KINDERGARTEN
By the end of kindergarten, students understand the consistency of small numbers, quantities and simple shapes in their everyday environment. They count, compare, describe and sort objects, and develop a sense about properties and patterns.
GRADE 1
By the end of first grade, students understand and use the concept of "ones" and "tens" in the place value number system. They add and subtract small numbers with ease. They measure with simple units and locate objects in space. They describe data and analyze and solve simple problem situations.
GRADE 2
By the end of second grade, students understand place value and number relationships as they add and subtract and they use simple concepts of multiplication. They measure quantities with appropriate units. They classify and see relationships among shapes by paying attention to the elements that compose them. They collect and analyze data and verify answers.
GRADE 3
By the end of third grade, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication and division of whole numbers. They estimate, measure and describe objects in space. They use patterns to help solve problems. They represent number relationships and conduct simple probability experiments.
GRADE 4
By the end of fourth grade, students understand large numbers and addition, subtraction, multiplication and division of whole numbers. They describe and compare simple fractions and decimals. They understand the properties of and the relationships between plane geometric figures. They collect, represent and analyze data to answer questions.
GRADE 5
By the end of fifth grade, students increase their facility with the four basic arithmetic operations applied to positive and negative numbers, fractions and decimals. They know and use common measuring units to determine length and area; they know and use formulas to determine the volume of simple geometric figures. Students know the concept of angle measurement and use a protractor and compass in solving problems. They use grids, tables, graphs, and charts to record and analyze data.
GRADE 6
By the end of sixth grade, students have mastered the four arithmetic operations with positive and negative numbers, whole numbers, fractions and decimals; they accurately compute and solve problems. They apply their knowledge to statistics and probability. Students understand the concept of and how to calculate the range, mean, median and mode of data sets. They analyze data and sampling processes for possible bias and misleading conclusions, and they use addition and multiplication of fractions routinely to calculate probabilities for compound events. Students conceptually understand and work with ratios and proportions; they compute percentages (e.g., tax, tips, interest). Students know about p and the formulas for the circumference and area of a circle. They use letters for numbers in formulas involving geometric shapes and in representing an unknown part of a ratio. They solve 1-step linear equations.
GRADE 7
By the end of seventh grade students are adept at manipulating numbers and equations and understand the general principles at work. They understand and use factoring of numerator and denominators and properties of exponents. They know the Pythagorean Theorem and solve problems where they compute the length of an unknown side. Students know how to compute the surface area and volume of basic 3-D objects and understand how they change under a change in scale. Students convert between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percent) and are proficient at changing from one to another. They increase their facility with ratio and proportion and compute percentages of increase and decrease and simple compound interest. They graph linear functions and understand the idea of slope and its relation to ratio.
ALGEBRA I
Symbolic reasoning and calculations with symbols are central in algebra. In the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem solving situations.
GEOMETRY
The geometric skills and concepts developed in this discipline are useful to all students. Aside from these skills and concepts, students will develop their ability to construct formal logical arguments and proofs in geometric settings and problems.
ALGEBRA II
This discipline complements and expands the mathematical content and concepts of Algebra I and Geometry. Students who master Algebra II will gain experience with algebraic solutions of problems in various content areas, including the solution of systems of quadratic equations, logarithmic and exponential functions, the binomial theorem, and the complex number system.
TRIGONOMETRY
Trigonometry is a discipline that utilizes the techniques of both the algebra and geometry that students have previously learned. The trigonometric functions studied are defined geometrically, rather than in terms of algebraic equations. Facility with these functions as well as being able to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college.
MATHEMATICAL ANALYSIS
This discipline combines many of the trigonometric, geometric, and algebraic techniques needed for the preparation of the study of Calculus, and strengthens conceptual understanding and mathematical reasoning when solving problems. These standards take a functional point of view to these topics. The most significant new concept is that of limits. Mathematical Analysis is often combined with Trigonometry or perhaps Linear Algebra to make a year long pre-Calculus course.
LINEAR ALGEBRA
The general goal in this discipline is that students learn the techniques of matrix manipulation so as to be able to solve systems of linear equations in any number of variables. Linear Algebra is most often combined with another subject, such as Trigonometry, Mathematical Analysis, or Pre-Calculus.
PROBABILITY AND STATISTICS
This discipline is an introduction to the study of probability, interpretation of data, and fundamental statistical problem solving. Mastery of this academic content will provide students with a solid foundation in probability and facility with processing statistical information.
PROBABILITY AND STATISTICS -Advanced
This discipline is a technical and in depth extension of probability and statistics. In particular, mastery of advanced placement academic content gives students the background for success on the Advanced Placement exam in the subject.
CALCULUS
When taught in high school, calculus should be presented with the same level of depth and rigor as entry level college and university calculus courses. These standards outline a complete college curriculum in one variable calculus. It is recognized that many high school programs may have insufficient time to cover all of the following content in a typical academic year. For example some districts may treat differential equations lightly and spend substantial time on infinite sequences and series. Others may do the opposite. Consideration of the College Board syllabi for the AB and BC Advanced Placement exams may be helpful in making curricular decisions. Calculus is a widely applied area of mathematics, and also involves a beautiful intrinsic theory. Students mastering this content will be exposed to both these important aspects of the subject.