Massachusetts Curriculum Framework



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53 In Algebra I, identify linear and exponential sequences that are defined recursively; continue the study of

sequences in Algebra II.



54 Limit exponential function to the form f(x) = bx + k.

55 Introduce in Algebra I; expand in Algebra II.

56 Linear focus; discuss as a general principle in Algebra I.

57 Adapted from the Common Core State Standards for Mathematics and Appendix A: Designing High School Courses based on the Common Core State Standards for Mathematics

58 Proving the converse of theorems should be included when appropriate.

59 Note: The 2011 Massachusetts grade 8 mathematics standards require that students know volume formulas for

cylinders, cones, and spheres.



60 Link to data from simulations or experiments.

61 Introductory only.

62 Replacing the hockey goalie with an extra skater.

63 Adapted from the Common Core State Standards for Mathematics and Appendix A: Designing High School Courses based on the Common Core State Standards for Mathematics.

64 The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.

65 Replacing the hockey goalie with an extra skater.

(+) indicates standard beyond College and Career Ready.



66 Adapted from the Common Core State Standards for Mathematics and Appendix A: Designing High School Courses based on the Common Core State Standards for Mathematics

67 Foundation for work with expressions, equations, and functions.

68 Limit Mathematics I to linear and exponential equations with integer exponents.

69 Limit Mathematics I to linear and exponential equations with integer exponents.

70 Limit to linear equations and inequalities.

71 Master for linear equations and inequalities; learn as general principle to be expanded in Mathematics II and III.

72 Limit Mathematics I to linear inequalities and exponential of a form 2x = 1/16.

73 Limit Mathematics I to systems of linear equations.

74 Limit Mathematics I to linear and exponential equations; learn as general principle to be expanded in

Mathematics II and III.



75 Focus on linear and exponential functions with integer domains and on arithmetic and geometric sequences.

76 Focus on linear and exponential functions with integer domains.

77 Limit Mathematics I to linear and exponential functions with integer domains.

78 Limit Mathematics I to linear and exponential functions with integer domains.

79 Limit Mathematics I to linear and exponential functions; focus on vertical translations for exponential functions.

80 Limit Mathematics I to linear and exponential models.

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82 Build on rigid motions as a familiar starting point for development of geometric proof.

83 Formalize proof, and focus on explanation of process.

84 Include the distance formula and relate to the Pythagorean Theorem.

85 Focus on linear applications; learn as general principle to be expanded in Mathematics II and III.

86 Adapted from the Common Core State Standards for Mathematics and Appendix A: Designing High School Courses based on the Common Core State Standards for Mathematics.

87 Limit Mathematics II to as highest power of i.

88 Limit Mathematics II to quadratic equations with real coefficients.

89 Expand to include quadratics and exponential expressions.

90 Expand to include quadratics and exponential expressions.

91 Focus on adding and multiplying polynomial expressions; factor expressions to identify and collect like terms; and

apply the distributive property.



92 Include formulas involving quadratic terms.

93 Limit to quadratic equations with real coefficients.

94 Expand to include linear/quadratic systems.

95 Expand to include quadratic functions.

96 Limit Mathematics II to linear, exponential, quadratic, piecewise-defined, and absolute value functions.

97 Expand to include quadratic and exponential functions.

(+) indicates standard beyond College and Career Ready.



98 Expand to include quadratic and absolute value functions.

99 Focus on validity underlying reasoning and use a variety of ways of writing proofs.

100 Focus on validity underlying reasoning and use a variety of ways of writing proofs.

101 Limit Mathematics II use of radian to unit of measure.

102 Include simple circle theorems.

103 Link to data from simulations and/or experiments.

104 Introductory only; apply counting rules.

105 Replacing the hockey goalie with an extra skater.

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Massachusetts Curriculum Framework for Mathematics Public Comment Draft November 29, 2016
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