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New York State Math a and B Key Ideas and Performance Indicators

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New York State Math a and B Key Ideas and Performance Indicators High School Math A Math B Some Manipulatives Algebra tiles Mirrors or miras Volume demonstration kits Dice Spinners Measuring tools Geometric models Geoboards Compasses Tessellation tiles Conic section models PentaBlocks Calculator Calculators will be required for use on Math A and B assessments. Scientific calculators are required for the Math A Regents examinations. Graphing calculators that do not allow for symbolic manipulation will be required for the Math B Regents examination and will be permitted (not required) for the Math A Regents examination starting in June 2000. Note The Math A exam may include any given topic listed in the Core Curriculum with any performance indicator. The con- tent includes most of the topics in the present Course I and a selection of topics from Course II. Programs other than Course I and II could be used as long as all the performance indicators and topics in the curriculum are part of the pro- gram. Examples of assessment items for Math A have been provided for most performance indicators. The items were taken from the 1997 pilot test and 1998 Test Sampler. Suggestions for classroom activities are substituted for any perfor- mance indicator that was not included in the sample test. The Math B exam may include any given topic listed in the Core Curriculum with any performance indicator. Programs other than Course II and III could be used as long as the performance indicators and topics mentioned are part of the program. Since there is no Math B exam at this time, no assessment items have been included for Math B. Suggestions for possible classroom activities or problems are given instead to provide clarification of most performance indicators. 117 ath A Key Idea 1 M Mathematical Reasoning Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument. PERFORMANCE INDICATORS INCLUDES EXAMPLES 1A. Construct valid arguments. • Truth value of compound sentences See Assessment Example 1A. (conjunction, disjunction, condi- tional, related conditionals such as converse, inverse, and contraposi- tive, and biconditional). • Truth value of simple sentences (closed sentences, open sentences with replacement set and solution set, negations). 1B. Follow and judge the validity of • Truth value of compound See Assessment Example 1B. arguments. sentences. 118 Key Idea 2 ath A Number and Numeration M Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas. PERFORMANCE INDICATORS INCLUDES EXAMPLES 2A. Understand and use rational and irra- • Real numbers including irrational See Assessment Example 2A. tional numbers. numbers such as non-repeating decimals, irrational roots, and pi. 2B. Recognize the order of real numbers. • Rational approximations of irra- See Assessment Example 2B. tional numbers. 2C. Apply the properties of real numbers to • Properties of real numbers includ- See Classroom Idea 2C. various subsets of numbers. ing closure, commutative, associa- tive, and distributive properties, and inverse and identity elements. 119 ath A Key Idea 3 M Operations Students use mathematical operations and relationships among them to under- stand mathematics. PERFORMANCE INDICATORS INCLUDES EXAMPLES 3A. Use addition, subtraction, multiplication, • Signed numbers. See Assessment Example 3A. division, and exponentiation with real • Use of variables: order of opera- numbers and algebraic expressions. tions and evaluating algebraic expressions and formulas. • Addition and subtraction of poly- nomials: combining like terms and fractions with like denominators. • Multiplication of polynomials: powers, products of monomials and binomials, equivalent fractions with unlike denominators, and multiplication of fractions. • Simplification of algebraic expres- sions. • Division of polynomials by mono- mials. • Operations with radicals: simplifi- cation, multiplication and division, and addition and subtraction. • Scientific notation. • Simplification of fractions. • Division of fractions. • Prime factorization. • Factoring: common monomials, binomial factors of trinomials. • Difference of two squares. 3B. Use integral exponents on integers and • Powers: positive, zero, and See Assessment Example 3B. algebraic expressions. negative exponents. 3C. Recognize and identify symmetry and • Intuitive notions of line reflection, See Assessment Example 3C. transformations on figures. translation, rotation, and dilation. • Line and point symmetry. 3D. Use field properties to justify mathemati- • Distributive and associative field See Classroom Idea 3D. cal procedures. properties as related to the solution of quadratic equations. • Distributive field property as relat- ed to factoring. 120 Key Idea 4 ath A Modeling/Multiple Representation M Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical informa- tion and relationships. PERFORMANCE INDICATORS INCLUDES EXAMPLES 4A. Represent problem situations symbolical- • Use of variables/Algebraic repre- See Assessment Example 4A. ly by using algebraic expressions, sentations. sequences, tree diagrams, geometric fig- • Inequalities. ures, and graphs. • Formulas and literal equations. • Undefined terms: point, line, and pl a n e . • Parallel and intersecting lines and perpendicular lines. • Angles: degree measure, right, acute, obtuse, straight, supplemen- tary, complementary, vertical, alter- nate interior and exteriors, and corresponding. • Simple closed curves: polygons and circles. • Sum of interior and exterior angles of a polygon. • Study of triangles: classifications of scalene, isosceles, equilateral, acute, obtuse, and right; triangular inequality; sum of the measures of angles of a triangle; exterior angle of a triangle, base angles of an isosceles triangle. • Study of quadrilaterals: classifica- tion and properties of parallelo- grams, rectangles, rhombi, squares, and trapezoids. • Study of solids: classification of prism, rectangular solid, pyramid, right cir- cular cylinder, cone, and sphere. • Sample spaces: list of ordered pairs of n-tuples, tree diagrams. 4B. Justify the procedures for basic geometric • Basic constructions: copy line and See Classroom Idea 4B. constructions. angle, bisect line segment and angle, perpendicular lines and par- allel lines. • Comparison of triangles: congru- ence and similarity. 4C. Use transformations in the coordinate • Reflection in a line and in a point. See Assessment Example 4C. plane. • Translations. • Dilations. 121 ath A Key Idea 4 M Modeling/Multiple Representation Continued PERFORMANCE INDICATORS INCLUDES EXAMPLES 4D. Develop and apply the concept of basic • Locus. See Assessment Example 4D. loci to compound loci. • At a fixed distance from a point. • At a fixed distance from a line. • Equidistant from two points. • Equidistant from two parallel lines. • Equidistant from two intersecting lines. • Compound locus. 4E. Model real-world problems with systems • Systems of linear equations and See Assessment Example 4E. of equations and inequalities. inequalities. 122 Key Idea 5 ath A Measurement M Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data. PERFORMANCE INDICATORS INCLUDES EXAMPLES 5A. Apply formulas to find measures such as • Perimeter of polygons and circum- See Assessment Example 5A. length, area, volume, weight, time, and ference of circles. angle in real-world contexts. • Area of polygons and circles. • Volume of solids. • Pythagorean theorem. 5B. Choose and apply appropriate units and • Converting to equivalent measure- See Classroom Idea 5B. tools in measurement situations. ments within metric and English measurement systems. • Direct and indirect measure. 5C. Use dimensional analysis techniques. • Dimensional analysis. See Assessment Example 5C. 5D. Use statistical methods including the mea- • Collecting and organizing data: See Assessment Example 5D. sures of central tendency to describe and sampling, tally, chart, frequency compare data. table, circle graphs, broken line graphs, frequency histogram, box and whisker plots, scatter plots, stem and leaf plots, and cumula- tive frequency histogram. • Measures of central tendency: mean, median, mode. • Quartiles and percentiles. 5E. Use trigonometry as a method to measure • Right triangle trigonometry. See Assessment Example 5E. indirectly. 5F. Apply proportions to scale drawings and • Ratio. See Assessment Example 5F. direct variation. • Proportion. • Scale drawings. • Percent. • Similar figures. • Similar polygons: ratio of perime- ters and areas. • Direct variation. 5G. Relate absolute value, distance between • Absolute value and length of a line See Assessment Example 5G. two points, and the slope of a line to the segment. coordinate plane. • Midpoint of a segment. • Equation of a line: point-slope and slope intercept form. • Comparison of parallel and per- pendicular lines. 123 ath A Key Idea 5 M Measurement Continued PERFORMANCE INDICATORS INCLUDES EXAMPLES 5H. Explain the role of error in measurement • Error of measurement and its con- See Classroom Idea 5H. and its consequence on subsequent sequences on calculation of calculations. perimeter of polygons and circum- ference of circles. • Area
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