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Grade 6 Math

29 curriculum outcomes with explicit teaching progressions

Select a record to inspect its progression

Ratios Proportional Relationships · 6.RP.A.1

Understand ratio concepts and language

Independently understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. across representations and contexts.

Component progression

  1. 1I can define a ratio as a relationship between two quantities showing how many times one contains the other.
  2. 2I can describe a ratio relationship between two quantities using correct ratio language, in the correct order.
  3. 3I can write a ratio to represent a described real-world relationship between two quantities.
Ratios Proportional Relationships · 6.RP.A.2

Understand unit rates

Independently 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. across representations and contexts.

Component progression

  1. 1I can compute the unit rate a/b for a ratio a:b by dividing a by b.
  2. 2I can describe a unit rate using correct rate language, such as 'miles per hour' or 'dollars per item'.
  3. 3I can interpret a computed unit rate in terms of the original real-world ratio relationship.
Ratios Proportional Relationships · 6.RP.A.3

Use ratio and rate reasoning to solve problems

Independently use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number lines, or equations, including making tables of equivalent ratios for quantities with whole-number measurements, finding missing values, plotting the pairs of values on the coordinate plane, and using tables to compare ratios; solving unit-rate problems, including those involving unit pricing and constant speed; finding a percent of a quantity as a rate per 100 and solving problems that find the whole given a part and the percent; and using ratio reasoning to convert measurement units, manipulating and transforming units appropriately when multiplying or dividing quantities. across representations and contexts.

Component progression

  1. 1I can use a table of equivalent ratios, tape diagram, or double number line to find missing values in a ratio problem, plot the pairs of values on a coordinate plane, and use tables to compare ratios.
  2. 2I can use a unit rate to solve a real-world problem, such as unit pricing or constant speed, finding a total cost or total distance.
  3. 3I can find a percent of a quantity as a rate per 100, solve a problem that finds the whole given a part and the percent, and convert measurement units using ratio reasoning.
Number System · 6.NS.A.1

Interpret and compute quotients of fractions

Independently interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, using visual fraction models and equations to represent the problem. across representations and contexts.

Component progression

  1. 1I can use a visual fraction model to represent and solve a fraction-by-fraction division problem.
  2. 2I can divide a fraction by a fraction by multiplying by the reciprocal of the divisor.
  3. 3I can solve a word problem requiring division of a fraction by a fraction.
Number System · 6.NS.B.2

Fluently divide multi-digit numbers

Independently fluently divide multi-digit numbers using the standard algorithm. across representations and contexts.

Component progression

  1. 1I can divide a multi-digit dividend by a multi-digit divisor using the standard long-division algorithm.
  2. 2I can correctly find and express the remainder, if any, when dividing multi-digit numbers.
  3. 3I can check a division result by multiplying the quotient by the divisor and adding any remainder.
Number System · 6.NS.B.3

Fluently operate with multi-digit decimals

Independently fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. across representations and contexts.

Component progression

  1. 1I can add and subtract multi-digit decimals fluently, aligning decimal points correctly.
  2. 2I can multiply multi-digit decimals fluently, correctly placing the decimal point in the product.
  3. 3I can divide multi-digit decimals fluently, including converting a decimal divisor to a whole number first.
Number System · 6.NS.B.4

Find greatest common factors and least common multiples

Independently 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, and use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. across representations and contexts.

Component progression

  1. 1I can find the greatest common factor of two whole numbers up to 100.
  2. 2I can find the least common multiple of two whole numbers up to 12.
  3. 3I can use the distributive property and a common factor to rewrite a sum of two whole numbers as a multiple of a sum with no common factor.
Number System · 6.NS.C.5

Interpret positive and negative numbers in context

Independently understand that positive and negative numbers are used together to describe quantities having opposite directions or values, and use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. across representations and contexts.

Component progression

  1. 1I can identify a real-world pair of opposite quantities, such as elevation above and below sea level, and represent each with a signed number.
  2. 2I can represent a real-world quantity with a positive or negative number based on its direction relative to a reference point.
  3. 3I can explain what a value of 0 represents in a given real-world context involving positive and negative numbers.
Number System · 6.NS.C.6

Represent rational numbers on number lines and coordinate planes

Independently understand a rational number as a point on the number line, extending number-line diagrams and coordinate axes to represent points with negative number coordinates, including recognizing that opposite signs indicate locations on opposite sides of 0, that the opposite of the opposite of a number is the number itself, and that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. across representations and contexts.

Component progression

  1. 1I can locate positive and negative rational numbers on a number line, recognizing that numbers with opposite signs lie on opposite sides of 0 and that the opposite of a number's opposite is the number itself.
  2. 2I can plot a point with positive or negative coordinates in any of the four quadrants of the coordinate plane.
  3. 3I can find the coordinates of a point reflected across the x-axis or y-axis.
Number System · 6.NS.C.7

Order rational numbers and interpret absolute value

Independently understand ordering and absolute value of rational numbers, interpreting statements of inequality as statements about the relative position of two numbers on a number line, writing and interpreting statements of order for rational numbers in real-world contexts, interpreting absolute value as magnitude for a positive or negative quantity in a real-world situation, and distinguishing comparisons of absolute value from statements about order. across representations and contexts.

Component progression

  1. 1I can interpret a statement of inequality as a statement about the relative position of two numbers on a number line, and write or interpret statements of order for rational numbers in real-world contexts, such as comparing temperatures.
  2. 2I can interpret the absolute value of a positive or negative number as its magnitude, such as the size of a debt, in a real-world context.
  3. 3I can distinguish a comparison of absolute values from a statement about order, recognizing for example that an account balance less than -30 dollars represents a debt greater than 30 dollars.
Number System · 6.NS.C.8

Solve coordinate-plane distance problems

Independently solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding the distance between two points with the same first or second coordinate, using absolute value to find distances. across representations and contexts.

Component progression

  1. 1I can graph points with positive and negative coordinates to represent a real-world or mathematical problem.
  2. 2I can find the distance between two points sharing a coordinate by finding the absolute value of the difference in their other coordinate.
  3. 3I can solve a real-world problem requiring the distance between two points plotted on a coordinate plane.
Expressions Equations · 6.EE.A.1

Write and evaluate expressions with exponents

Independently write and evaluate numerical expressions involving whole-number exponents. across representations and contexts.

Component progression

  1. 1I can write a repeated multiplication expression using exponent notation.
  2. 2I can evaluate a numerical expression containing a whole-number exponent.
  3. 3I can evaluate a numerical expression that combines exponents with other operations, applying the correct order of operations.
Expressions Equations · 6.EE.A.2

Write, read, and evaluate algebraic expressions

Independently write, read, and evaluate expressions in which letters stand for numbers: write expressions that record operations with numbers and with letters standing for numbers; identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient, and view one or more parts of an expression as a single entity; and evaluate expressions, including those arising from formulas used in real-world problems, at specific values of their variables, performing arithmetic operations in the conventional order when there are no parentheses to specify a particular order. across representations and contexts.

Component progression

  1. 1I can write an expression that records operations with numbers and with letters standing for numbers, such as expressing 'subtract y from 5' as 5 − y.
  2. 2I can identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient, and view one or more parts of an expression as a single entity.
  3. 3I can evaluate an algebraic expression, including one arising from a real-world formula, by substituting given values for its variables and applying the conventional order of operations.
Expressions Equations · 6.EE.A.3

Apply properties to generate equivalent expressions

Independently apply the properties of operations to generate equivalent expressions, such as applying the distributive property to expand a product like 3(2 + x) into 6 + 3x, applying the distributive property to factor a sum like 24x + 18y into 6(4x + 3y), or applying properties of operations to rewrite a repeated sum like y + y + y as 3y. across representations and contexts.

Component progression

  1. 1I can use the distributive property to expand an expression, multiplying a factor across every term inside parentheses.
  2. 2I can factor an expression by identifying and pulling out a common factor from every term.
  3. 3I can combine like terms within an expression to write it in simplest equivalent form.
Expressions Equations · 6.EE.A.4

Identify equivalent expressions

Independently identify when two expressions are equivalent, meaning that the expressions produce the same number for any value substituted for the variable. across representations and contexts.

Component progression

  1. 1I can substitute a chosen value into two expressions to test whether they produce the same result.
  2. 2I can test two expressions with more than one value to build confidence about whether they are equivalent.
  3. 3I can justify that two expressions are equivalent by showing one can be transformed into the other using properties of operations.
Expressions Equations · 6.EE.B.5

Understand solving equations and inequalities

Independently understand solving an equation or inequality as a process of answering which values from a specified set, if any, make the equation or inequality true, using substitution to determine whether a given value is a solution. across representations and contexts.

Component progression

  1. 1I can substitute a given value into an equation or inequality to test whether it is a solution.
  2. 2I can explain what it means for a value to be a solution of an equation or inequality.
  3. 3I can determine which values from a specified set of numbers are solutions to a given equation or inequality.
Expressions Equations · 6.EE.B.6

Use variables to represent numbers in problems

Independently use variables to represent numbers, and write expressions when solving a real-world or mathematical problem, understanding that a variable can represent an unknown number or any number in a specified set. across representations and contexts.

Component progression

  1. 1I can define a variable to represent an unknown number in a real-world or mathematical problem.
  2. 2I can write an expression using the defined variable that correctly represents the problem's relationship.
  3. 3I can explain what set of numbers a variable in a given problem could represent.
Expressions Equations · 6.EE.B.7

Solve one-step equations

Independently 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. across representations and contexts.

Component progression

  1. 1I can write a one-step equation of the form x + p = q or px = q to represent a real-world problem.
  2. 2I can solve a one-step equation of the form x + p = q using the inverse operation.
  3. 3I can solve a one-step equation of the form px = q using the inverse operation.
Expressions Equations · 6.EE.B.8

Write and graph one-variable inequalities

Independently write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem, and recognize that inequalities of this form have infinitely many solutions, representing solutions on a number-line diagram. across representations and contexts.

Component progression

  1. 1I can write an inequality of the form x > c or x < c representing a real-world constraint.
  2. 2I can graph the solutions to a one-variable inequality on a number line, using an open or closed dot appropriately.
  3. 3I can explain why an inequality of this form has infinitely many solutions.
Expressions Equations · 6.EE.C.9

Analyze dependent and independent variable relationships

Independently 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, the dependent variable, in terms of the other quantity, the independent variable, and analyze the relationship between the dependent and independent variables using tables and graphs, relating these representations to the equation. across representations and contexts.

Component progression

  1. 1I can identify which quantity in a real-world relationship is the independent variable and which is the dependent variable.
  2. 2I can write an equation expressing the dependent variable in terms of the independent variable.
  3. 3I can use a table of values or a graph to analyze how the dependent variable changes as the independent variable changes, and relate the table or graph back to the equation.
Geometry · 6.G.A.1

Find areas of triangles, quadrilaterals, and polygons

Independently find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes, applying these techniques to solve real-world and mathematical problems. across representations and contexts.

Component progression

  1. 1I can find the area of a right or other triangle by relating it to half of a rectangle or parallelogram.
  2. 2I can find the area of a parallelogram, trapezoid, or other special quadrilateral by decomposing it into triangles or rectangles.
  3. 3I can find the area of an irregular polygon by decomposing it into triangles, rectangles, and other familiar shapes without gaps or overlaps.
Geometry · 6.G.A.2

Find volumes of prisms with fractional edge lengths

Independently 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, applying the formulas v = l × w × h and v = b × h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. across representations and contexts.

Component progression

  1. 1I can determine how many unit cubes with fractional edge length are needed to pack a rectangular prism with fractional dimensions, and show this count matches multiplying the edge lengths.
  2. 2I can apply the formulas v = l × w × h and v = b × h to a rectangular prism with fractional edge lengths.
  3. 3I can solve a real-world problem requiring the volume of a rectangular prism with fractional edge lengths.
Geometry · 6.G.A.3

Draw polygons in the coordinate plane and find side lengths

Independently draw polygons in the coordinate plane given coordinates for the vertices, and use coordinates to find the length of a side joining points with the same first or second coordinate, applying this in real-world and mathematical problems. across representations and contexts.

Component progression

  1. 1I can plot a set of given vertices on a coordinate plane and connect them in order to draw the polygon.
  2. 2I can find the length of a polygon's side that lies on a horizontal or vertical line, using the coordinates of its endpoints.
  3. 3I can solve a real-world problem involving a polygon drawn on a coordinate plane using its vertex coordinates.
Geometry · 6.G.A.4

Represent solids with nets and find surface area

Independently represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures, applying this technique to solve real-world and mathematical problems. across representations and contexts.

Component progression

  1. 1I can construct or identify a correct net made of rectangles and triangles for a given three-dimensional figure.
  2. 2I can find the area of each individual face shown in a net.
  3. 3I can add the areas of all faces in a net to find the total surface area of the three-dimensional figure.
Statistics Probability · 6.SP.A.1

Recognize statistical questions

Independently recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. across representations and contexts.

Component progression

  1. 1I can distinguish a statistical question, which anticipates variability, from a question with a single fixed answer.
  2. 2I can identify the kind of variability a given statistical question anticipates in its data.
  3. 3I can write an original statistical question about a topic that anticipates variability in its responses.
Statistics Probability · 6.SP.A.2

Understand distributions by center, spread, and shape

Independently 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. across representations and contexts.

Component progression

  1. 1I can describe the center of a data distribution using an appropriate measure.
  2. 2I can describe the spread of a data distribution, indicating how varied the data values are.
  3. 3I can describe the overall shape of a data distribution, such as symmetric, skewed, or having gaps and clusters.
Statistics Probability · 6.SP.A.3

Recognize measures of center and variation

Independently 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. across representations and contexts.

Component progression

  1. 1I can identify mean and median as measures of center that summarize a data set with a single value.
  2. 2I can identify range and interquartile range as measures of variation that describe spread with a single value.
  3. 3I can explain the difference between what a measure of center summarizes and what a measure of variation summarizes.
Statistics Probability · 6.SP.B.4

Display numerical data in plots

Independently display numerical data in plots on a number line, including dot plots, histograms, and box plots. across representations and contexts.

Component progression

  1. 1I can construct a dot plot to display a numerical data set on a number line.
  2. 2I can construct a histogram with equal interval widths to display a numerical data set.
  3. 3I can construct a box plot to display a numerical data set's five-number summary.
Statistics Probability · 6.SP.B.5

Summarize numerical data in context

Independently summarize numerical data sets in relation to their context, 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) while describing the overall pattern and any striking deviations with reference to the context; and 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. across representations and contexts.

Component progression

  1. 1I can report the number of observations in a data set and describe the attribute being investigated, including how it was measured and its units of measurement.
  2. 2I can give quantitative measures of center and variability for a data set, and describe the overall pattern and any striking deviations from it with reference to the context.
  3. 3I can relate the choice of measures of center and variability to the shape of a data distribution and to the context in which the data were gathered.
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