 Ratio and Proportional Relationships 6.RP.1.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.1.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.1.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 6.RP.1.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 6.RP.1.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Equivalent ratios Ratio tables Unit rates and unit prices Percentages 13. Unit conversions Concept of pi 6.RP.1.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Equivalent ratios Ratio tables Unit rates and unit prices Percentages 13. Unit conversions Concept of pi
 Expressions and Equations 6.EE.1.1 Write and evaluate numerical expressions involving whole-number exponents. Write expressions Evaluate expressions 6.EE.1.1 Write and evaluate numerical expressions involving whole-number exponents. Write expressions Evaluate expressions 6.EE.1.2 Write, read, and evaluate expressions in which letters stand for numbers. Write variable expressions Identify terms and coefficients Order of operations Evaluate variable expressions Real-world formulas Sort factors 6.EE.1.2 Write, read, and evaluate expressions in which letters stand for numbers. Write variable expressions Identify terms and coefficients Order of operations Evaluate variable expressions Real-world formulas Sort factors 6.EE.1.3 Apply the properties of operations to generate equivalent expressions. Distributive property Equivalent expressions 6.EE.1.3 Apply the properties of operations to generate equivalent expressions. Distributive property Equivalent expressions 6.EE.1.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). 6.EE.1.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). 6.EE.2.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.2.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.2.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.2.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.2.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Solve equations Real-world problems 6.EE.2.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Solve equations Real-world problems 6.EE.2.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 6.EE.2.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 6.EE.3.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Independent and dependent variables Find values Make and interpret graphs Write equations 6.EE.3.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Independent and dependent variables Find values Make and interpret graphs Write equations
 Geometry 6.G.1.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Triangles Quadrilaterals Compound figures 6.G.1.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Triangles Quadrilaterals Compound figures 6.G.1.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.1.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.1.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 6.G.1.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 6.G.1.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Nets of three-dimensional figures Surface area 6.G.1.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Nets of three-dimensional figures Surface area
 Statistics and Probability 6.SP.1.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 6.SP.1.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 6.SP.1.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Line plots Stem-and-leaf plots Box-and-whisker plots Quartiles 6.SP.1.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Line plots Stem-and-leaf plots Box-and-whisker plots Quartiles 6.SP.1.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.1.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.2.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Line plots Histograms Box-and-whisker plots 6.SP.2.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Line plots Histograms Box-and-whisker plots 6.SP.2.5 Summarize numerical data sets in relation to their context, such as by reporting the number of observations; describing the nature of the attribute under investigation, including how it was measured and its units of measurement; giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered; relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Line plots Histograms Random and representative samples Measures of center Measures of variability Outliers 6.SP.2.5 Summarize numerical data sets in relation to their context, such as by reporting the number of observations; describing the nature of the attribute under investigation, including how it was measured and its units of measurement; giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered; relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Line plots Histograms Random and representative samples Measures of center Measures of variability Outliers
 The Number System 6.NS.1.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Divide fractions Word problems 6.NS.1.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Divide fractions Word problems 6.NS.2.2 Fluently divide multi-digit numbers using the standard algorithm. 6.NS.2.2 Fluently divide multi-digit numbers using the standard algorithm. 6.NS.2.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Add and subtract Multiply and divide Mixed operations 6.NS.2.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Add and subtract Multiply and divide Mixed operations 6.NS.2.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Factors GCF and LCM 6.NS.2.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Factors GCF and LCM 6.NS.3.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.3.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.3.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.Also assesses:6.NS.3.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Opposite integers Find the sign Number lines Coordinate plane 10. 6.NS.3.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.Also assesses:6.NS.3.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Opposite integers Find the sign Number lines Coordinate plane 10. 6.NS.3.7 Understand ordering and absolute value of rational numbers. Compare numbers Order numbers Absolute value 6.NS.3.7 Understand ordering and absolute value of rational numbers. Compare numbers Order numbers Absolute value
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