The two areas of focus at the kindergarten level are representing and comparing whole numbers and describing shapes and space. Students use numbers to represent quantities and to solve quantitative problems. They choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away. Students describe their physical world using geometric ideas. They identify, name, and describe basic two-dimensional shapes. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.
The areas of focus at the first grade level are developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; developing understanding of whole number relationships and place value; developing understanding of linear measurement; and reasoning about attributes of, and composing and decomposing geometric shapes. Students employ use of a variety of models in developing strategies for adding and subtracting whole numbers. They understand connections between counting and addition and subtraction. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction. Students develop methods to add within 100 and subtract multiples of 10. Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes. In addressing measurement, students develop an understanding of the meaning, underlying concepts, and processes of measurement. Finally, as students at the first grade level combine shapes and build understanding of part-whole relationships, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different.
The areas of focus at the second grade level are extending understanding of base-ten notation, building fluency with addition and subtraction, using standard units of measure, and describing and analyzing shapes. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones. Students use their understanding of addition to develop fluency with addition and subtraction. They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds. Students recognize the need for standard units of measure, and they use rulers and other measurement tools with the understanding that linear measure involves an iteration of units. Finally, students describe and analyze shapes by examining their sides and angles. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades.
The areas of focus at the third grade level are developing understanding of multiplication and division and strategies for multiplication and division within 100, developing understanding of fractions, developing understanding of the structure of rectangular arrays and of areas, and describing and analyzing two-dimensional shapes. Students develop an understanding of the meanings of multiplication and division of whole numbers. They use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division. Students develop an understanding of fractions. They are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. Students recognize area as an attribute of two-dimensional regions. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles and connect these with definitions of shapes.
The areas of focus at the fourth grade level are developing understanding and fluency with multi-digit multiplication and developing understanding of dividing to find quotients involving multi-digit dividends; developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and understanding that geometric figures can be analyzed and classified based on their properties. Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.
The areas of focus at the fifth grade level are developing fluency with addition and subtraction of fractions and developing understanding of the multiplication of fractions and of division of fractions in limited cases; extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and developing understanding of volume. Students apply their understanding of fractions and reaction models to represent the addition and subtraction of fractions. Multiplication and division of fractions is limited at this level. Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They compute products and quotients of decimals to hundredths efficiently and accurately. Students recognize volume as an attribute of three-dimensional space. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They measure necessary attributes of shapes in order to determine volumes to solve real-world and mathematical problems.
......................................................................................................................................... Published by Valerie Robinson on January 23, 2018 |

Mathematics Curriculum Standards for Grades K-5