Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content
The Standards for Mathematical Practice( http://www.corestandards.org/Math/Practice) describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.
The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.
This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. This course emphasizes developing skills and processes to successfully solve problems and become more mathematically confident through the study of elementary algebra. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe for students to experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. It is aligned to the Common Core Learning Standards and is intended to be the second year of a three year sequence. This course employs an integrated approach to the study of connecting algebra to geometric relationships and proofs. Properties of triangles, quadrilaterals, and circles will receive particular attention. Congruence and similarity of triangles will be established using appropriate theorems; transformations including rotations, reflections, translations, and glide reflections and coordinate geometry will be used to establish and verify geometric relationships; and topics in trigonometry extending to three-dimensional geometry will be explored.
This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. It is aligned to the New York State Learning Standards for Mathematics and is intended to be the third year of a three-year sequence. In Algebra 2, students will further develop the concepts learned in Algebra 1 and Geometry and extend those into advanced algebraic applications that require more complex and technical calculations and transformations, but sense-making is still paramount. Topics of study include: the Real and Complex Number systems; seeing structure in expressions; arithmetic with polynomials and rational expressions; creating equations; reasoning with equations and inequalities; building and interpreting functions; linear, quadratic, logarithmic, and exponential models; trigonometric functions; expressing geometric properties with equations; interpreting categorical and quantitative data; making inferences and justifying conclusions; and conditional probability and the rules of probability.
This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. It is aligned to the New York State Learning Standards for Mathematics and is highly recommended preparation for students whose plans include the possibility of formal education beyond high school. In Pre-Calculus, students will further develop the concepts learned in Algebra 2 and extend those into advanced applications that require more complex and technical calculations while sense-making is still paramount. Topics of study include: fundamental concepts of algebra, polynomial equations of higher degrees, complex numbers, solving equations and inequalities, functions and graphs, polynomial functions, rational functions and functions involving radicals, exponential and logarithmic functions, trigonometric functions, sequences and series, conic sections, and advanced probability and stats. The main goal of this course is for students to continue their formal study of functions begun in Algebra 1 and Algebra 2 and develop a deeper understanding of the fundamental concepts and relationships of functions while to reinforcing one’s mathematical skills in preparation for college.
Explore the concepts, methods, and applications of differential and integral calculus. You’ll work to understand the theoretical basis and solve problems by applying your knowledge and skills.
Unit 1: Limits and Continuity
Unit 2: Differentiation: Definition and Fundamental Properties
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 4: Contextual Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
Unit 6: Integration and Accumulation of Change
Unit 7: Differential Equations
Unit 8: Applications of Integration
Learn about the major concepts and tools used for collecting, analyzing, and drawing conclusions from data. You’ll explore statistics through discussion and activities, and you'll design surveys and experiments.
Unit 1: Exploring One-Variable Data
Unit 2: Exploring Two-Variable Data
Unit 3: Collecting Data
Unit 4: Probability, Random Variables, and Probability Distributions
Unit 5: Sampling Distributions
Unit 6: Inference for Categorical Data: Proportions
Unit 7: Inference for Quantitative Data: Means
Unit 8: Inference for Categorical Data: Chi-Square
Unit 9: Inference for Quantitative Data: Slopes
Next Generation Standards
Using the Core Curriculum Learning Standards as a foundation for mathematics instruction, teachers engage their students in a rigorous mathematics program and study of looking at student work. Innovative teaching strategies include use of the workshop model, student grouping, standard and alternate assessment, and hands-on instruction with the use of manipulatives, with a concentrated focus on critical thinking, problem solving and the metacognitive process.