6th+Grade+COMMON+CORE+Mathematics+Grade+Level+Expectations

**Grade Level Expectations at a Glance **
 * **Mathematics **
 * **Standard ** || **Grade Level Expectation ** ||
 * **Sixth Grade ** ||
 * 1. Number Sense, Properties, and Operations |||| # Quantities can be expressed and compared using ratios and rates
 * 1) Formulate, represent, and use algorithms with positive rational numbers with flexibility, accuracy, and efficiency
 * 2) In the real number system, rational numbers have a unique location on the number line and in space ||
 * 2. Patterns, Functions, and Algebraic Structures |||| # Algebraic expressions can be used to generalize properties of arithmetic
 * 1) Variables are used to represent unknown quantities within equations and inequalities ||
 * 3. Data Analysis, Statistics, and Probability |||| # Visual displays and summary statistics of one-variable data condense the information in data sets into usable knowledge ||
 * 4. Shape, Dimension, and Geometric Relationships |||| # Objects in space and their parts and attributes can be measured and analyzed ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">4. Shape, Dimension, and Geometric Relationships |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Objects in space and their parts and attributes can be measured and analyzed ||

__<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">From the Common State Standards for Mathematics, Pages 39-40 __

**//<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Mathematics | Grade 6 //** //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">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. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(1) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(2) Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(3) Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">and they use equations (such as 3 ////<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">x ////<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">= ////<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">y ////<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">) to describe relationships between quantities. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(4) Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. 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. //

|||||| **<span style="font-family: 'Verdana','sans-serif'; font-size: 21px;">Mathematics ** **<span style="font-family: 'Verdana','sans-serif'; font-size: 21px;">Grade Level Expectations at a Glance **
 * **<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Standard ** || **<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Grade Level Expectation ** ||
 * **<span style="font-family: 'Verdana','sans-serif';">Fifth Grade ** ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">1. Number Sense, Properties, and Operations |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Formulate, represent, and use algorithms with multi-digit whole numbers and decimals with flexibility, accuracy, and efficiency
 * 2) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Formulate, represent, and use algorithms to add and subtract fractions with flexibility, accuracy, and efficiency
 * 3) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">The concepts of multiplication and division can be applied to multiply and divide fractions ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">2. Patterns, Functions, and Algebraic Structures |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Number patterns are based on operations and relationships ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">3. Data Analysis, Statistics, and Probability |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Visual displays are used to interpret data ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">4. Shape, Dimension, and Geometric Relationships |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Properties of multiplication and addition provide the foundation for volume an attribute of solids
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Geometric figures can be described by their attributes and specific locations in the plane ||
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Geometric figures can be described by their attributes and specific locations in the plane ||

__<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">From the Common State Standards for Mathematics, Page 33. __

**//<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Mathematics | Grade 5 //** //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">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. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(1) Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.) // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(2) 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 apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(3) Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems. //

|||||| **<span style="font-family: 'Verdana','sans-serif'; font-size: 21px;">Mathematics ** **<span style="font-family: 'Verdana','sans-serif'; font-size: 21px;">Grade Level Expectations at a Glance **
 * **<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Standard ** || **<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Grade Level Expectation ** ||
 * **<span style="font-family: 'Verdana','sans-serif';">Fourth Grade ** ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">1. Number Sense, Properties, and Operations |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">The decimal number system to the hundredths place describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Different models and representations can be used to compare fractional parts
 * 2) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Formulate, represent, and use algorithms to compute with flexibility, accuracy, and efficiency ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">2. Patterns, Functions, and Algebraic Structures |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Number patterns and relationships can be represented by symbols ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">3. Data Analysis, Statistics, and Probability |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Visual displays are used to represent data ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">4. Shape, Dimension, and Geometric Relationships |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Appropriate measurement tools, units, and systems are used to measure different attributes of objects and time
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Geometric figures in the plane and in space are described and analyzed by their attributes ||
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Geometric figures in the plane and in space are described and analyzed by their attributes ||

__<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">From the Common State Standards for Mathematics, Page 27. __ **//<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Mathematics | Grade 4 //** //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">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. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(1) 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 multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students 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. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(2) Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. 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. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(3) Students describe, analyze, compare, and classify two-dimensional shapes. 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. //

|||||| **<span style="font-family: 'Verdana','sans-serif'; font-size: 21px;">Mathematics ** **<span style="font-family: 'Verdana','sans-serif'; font-size: 21px;">Grade Level Expectations at a Glance **
 * **<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Standard ** || **<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Grade Level Expectation ** ||
 * **<span style="font-family: 'Verdana','sans-serif';">Third Grade ** ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">1. Number Sense, Properties, and Operations |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">The whole number system describes place value relationships and forms the foundation for efficient algorithms
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Parts of a whole can be modeled and represented in different ways
 * 2) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Multiplication and division are inverse operations and can be modeled in a variety of ways ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">2. Patterns, Functions, and Algebraic Structures |||| <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Expectations for this standard are integrated into the other standards at this grade level.  ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">3. Data Analysis, Statistics, and Probability |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Visual displays are used to describe data ||
 * <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">4. Shape, Dimension, and Geometric Relationships |||| # <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Geometric figures are described by their attributes
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Linear and area measurement are fundamentally different and require different units of measure
 * 2) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Time and attributes of objects can be measured with appropriate tools ||
 * 1) <span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Time and attributes of objects can be measured with appropriate tools ||

__<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">From the Common State Standards for Mathematics, Page 21. __

**//<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">Mathematics | Grade 3 //** //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(1) Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students 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. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(2) Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students 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. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(3) Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. // //<span style="font-family: 'Verdana','sans-serif'; font-size: 13px;">(4) 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. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole. //