Grade-Level General Education Curriculum Expectations for Math
Kindergarten students learn to count to 100 and write numbers to 20. Attention is given to numbers 11-20 where emphasis is placed on tens and ones building a foundation for place value understanding. Beginning addition and subtraction starts in kindergarten. Students sort and classify groups of objects and identify basic shapes.
First grade students extend their understanding of addition and subtraction by learning to use adding and subtracting to solve word problems within 20. They understand the meaning of the equal sign and are expected to count to 120. Place value knowledge is deepened and students use this knowledge to compare two-digit numbers within 100. Students practice their measurement skills with linear measurement and begin to organize data from surveys. Students also tell and write time in hours and half-hours using analog and digital clocks.
Second grade students use addition and subtraction within 100 to solve word problems and are expected to know from memory all sums of two one-digit numbers by the end of second grade. Place value understanding is extended to 1000 and students compare three digit numbers based on their knowledge of hundreds, tens and ones. Second grade students compute with money and learn to estimate and compare lengths using appropriate measurement tools. Second graders refine their understanding of geometry by drawing shapes based on the number of faces and angles.
Third grade students develop an understanding of multiplication and division and learn to fluently multiply and divide within 100. Students are expected to know from memory all products of two one-digit numbers by the end of third grade. Place value understanding is used for multi-digit computation and estimation. Fractions are introduced in the third grade with an emphasis on understanding fractions as numbers and their relative size and placement on the number line. In third grade students understand concepts of area and perimeter and solve problems using liquid volume and mass.
Fourth graders use their knowledge of place value to generalize to 1,000,000 and learn to round multi-digit whole numbers to any place. They fluently add and subtract using the standard algorithm and multiply and divide with multi-digit numbers. Fourth graders extend understanding of fractions to include equivalence, ordering and simple decimal notation. Students measure angles and classify geometric shapes by lines (parallel, perpendicular, etc.) and angles (right, acute, obtuse, etc.).
Fifth grade students finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understanding of fractions to the addition and subtraction of fractions with unlike denominators, the concept of fraction multiplication and division, and decimal addition and subtraction. They analyze numeric patterns and relationships and graph ordered pairs on a coordinate plane. Students build on their understanding of geometry by recognizing attributes of geometrical shapes and calculating inside angle measurement and area of triangles and parallelograms.
Sixth grade students use their knowledge of multiplication and division to solve ratio and rate problems. They finalize their understanding of division of fractions and begin the study of negative integers. They understand the use of variables in mathematical expressions, write expressions and equations that correspond to situations, and use expressions and equations to solve problems. Students begin the study of probability and statistics and use their geometrical foundations to solve problems involving area, surface area, and volume.
Seventh grade students deepen their understanding of proportional relationships to solve complicated problems. They extend their understanding of rational numbers to include computation (add, subtract, multiply, and divide). Irrational numbers are introduced in seventh grade. Algebraic foundations are practiced and extended. Students continue to extend their understanding of probability and statistics by describing populations based on sampling, and investigate chance to develop, use, and evaluate probability models.
Eighth grade students deepen their understanding of rational and irrational numbers. Algebraically, students compute with radicals and exponents, solve linear equations and define, solve, compare, and graph functions. In geometry, eighth grade students understand and use the Pythagorean Theorem and solve problems involving volumes of cylinders, cones, and spheres.
Students in Mathematics I focus on deepening and extending understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Mathematics 1 uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied.
Students in Mathematics II focus on quadratic expressions, equations, and functions; comparing their characteristics and behavior to those of linear and exponential relationships from Mathematics I as organized into six critical areas, or units. The need for extending the set of rational numbers arises and real and complex numbers are introduced so that all quadratic equations can be solved. The link between probability and data is explored through conditional probability and counting methods, including their use in making and evaluating decisions. The study of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships. Circles, with their quadratic algebraic representations, round out the course.
Students in Mathematics III apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include polynomial, rational and radical functions. They expand their study of right triangle trigonometry to include general triangles. Finally, students bring together all of their experience with functions and geometry to create models and solve contextual problems.
Students in Mathematics IV take an extensive look at the relationships among complex numbers, vectors, and matrices. They build on their understanding of functions, analyze rational functions using an intuitive approach to limits and synthesize functions by considering compositions and inverses. Students expand their work with trigonometric functions and their inverses and complete the study of the conic sections begun in Mathematics II. They enhance their understanding of probability by considering probability distributions. Previous experiences with series are augmented.