Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
| Standard | Definition | Code |
|---|---|---|
| Display perseverance and patience in problem-solving | Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals. | 6.MP |
| Make sense of problems and persevere in solving them | Make sense of problems and persevere in solving them. | 6.MP.1 |
| Reason abstractly and quantitatively | Reason abstractly and quantitatively. | 6.MP.2 |
| Construct viable arguments and critique the reasoning of others | Construct viable arguments and critique the reasoning of others. | 6.MP.3 |
| Model with mathematics | Model with mathematics. | 6.MP.4 |
| Use appropriate tools strategically | Use appropriate tools strategically. | 6.MP.5 |
| Attend to precision | Attend to precision. | 6.MP.6 |
| Look for and make use of structure | Look for and make use of structure. | 6.MP.7 |
| Look for and express regularity in repeated reasoning | Look for and express regularity in repeated reasoning. | 6.MP.8 |
Rational numbers as a concept<ul><li>Integers</li><li>Fractions</li><li>Decimal numbers</li></ul>
All operations with whole numbers, fractions, and decimal numbers
Write & evaluate numerical expressions
Convert fractions with denominators of 2, 4, 5 and 10 to the decimal notation
Integers
Unit rates
Ratios
Numerical data distributions
Measures of variation
Absolute value
Display and analyze categorical and quantitative (numerical) data
Greatest common factor & least common multiple
Write, analyze, and evaluate numerical and algebraic expressions
Identify, generate, and evaluate algebraic expressions
Identify like terms in an algebraic expression
Write and solve one-step equations & inequalities
Concept of ratio and rate (Numerical Reasoning with ratios and rates)
Equivalent ratios, percentages, unit rates (Numerical Reasoning with ratios and rates)
Convert within measurement systems (Numerical Reasoning with ratios and rates)
Plot order pairs in all four quadrants
Show rational numbers on a number line
Draw polygons on a coordinate grid
Find the side length of a polygon graphed on the coordinate plane (same x- or y- coordinate)
Area of triangles, quadrilaterals, and polygons
Surface area
Volume of right rectangular prisms with fractional edge lengths
| Standard | Definition | Code |
|---|---|---|
| Rational numbers as a concept<ul><li>Integers</li><li>Fractions</li><li>Decimal… | Rational numbers as a concept<ul><li>Integers</li><li>Fractions</li><li>Decimal numbers</li></ul> | 6.LP5.1.1 |
| All operations with whole numbers, fractions | All operations with whole numbers, fractions, and decimal numbers | 6.LP5.2.1 |
| Write & evaluate numerical expressions | Write & evaluate numerical expressions | 6.LP5.2.2 |
| Convert fractions with denominators of 2, 4, 5 and 10 to the decimal notation | Convert fractions with denominators of 2, 4, 5 and 10 to the decimal notation | 6.LP5.2.3 |
| Integers | Integers | 6.LP5.3.1 |
| Unit rates | Unit rates | 6.LP5.3.2 |
| Ratios | Ratios | 6.LP5.3.3 |
| Numerical data distributions | Numerical data distributions | 6.LP5.3.4 |
| Measures of variation | Measures of variation | 6.LP5.3.5 |
| Absolute value | Absolute value | 6.LP5.3.6 |
| Display and analyze categorical and quantitative | Display and analyze categorical and quantitative (numerical) data | 6.LP5.3.7 |
| Greatest common factor & least common multiple | Greatest common factor & least common multiple | 6.LP6.1.1 |
| Write, analyze, and evaluate numerical and algebraic expressions | Write, analyze, and evaluate numerical and algebraic expressions | 6.LP6.2.1 |
| Identify, generate, and evaluate algebraic expressions | Identify, generate, and evaluate algebraic expressions | 6.LP6.2.2 |
| Identify like terms in an algebraic expression | Identify like terms in an algebraic expression | 6.LP6.2.3 |
| Write and solve one-step equations & inequalities | Write and solve one-step equations & inequalities | 6.LP6.3.1 |
| Concept of ratio and rate | Concept of ratio and rate (Numerical Reasoning with ratios and rates) | 6.LP6.4.1 |
| Equivalent ratios, percentages, unit rates | Equivalent ratios, percentages, unit rates (Numerical Reasoning with ratios and rates) | 6.LP6.4.2 |
| Convert within measurement systems | Convert within measurement systems (Numerical Reasoning with ratios and rates) | 6.LP6.4.3 |
| Plot order pairs in all four quadrants | Plot order pairs in all four quadrants | 6.LP6.6.1 |
| Show rational numbers on a number line | Show rational numbers on a number line | 6.LP6.6.2 |
| Draw polygons on a coordinate grid | Draw polygons on a coordinate grid | 6.LP6.6.3 |
| Find the side length of a polygon graphed on the coordinate plane | Find the side length of a polygon graphed on the coordinate plane (same x- or y- coordinate) | 6.LP6.6.4 |
| Area of triangles, quadrilaterals | Area of triangles, quadrilaterals, and polygons | 6.LP8.2.1 |
| Surface area | Surface area | 6.LP8.2.2 |
| Volume of right rectangular prisms with fractional edge lengths | Volume of right rectangular prisms with fractional edge lengths | 6.LP8.2.3 |
Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers.
Fluently add and subtract any combination of fractions to solve problems.
Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems.
Perform operations with multi-digit decimal numbers fluently using models and student-selected strategies.
Apply operations with whole numbers, fractions and decimals within relevant applications.
Describe and interpret the center of the distribution by the equal share value (mean).
Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs.
Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape.
Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions.
Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact.
Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to describe problems presented in relevant, mathematical situations.
Identify and compare integers and explain the meaning of zero based on multiple authentic situations.
Order and plot integers on a number line and use distance from zero to discover the connection between integers and their opposites.
Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; recognize and explain that the opposite of the opposite of a number is the number itself.
Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare rational numbers, including integers, using equality and inequality symbols.
Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative quantity in a relevant situation.
Distinguish comparisons of absolute value from statements about order.
Solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning.
Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities.
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
Solve problems involving proportions using a variety of student-selected strategies.
Describe the concept of rates and unit rate in the context of a ratio relationship.
Solve unit rate problems including those involving unit pricing and constant speed.
Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent.
Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyday life.
| Standard | Definition | Code |
|---|---|---|
| Solve relevant, mathematical problems involving operations with whole numbers… | Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers. | 6.NR.1 |
| Fluently add and subtract any combination of fractions to solve problems | Fluently add and subtract any combination of fractions to solve problems. | 6.NR.1.1 |
| Multiply and divide any combination of whole numbers, fractions | Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems. | 6.NR.1.2 |
| Perform operations with multi-digit decimal numbers fluently using models and… | Perform operations with multi-digit decimal numbers fluently using models and student-selected strategies. | 6.NR.1.3 |
| Apply operations with whole numbers, fractions and decimals within relevant… | Apply operations with whole numbers, fractions and decimals within relevant applications. | 6.NR.2 |
| Describe and interpret the center of the distribution by the equal share value | Describe and interpret the center of the distribution by the equal share value (mean). | 6.NR.2.1 |
| Summarize categorical and quantitative | Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs. | 6.NR.2.2 |
| Interpret numerical data to answer a statistical investigative question created | Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. | 6.NR.2.3 |
| Design simple experiments and collect data | Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. | 6.NR.2.4 |
| Relate the choice of measures of center and variability to the shape of the… | Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. | 6.NR.2.5 |
| Describe the impact that inserting or deleting a data point has on the mean and… | Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact. | 6.NR.2.6 |
| Solve a variety of problems involving whole numbers and their opposites | Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to describe problems presented in relevant, mathematical situations. | 6.NR.3 |
| Identify and compare integers and explain the meaning of zero based on multiple… | Identify and compare integers and explain the meaning of zero based on multiple authentic situations. | 6.NR.3.1 |
| Order and plot integers on a number line and use distance from zero to discover… | Order and plot integers on a number line and use distance from zero to discover the connection between integers and their opposites. | 6.NR.3.2 |
| Recognize and explain that opposite signs of integers indicate locations on… | Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; recognize and explain that the opposite of the opposite of a number is the number itself. | 6.NR.3.3 |
| Write, interpret, and explain statements of order for rational numbers in… | Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare rational numbers, including integers, using equality and inequality symbols. | 6.NR.3.4 |
| Explain the absolute value of a rational number as its distance from zero on… | Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative quantity in a relevant situation. | 6.NR.3.5 |
| Distinguish comparisons of absolute value from statements about order | Distinguish comparisons of absolute value from statements about order. | 6.NR.3.6 |
| Solve a variety of contextual problems involving ratios, unit rates, equivalent… | Solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning. | 6.NR.4 |
| Explain the concept of a ratio, represent ratios | Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities. | 6.NR.4.1 |
| Make tables of equivalent ratios relating quantities with whole-number… | Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. | 6.NR.4.2 |
| Solve problems involving proportions using a variety of student-selected… | Solve problems involving proportions using a variety of student-selected strategies. | 6.NR.4.3 |
| Describe the concept of rates and unit rate in the context of a ratio… | Describe the concept of rates and unit rate in the context of a ratio relationship. | 6.NR.4.4 |
| Solve unit rate problems including those involving unit pricing and constant… | Solve unit rate problems including those involving unit pricing and constant speed. | 6.NR.4.5 |
| Calculate a percent of a quantity as a rate per 100 and solve everyday problems… | Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent. | 6.NR.4.6 |
| Use ratios to convert within measurement systems | Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyday life. | 6.NR.4.7 |
Solve relevant problems involving area, surface area, and volume.
Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems.
Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures.
Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height).
| Standard | Definition | Code |
|---|---|---|
| Solve relevant problems involving area, surface area | Solve relevant problems involving area, surface area, and volume. | 6.GSR.5 |
| Explore area as a measurable attribute of triangles, quadrilaterals | Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems. | 6.GSR.5.1 |
| Given the net of three-dimensional figures with rectangular and triangular… | Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures. | 6.GSR.5.2 |
| Calculate the volume of right rectangular prisms with fractional edge lengths… | Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height). | 6.GSR.5.3 |
Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant situations.
Write and evaluate numerical expressions involving rational bases and whole-number exponents.
Determine greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems.
Write and read expressions that represent operations with numbers and variables in realistic situations.
Evaluate expressions when given values for the variables, including expressions that arise in everyday situations.
Apply the properties of operations to identify and generate equivalent expressions.
Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations.
Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable.
Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number or any number in a specified set.
Solve problems by writing and solving equations of the form x + p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers.
Recognize and generate inequalities of the form x > c, x ≥ c, x ≤ c, or x < c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line.
Graph rational numbers as points on the coordinate plane to represent and solve contextual, mathematical problems; draw polygons using the coordinates for their vertices and find the length of a side of a polygon.
Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane.
Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and determine how two ordered pairs may differ based only on the signs.
Solve 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 x-coordinate or the same y-coordinate.
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 x-coordinate or the same y-coordinate.
| Standard | Definition | Code |
|---|---|---|
| Identify, write, evaluate | Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant situations. | 6.PAR.6 |
| Write and evaluate numerical expressions involving rational bases and… | Write and evaluate numerical expressions involving rational bases and whole-number exponents. | 6.PAR.6.1 |
| Determine greatest common factors and least common multiples using a variety of… | Determine greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems. | 6.PAR.6.2 |
| Write and read expressions that represent operations with numbers and variables… | Write and read expressions that represent operations with numbers and variables in realistic situations. | 6.PAR.6.3 |
| Evaluate expressions when given values for the variables, including expressions… | Evaluate expressions when given values for the variables, including expressions that arise in everyday situations. | 6.PAR.6.4 |
| Apply the properties of operations to identify and generate equivalent… | Apply the properties of operations to identify and generate equivalent expressions. | 6.PAR.6.5 |
| Write and solve one-step equations and inequalities as mathematical models to… | Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations. | 6.PAR.7 |
| Solve one-step equations and inequalities involving variables when values for… | Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable. | 6.PAR.7.1 |
| Write one-step equations and inequalities to represent and solve problems | Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number or any number in a specified set. | 6.PAR.7.2 |
| Solve problems by writing and solving equations of the form x + p = q, px = q… | Solve problems by writing and solving equations of the form x + p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers. | 6.PAR.7.3 |
| Recognize and generate inequalities of the form x > c, x ≥ c, x ≤ c | Recognize and generate inequalities of the form x > c, x ≥ c, x ≤ c, or x < c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line. | 6.PAR.7.4 |
| Graph rational numbers as points on the coordinate plane to represent and solve… | Graph rational numbers as points on the coordinate plane to represent and solve contextual, mathematical problems; draw polygons using the coordinates for their vertices and find the length of a side of a polygon. | 6.PAR.8 |
| Locate and position rational numbers on a horizontal or vertical number line | Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane. | 6.PAR.8.1 |
| Show and explain that signs of numbers in ordered pairs indicate locations in… | Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and determine how two ordered pairs may differ based only on the signs. | 6.PAR.8.2 |
| Solve problems by graphing points in all four quadrants of the coordinate plane | Solve 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 x-coordinate or the same y-coordinate. | 6.PAR.8.3 |
| Draw polygons in the coordinate plane given coordinates for the vertices | 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 x-coordinate or the same y-coordinate. | 6.PAR.8.4 |