BF.4b, 4c, 4d, 5 Functions from existing functions. functions. Include simple Linear, exponential, radical, rational, and quadratic, and absolute exponential functions; value; for F.BF.4a, linear emphasize common appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | only effect of each transformation across F.BF.3, 4a function types F.BF.3, 4a • onstruct and C • onstruct and C compare linear, compare linear, quadratic, and quadratic, and exponential models exponential modelsFunctions and solve problems. and solve problems. Linear, F.LE.1a, 1b, 1c, 2, 3 Logarithms as solutions Quadratic, and for exponentials Exponential • nterpret expressions I F.LE.4 Models for functions in terms of the situation they model. Linear and exponential of form f(x)=bx+k F.LE.5 • xtend the domain E • xtend the domain E of trigonometric of trigonometric functions using the functions using the unit circle. unit circle. F.TF.1, 2 (+) F.TF.3, 4 • odel periodic M • odel periodic M Trigonometric phenomena with phenomena with Functions trigonometric trigonometric functions. functions. F.TF.5 (+) F.TF. 6, 7 • rove and apply P • rove and apply P trigonometric trigonometric identities. identities. F.TF.8 (+) F.TF. 9 11
12. 12. Common Core State StandardS for matHematICS Domains High School Algebra I Geometry Algebra II Fourth Courses • xperiment with E transformations in the plane. G.CO.1, 2, 3, 4, 5 • nderstand U congruence in terms of rigid motions. Build on rigid motions as a familiar starting point for development of concept of geometric proof G.CO.6, 7, 8 Congruence appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | • rove geometric P theorems. Focus on validity of underlying reasoning while using variety of ways of writing proofs G.CO.9, 10, 11Geometry • ake geometric M constructions. Formalize and explain processes G.CO.12, 13 • nderstand similarity U in terms of similarity transformations. G.SRT.1a, 1b, 2, 3 • rove theorems P involving similarity. Similarity, G.SRT.4, 5 Right Triangles, and • efine trigonometric D Trigonometry ratios and solve problems involving right triangles. G.SRT.6, 7, 8 • pply trigonometry to A general triangles. G.SRT.9. 10, 11 12
13. 13. Common Core State StandardS for matHematICS Domains High School Algebra I Geometry Algebra II Fourth Courses • nderstand and U apply theorems about circles. G.C.1, 2, 3, (+) 4 Circles • ind arc lengths and F areas of sectors of circles. Radian introduced only as unit of measure G.C.5 • ranslate between the T • ranslate between the T geometric description geometric description and the equation for a and the equation for a conic section. conic section. appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | G.GPE.1, 2 (+) G.GPE.3 Expressing Geometric • se coordinates UGeometry Properties to prove simple with Equations geometric theorems algebraically. Include distance formula; relate to Pythagorean theorem G.GPE. 4, 5, 6, 7 • xplain volume E • xplain volume E formulas and use them formulas and use them to solve problems. to solve problems. G.GMD.1, 3 (+) G.GMD.2 Geometric Measurement • isualize the relation V and Dimension between two- dimensional and three- dimensional objects. G.GMD.4 • pply geometric A Modeling with concepts in modeling Geometry situations. G.MG.1, 2, 3 • ummarize, represent, S • ummarize, represent, S and interpret data and interpret data on a single count or on a single count or measurement variable. measurement variable.Statistics and Probability S.ID.1, 2, 3 S.ID.4 Interpreting • ummarize, represent, S Categorical and interpret data on and two categorical and Quantitative quantitative variables. Data Linear focus, discuss general principle S.ID.5, 6a, 6b, 6c • nterpret linear models I S.ID.7, 8, 9 13
14. 14. Common Core State StandardS for matHematICS Domains High School Algebra I Geometry Algebra II Fourth Courses • nderstand and U evaluate random processes underlying statistical experiments. Making S.IC.1, 2 Inferences and Justifying • ake inferences and M Conclusions justify conclusions from sample surveys, experiments and observational studies. S.IC.3, 4, 5, 6 • nderstand U independence and conditional probabilityStatistics and Probability appendIx a: deSIgnIng HIgH SCHool matHematICS CourSeS baSed on tHe Common Core State StandardS | and use them to interpret data. Link to data from simulations or Conditional experiments Probability and the Rules S.CP.1, 2, 3, 4, 5 of Probability • se the rules of U probability to compute probabilities of compound events in a uniform probability model. S.CP.6, 7, (+) 8, (+) 9 • se probability to U • se probability to U • alculate expected C evaluate outcomes of evaluate outcomes of values and use them to decisions. decisions. solve problems. Using Introductory; apply Include more complex (+) S.MD.1, 2, 3, 4 Probability counting rules situations to Make • se probability to U Decisions (+) S.MD.6, 7 (+) S.MD.6, 7 evaluate outcomes of decisions.. (+) S.MD. 5a, 5b 14