The Common Core State Standards Initiative, adopted by 45 out of 50 states by July 2013, details the key concepts taught in elementary schools nationwide. The Common Core, as it is usually called, identifies five domains for elementary mathematics. These domains are Counting & Cardinality, Operations & Algebraic Thinking, Number & Operations, Measurement & Data and Geometry. Key skills and concepts within these domains are introduced and reinforced as students move through the grades. It is common for teachers to revisit lessons from previous grades at the reintroduction of each topic, reviewing and reinforcing the basic information that students should have already mastered before moving on to new details and skills.

Counting & Cardinality

Counting & Cardinality primarily applies to children in kindergarten. Within this domain, young students learn the names of whole numbers and the correct sequencing of these numbers. Once children are able to recognize and identify numbers, they move on to counting groups of objects, applying the concept of one-to-one correspondence. Finally, kindergarten students learn to compare numbers and identify which number in a pair is larger or smaller. By the end of kindergarten, children should be able to count to 100 by ones and tens, write numbers up to 20 and count to identify how many objects are in a group (up to 20).

Operations & Algebraic Thinking

Operations & Algebraic thinking begins with simple addition and subtraction skills. Children in kindergarten learn to represent addition and subtraction equations with objects, to count to solve problems and to puzzle out simple word problems. These skills are then carried through the higher elementary grades as multiplication and division are added for an understanding of the four basic operations. The focus remains on whole numbers through the elementary years. In third and fourth grades, students become familiar with factors and multiples, and by the end of fourth grade they begin generating and analyzing algebraic patterns.

Number & Operations

There are two Number & Operations domains -- Number & Operations in Base 10 and Number & Operations with Fractions. Children in kindergarten through second grade focus solely on Number & Operations in Base 10. In these grades, students begin with an understanding of place value and numbers 11 through 19 and move through an understanding of place value in three-digit numbers. Students finishing second grade should be able to add and subtract numbers within the thousands, add up to four two-digit numbers, and mentally add with tens and hundreds. Third- and fourth-grade students continue to work with these skills. In addition to base 10, older students also gain an understanding of fraction equivalencies and ordering. They are also introduced to decimals and begin comparing decimal quantities.

Measurement & Data

The Measurement & Data domain incorporates a large number of crucial elementary-school concepts. Children in kindergarten begin learning how to describe and compare measurable attributes and spend a great deal of time classifying objects by size, shape, color and texture. They also begin working with time, money and standard units. As they move through elementary school, children gain the ability solve problems that involve measurement, to convert larger units to smaller units and to represent data in a variety of ways. Creating and interpreting graphs is practiced at all levels.

Geometry

Elementary geometry begins with students' ability to identify, describe and create basic two-dimensional shapes -- circle, square, rectangle, triangle, rhombus, trapezoid and hexagon. Students then move on to partition shapes into equal parts and to describe these parts using fraction words -- half, third, quarter or fourth. By the time they are ready to leave elementary school, students should be able to draw and identify shapes based on the properties of their lines, angles and points of symmetry.

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