## Common Core State Standards

Common Core State Standards for education are challenging standards that are being developed and adopted throughout most of the nation. These standards define the knowledge and skills students should have to succeed in college and in the workforce.

Click here for the Common Core State Standards for sixth grade math. They are complicated! The Mathematical Practice Standards (described further here) are about ways we want all students to learn to approach mathematics, solve problems, and analyze and communicate their results. The Mathematical Content Standards for sixth grade focus on ratio and rate; the number system, including negative numbers, rational numbers, and division of fractions; writing, interpreting, and using algebraic expressions and equations; developing understanding of statistical thinking; and area, surface area, and volume of two- and three-dimensional shapes.

These links may also be of interest:

PPS Information on Common Core State Standards

PPS information on Mathematics and Common Core State Standards

Oregon Department of Education Common Core Information for Parents

Portland Public Schools' learning targets for sixth grade math are based on the Common Core standards. The PPS learning targets for the year are listed below. I will try to more add information soon on which standards are covered when, but essentially, first semester has focused on The Number System, Geometry, and Expressions and Equations, and second semester will focus more on Ratios and Proportional Relationships, The Number System, and Statistics and Probability. Detailed information on the PPS curriculum and calendar is available here. (There are some variations in the calendar, however -- for example, for Outdoor School.)

6-A2: I can identify and calculate a unit rate for a ratio relationship.

6-A3: I can use the language of unit rate to describe a ratio.

6-A4: I can make a table of equivalent ratios and use it to find missing values and/or graph the values on a coordinate plane.

6-A5: I can use tables to compare ratios.

6-A6: I can solve unit rate problems, including unit pricing and constant speed.

6-A7: I can find percent of a quantity as rate per 100.

6-A8: I can find the whole, given a part and percent.

6-A9: I can convert measurement units using ratios.

6-B2: I can solve word problems involving division of fractions by fractions, using visual models and equations.

6-B3: I can find the Greatest Common Factor of two whole numbers less than or equal to 100.

6-B4: I can find the Least Common Multiple of two whole numbers less than or equal to 12.

6-B5: I can use Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor.

6-B6: I can fluently divide multi-digit numbers using the standard algorithm.

6-B7: I can fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithms for each operation.

6-B8: I can find the Greatest Common Factor of two whole numbers less than or equal to 100.

6-B9: I can find the Least Common Multiple of two whole numbers less than or equal to 12.

6-B10: I can use Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor.

6-B11: I can use integers to describe quantities having opposite directions or values.

6-B12: I can explain where zero fits into a situation represented by positive and negative rational numbers.

6-B13: I can use numbers lines to represent positive and negative rational numbers.

6-B14: I can describe how opposite quantities are represented by locations on opposite sides of zero on the number line.

6-B15: I can describe the value of the opposite of the opposite of a number, and know zero is its own opposite.

6-B16: I can locate and describe positive and negative rational numbers on horizontal or vertical number lines.

6-B17: I can locate and describe pairs of positive and negative rational numbers on the coordinate plane and use their signs to identify the quadrant they are located in.

6-B18: I can interpret and describe statements of inequality as statements about the relative position of two numbers on a number line.

6-B19: I can write, interpret and explain statements of inequality for rational numbers in real-world situations.

6-B20: I can interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

6-B21: I can distinguish comparisons of absolute value from statements about order and apply them to real world contexts.

6-B22: I can solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane.

6-B23: I can use coordinates and absolute value to calculate the distance between points with the same first coordinate or the same second coordinate.

6C-2: I can translate written phrases into algebraic expressions.

6C-3: I can translate algebraic expressions into written phrases.

6C-4: I can identify parts of an expression using mathematical terms (such as sum, term, coefficient, factor, product, quotient).

6C-5: I can describe one or more parts of an expression as a single entity.

6C-6: I can evaluate expressions, including those from real-world formulas.

6C-7: I can use Order of Operations for expressions with no parentheses, including whole number exponents.

6C-8: I can apply properties of operations to write equivalent expressions.

6C-9: I can identify two equivalent expressions and prove they are equivalent no matter what number is substituted.

6C-10: I can use substitution to find if a given value makes an equation or inequality true.

6C-11: I can explain how solving an equation is the process to find the value(s), if any, that make the equation true.

6C-12: I can explain how a variable can represent an unknown number or any number in a specific set.

6C-13: I can use variables to write expressions when solving real world problems.

6C-14: I can solve real world and mathematical problems by writing and solving equations of the form x + p = q and px = q when p, q, and x are all non-negative rational numbers.

6C-15: I can write an inequality to represent a constraint or condition in a real world or mathematical problem.

6C-16: I can represent inequalities of the form x<c or x>c on a number line.

6C-17: I can explain how inequalities of the form x<c or x>c have infinitely many solutions.

6C-18: I can use variables to represent two quantities in a real world problem that change in relationship to each other.

6C-19: I can describe and analyze the relationship between two variables in tables and graphs and relate them to the equation.

6C-20: I can write an equation to represent a dependent variable in terms of an independent variable.

6D-2: I can find the volume of a right rectangular prism with fractional edge lengths using a model packed with cubes of appropriate fractional edge length.

6D-3: I can show how to find the volume of a right rectangular prism with fractional edge lengths by using formulas V=lwh and V=bh when solving real-world and mathematical problems.

6D-4: I can draw figures on a coordinate plane given coordinates for the vertices and use this to solve real-world and mathematical problems.

6D-5: I can use coordinates to find the length of a side given coordinates with the same first coordinate or the same second coordinate, and use this to solve real-world and mathematical problems.

6D-6: I can model three dimensional figures using nets made of rectangles and triangles and use this to solve real-world and mathematical problems.

6D-7: I can use nets to find the surface area of three dimensional figures to solve real-world and mathematical problems.

6E-2: I can explain how the data gathered from a statistical question can be described by its center, spread and overall shape.

6E-3: I can calculate measures of center for a set of data.

6E-4: I can explain how a measure of center of a set of numerical data summarizes all the data with a single number.

6E-5: I can calculate interquartile range and mean absolute deviation for a set of data.

6E-6: I can explain how a measure of variation for a set of numerical data describes how the values vary with a single number.

6E-7: I can display numerical data in plots on a number line, including dot plots, histograms and box plots.

6E-8: I can summarize numerical data sets in relation to their context by reporting the number of observations.

6E-9: I can describe how an attribute of a set of numerical data was measured and its units of measurement.

6E-10: I can describe the mean and/or median of a set of data in relation to its context.

6E-11: I can describe the interquartile range and/or mean absolute deviation of a set of data in relation to its context.

6E-12: I can describe any overall pattern and any striking deviations from the overall pattern of a set of data in relation to its context.

6E-13: I can relate the choices of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.

Click here for the Common Core State Standards for sixth grade math. They are complicated! The Mathematical Practice Standards (described further here) are about ways we want all students to learn to approach mathematics, solve problems, and analyze and communicate their results. The Mathematical Content Standards for sixth grade focus on ratio and rate; the number system, including negative numbers, rational numbers, and division of fractions; writing, interpreting, and using algebraic expressions and equations; developing understanding of statistical thinking; and area, surface area, and volume of two- and three-dimensional shapes.

These links may also be of interest:

PPS Information on Common Core State Standards

PPS information on Mathematics and Common Core State Standards

Oregon Department of Education Common Core Information for Parents

**PPS Math 6 Learning Targets**Portland Public Schools' learning targets for sixth grade math are based on the Common Core standards. The PPS learning targets for the year are listed below. I will try to more add information soon on which standards are covered when, but essentially, first semester has focused on The Number System, Geometry, and Expressions and Equations, and second semester will focus more on Ratios and Proportional Relationships, The Number System, and Statistics and Probability. Detailed information on the PPS curriculum and calendar is available here. (There are some variations in the calendar, however -- for example, for Outdoor School.)

**RATIOS AND PROPORTIONAL RELATIONSHIPS**

6-A1: I can use ratio language to describe a relationship between two quantities.6-A2: I can identify and calculate a unit rate for a ratio relationship.

6-A3: I can use the language of unit rate to describe a ratio.

6-A4: I can make a table of equivalent ratios and use it to find missing values and/or graph the values on a coordinate plane.

6-A5: I can use tables to compare ratios.

6-A6: I can solve unit rate problems, including unit pricing and constant speed.

6-A7: I can find percent of a quantity as rate per 100.

6-A8: I can find the whole, given a part and percent.

6-A9: I can convert measurement units using ratios.

**THE NUMBER SYSTEM**

6-B1: I can interpret and compute quotients of fractions.6-B2: I can solve word problems involving division of fractions by fractions, using visual models and equations.

6-B3: I can find the Greatest Common Factor of two whole numbers less than or equal to 100.

6-B4: I can find the Least Common Multiple of two whole numbers less than or equal to 12.

6-B5: I can use Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor.

6-B6: I can fluently divide multi-digit numbers using the standard algorithm.

6-B7: I can fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithms for each operation.

6-B8: I can find the Greatest Common Factor of two whole numbers less than or equal to 100.

6-B9: I can find the Least Common Multiple of two whole numbers less than or equal to 12.

6-B10: I can use Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor.

6-B11: I can use integers to describe quantities having opposite directions or values.

6-B12: I can explain where zero fits into a situation represented by positive and negative rational numbers.

6-B13: I can use numbers lines to represent positive and negative rational numbers.

6-B14: I can describe how opposite quantities are represented by locations on opposite sides of zero on the number line.

6-B15: I can describe the value of the opposite of the opposite of a number, and know zero is its own opposite.

6-B16: I can locate and describe positive and negative rational numbers on horizontal or vertical number lines.

6-B17: I can locate and describe pairs of positive and negative rational numbers on the coordinate plane and use their signs to identify the quadrant they are located in.

6-B18: I can interpret and describe statements of inequality as statements about the relative position of two numbers on a number line.

6-B19: I can write, interpret and explain statements of inequality for rational numbers in real-world situations.

6-B20: I can interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

6-B21: I can distinguish comparisons of absolute value from statements about order and apply them to real world contexts.

6-B22: I can solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane.

6-B23: I can use coordinates and absolute value to calculate the distance between points with the same first coordinate or the same second coordinate.

**EXPRESSIONS AND EQUATIONS**

6C-1: I can write and evaluate numerical expressions with whole number exponents.6C-2: I can translate written phrases into algebraic expressions.

6C-3: I can translate algebraic expressions into written phrases.

6C-4: I can identify parts of an expression using mathematical terms (such as sum, term, coefficient, factor, product, quotient).

6C-5: I can describe one or more parts of an expression as a single entity.

6C-6: I can evaluate expressions, including those from real-world formulas.

6C-7: I can use Order of Operations for expressions with no parentheses, including whole number exponents.

6C-8: I can apply properties of operations to write equivalent expressions.

6C-9: I can identify two equivalent expressions and prove they are equivalent no matter what number is substituted.

6C-10: I can use substitution to find if a given value makes an equation or inequality true.

6C-11: I can explain how solving an equation is the process to find the value(s), if any, that make the equation true.

6C-12: I can explain how a variable can represent an unknown number or any number in a specific set.

6C-13: I can use variables to write expressions when solving real world problems.

6C-14: I can solve real world and mathematical problems by writing and solving equations of the form x + p = q and px = q when p, q, and x are all non-negative rational numbers.

6C-15: I can write an inequality to represent a constraint or condition in a real world or mathematical problem.

6C-16: I can represent inequalities of the form x<c or x>c on a number line.

6C-17: I can explain how inequalities of the form x<c or x>c have infinitely many solutions.

6C-18: I can use variables to represent two quantities in a real world problem that change in relationship to each other.

6C-19: I can describe and analyze the relationship between two variables in tables and graphs and relate them to the equation.

6C-20: I can write an equation to represent a dependent variable in terms of an independent variable.

**GEOMETRY**

6D-1: I can solve real-world and mathematical problems involving finding the area of triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes.6D-2: I can find the volume of a right rectangular prism with fractional edge lengths using a model packed with cubes of appropriate fractional edge length.

6D-3: I can show how to find the volume of a right rectangular prism with fractional edge lengths by using formulas V=lwh and V=bh when solving real-world and mathematical problems.

6D-4: I can draw figures on a coordinate plane given coordinates for the vertices and use this to solve real-world and mathematical problems.

6D-5: I can use coordinates to find the length of a side given coordinates with the same first coordinate or the same second coordinate, and use this to solve real-world and mathematical problems.

6D-6: I can model three dimensional figures using nets made of rectangles and triangles and use this to solve real-world and mathematical problems.

6D-7: I can use nets to find the surface area of three dimensional figures to solve real-world and mathematical problems.

**STATISTICS AND PROBABILITY**

6E-1: I can ask an appropriate statistical question and explain that there will be variability in the answers.6E-2: I can explain how the data gathered from a statistical question can be described by its center, spread and overall shape.

6E-3: I can calculate measures of center for a set of data.

6E-4: I can explain how a measure of center of a set of numerical data summarizes all the data with a single number.

6E-5: I can calculate interquartile range and mean absolute deviation for a set of data.

6E-6: I can explain how a measure of variation for a set of numerical data describes how the values vary with a single number.

6E-7: I can display numerical data in plots on a number line, including dot plots, histograms and box plots.

6E-8: I can summarize numerical data sets in relation to their context by reporting the number of observations.

6E-9: I can describe how an attribute of a set of numerical data was measured and its units of measurement.

6E-10: I can describe the mean and/or median of a set of data in relation to its context.

6E-11: I can describe the interquartile range and/or mean absolute deviation of a set of data in relation to its context.

6E-12: I can describe any overall pattern and any striking deviations from the overall pattern of a set of data in relation to its context.

6E-13: I can relate the choices of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.