Common+Core+Instructional+Focuses

=**OVERVIEW OF COMMON CORE** **or The Big Ideas for Each Grade Level**= In the years prior to Grade 4, students gained an understanding of multiplication and division of whole numbers, generalized strategies for addition and subtraction to multi-­digit numbers, developed understanding of fractions as numbers, and reasoned with shapes and their attributes. They worked with arrays for multiplication and area.
 * Fourth Grade**

In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

In previous grades, students learned strategies for multiplication and division, developed understanding of structure of the place value system, and applied understanding of fractions to addition and subtraction with like denominators. Students gained understanding that geometric figures can be analyzed and classified based on their properties.
 * Fifth Grade**

In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) 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 (3) developing understanding of volume.

In the three years prior to Grade 6, students acquired a strong foundation in numbers and operations, geometry, measurement and data. Students are fluent in multiplication of multi-digit whole numbers and have a solid conceptual understanding of all four operations with positive rational numbers. Understanding of measurement concepts (e.g. length, area, volume, angles), as well as the representation and interpretation of data, is also emerging.
 * Sixth Grade**

In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.

Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.

In Grade 6, students developed an understanding of variables from two perspectives‐as placeholders for specific values and as representing sets of values represented in algebraic relationships. They applied properties of operations to write and solve simple one‐step equations. By the end of sixth grade, students were fluent in all positive rational number operations, and they developed a solid foundation for understanding area, surface area and volume of geometric figures.
 * Seventh Grade**

In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

In the years prior to Grade 8, students began their study of algebraic concepts. They wrote and interpreted expressions, solved equations and inequalities, explored quantitative relationships between dependent and independent variables, and solved problems involving area, surface area, and volume. Students have also begun to develop an understanding of statistical thinking.
 * Eighth Grade**

In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.