6th Grade Standards Guide
6th Grade Standards Guide
Table of Contents
Content Overview to the Math Standards Guide Expressions & Equations Geometry The Number System Ratios & Proportional Relationships Statistics & Probability
Page Number 2-3 4-5 6 7-8 9 10
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Overview to the Math Standards Guide What is the Math Standards Guide?1 Teachers know the Common Core standard language is important, yet it can often be dense or confusing. The Math Standards Guide is designed to shed light on each Common Core standard, including the key parts of the standard and the aspect(s) of rigor (Conceptual, Procedural, or Application) to which each standard most appropriately aligns. How should I use the Math Standards Guide? Use the Standards Guide to deeply study the standards. We suggest using this document during annual and unit planning as it is designed to help you better understand the key components of each standard and see how standards fit together within their cluster and domain.
What is different about the Math Standards Guide in 2016-17? We have revised this document, as we do every year, to best reflect our deepening knowledge of the Common Core. We have updated the aspects of rigor for some standards to give you a better understanding of which standards call for conceptual understanding of key concepts, speed and accuracy in calculations (procedural rigor), and/or to use math flexibly for applications in problem-solving contexts. In addition, each standard code is now hyperlinked to their standard page on myANet. The revisions represent feedback from Achievement Network’s assessment and coaching teams, Student Achievement Partners, and our schools. When planning, be sure to consider how the parts fit together, representing the breadth of the standard, as well as how the standards fit within the appropriate cluster and domain. It’s important to note that fragmenting the standards may prevent you from recognizing the full scope and rigor of the standards, so avoid interpreting the parts of the standard as individual or daily objectives.
1
The content in this guide is an interpretation of the standards, and could differ from other sources. However, this guide represents feedback from Achievement Network’s assessment and coaching teams, Student Achievement Partners, and our schools.
For example: Domain
Cluster
4.NBT.A
CC Standard
CC Standard Language
4.NBT.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Major
Number & Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.2
4.NBT.3
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.(4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) Use place value understanding to round multi-digit whole numbers to any place. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Aspect(s) of Rigor
Parts of the Standard
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Conceptual
Recognize that 10 tens is 100, 10 hundreds is 1,000, so forth up to 1,000,000. Apply concepts of place value to recognize quotients and products in multiplication and division problems involving whole numbers and a factor of 10.
Conceptual Procedural
tsbienrdsivuisdin ua lyatsoe-btetnter Read multi-diR gietawdhtohlee pnaurm glb erbsetrandam thees,s& taenxdpaarn d’s rements numerals,unnudm derdeq fourim but avoid treating them as discrete or daily objectives. Instead, consider how Write multit-hdeigpitaw rthsofliet tnougmeb theersr,upslianngnbinagset-ot ensure numeralst,hneuym wbilel ran llabm e easd,d&resxspeadnidneydofuorrm lesson(s). Compare multi-digit numbers based on the meaning of the digits
Standards e ach fit within a cluster and domain. Use the symbols , and = to compare two multiers When planning, read the language odfigeiatcnhum stb an dard within the cluster to see how, together, they achieve the cluster-level requirements. Note that major, supporting, u smtebrelresvteol.any place (with and additional emRpohuansdesmaurletig-d iviegn hleecnlu it awthto Conceptual specific attention to thousands, ten thousands, Are there deeper connections across standards (or Procedural hundred thousands, and millions places as these are clusters) that can be made during in struction? Is there an new in Grade 4.) opportunity for supporting or additional standards to
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
6.EE.A.1
CC Standard Language
Write and evaluate numerical expressions involving wholenumber exponents.
Aspect(s) of Rigor Conceptual, Procedural
Parts of the Standard Write numerical expressions involving whole-number exponents in the form a^b, where a and b are non-zero whole numbers Evaluate numerical expressions involving whole-number exponents in the form a^b, where a and b are non-zero whole numbers Identify or write an expression that records operations with numerical values (whole numbers, fractions, and/or decimals) and with letters standing for numbers for a given phrase
6.EE.A.2a
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.
Conceptual
Identify or write a phrase that describes a given expression with operations, numerical values (whole numbers, fractions, and/or decimals) and with letters standing for numbers Identify or write equivalent descriptions of a given expression with operations, numerical values (whole numbers, fractions, and/or decimals) and with letters standing for numbers
6.EE.A.2b 6.EE.A
< Expressions & Equations
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
Identify parts of an expression with numerical values (whole numbers, fractions, and decimals) and variables using mathematical terms (sum, term, product, factor, quotient, and coefficient) Conceptual
View one or more parts of an expression with numerical values (whole numbers, fractions, and decimals) and variables as a single entity
Major Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2c
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
Evaluate expressions at specific values of their variables in mathematical and real-world contexts, including formulas for volume or surface area of a geometric figure Procedural, Application
For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.
Apply the properties of operations to generate equivalent expressions. 6.EE.A.3
6.EE.A.4
For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Identify a combination of terms (ie. a term with a given coefficient)
Perform arithmetic operations, including those involving whole-number exponents and whole numbers, fractions, and/or decimals, in the conventional order when there are no parentheses to specify a particular order Apply the distributive property to expand and factor simple expressions
Conceptual, Procedural
Generate one or more equivalent expressions using the associative and commutative properties, including combining and separating like terms Explain whether expressions are equivalent using the properties of operations and substitution of the variable
Conceptual
Identify whether expressions are equivalent using the properties of operations to simplify or expand expressions to look the same Identify whether expressions are equivalent by substituting the same numerical values for the variables to see if they result in the same result
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Understand that an equation or inequality is true when the values on either side of the equal or inequality signs reflect the relationship being expressed
6.EE.B.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.
Conceptual, Procedural
Understand that the solution of an equation or inequality is the value of the variable that will make the equation or inequality true Understand that substituting a number in the expression or inequality is one way to determine what values that will solve an equation or inequality or make the equation or inequality true Use substitution to determine whether a number or a set of numbers makes an equation or inequality true
6.EE.B.6 6.EE.B
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.
Understand that variables are used in expressions to represent unknown numbers or any number in a set of numbers Conceptual, Application
Create a real-world situation to represent an expression using variables to represent numbers
< Major Reason about and solve onevariable equations and inequalities.
Solve a real world or math problem by writing an expression to represent the situation using variables to represent unknown numbers
Solve equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers 6.EE.B.7
Expressions & Equations
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.
Procedural, Application
Write equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers given a real-world context Write and solve equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers in the context of a real-world problem Recognize that an inequality represents a real world or math problem where there is a range of values that make the inequality true
6.EE.B.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.
Recognize that inequalities of the form x > c or x < c have infinitely many solutions that include not only whole numbers but also fractions and decimals Conceptual, Application
Write inequalities to represent real-world problems Write inequalities to represent mathematical problems Represent solutions of inequalities of the form x > c or x < c on number line diagrams using an open circle to represent solutions greater or less than
6.EE.C
< Major Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.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. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Use information about a real-world situation presented in a table or other form to write an equation using two different variables to represent two quantities where the dependent variable (y) is expressed in terms of the independent variable (x) Conceptual, Application
Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation Solve real-world problems by writing an equation to reflect the relationship between independent and dependent variables and graphing those to analyze the relationship between them
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Recognize that triangles, special quadrilaterals, and polygons can be decomposed into triangles and other shapes or composed into rectangles
6.G.A.1
Find 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.
Procedural, Application
Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles Find area of right triangles, other triangles, special quadrilaterals, and polygons by decomposing into triangles and other shapes Solve real-world and mathematical that involve finding the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes Understand that the volume of right rectangular prisms with fractional edge lengths can be determined by packing it with unit cubes of the appropriate unit fraction edge lengths
6.G.A.2 6.G.A
p Supporting Geometry
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 = 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.
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 Conceptual, Procedural, Application
Use the formula V=lwh to find volumes of right rectangular prism with fractional edge lengths in the context of solving real-world and mathematical problems Use the formula V=bh to find volumes of right rectangular prism with fractional edge lengths in the context of solving real-world and mathematical problems Demonstrate that the volume of a right rectangular prism with fractional edge lengths by packed with unit cubes of the appropriate unit fraction edge lengths is the is the same as it would be found by multiplying the fractional edge lengths or multiplying the area of the base by the height
Solve real-world and mathematical problems involving area, surface area, and volume.
Draw polygons in the coordinate plane given coordinates from any of the four quadrants for the vertices
6.G.A.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.
Identify the coordinates of missing vertices to to complete the construction of a polygon Procedural, Application
Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate Solve real-world and mathematical problems by drawing polygons in the coordinate plane given coordinates for vertices or by identifying the coordinates of missing vertices Solve real-world and mathematical problems by using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate Understand that the surface of a three-dimensional figure can be decomposed into a net made up of rectangles and triangles
6.G.A.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.
Conceptual, Procedural, Application
Represent three-dimensional figures using nets made up of rectangles and triangles Use nets to find the surface area of a three-dimensional figures Solve real-world and mathematical problems using nets to find the surface area of threedimensional figures
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
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. For example, create a story context for
6.NS.A
< Major Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.A.1
(2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. [In general, (a/b) ÷ (c/d) = ad/bc.] How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Aspect(s) of Rigor
Parts of the Standard Interpret quotients of fractions
Conceptual, Procedural, Application
Compute quotients of fractions
Solve word problems involving division of fractions by fractions
6.NS.B.2
Fluently divide multi-digit numbers using the standard algorithm.
Procedural
Fluently divide multi-digit whole numbers using the standard algorithm
6.NS.B.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Procedural
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation
6.NS.B.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. For example, express 36 + 8 as 4 (9 + 2).
6.NS.B
o
CC Standard Language
Additional Compute fluently with multidigit numbers and find common factors and multiples.
The Number System 6.NS.C.5
6.NS.C
< Major
6.NS.C.6a
Apply and extend previous understandings of numbers to the system of rational numbers.
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.
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
Find the greatest common factor of two whole numbers less than or equal to 100 Conceptual, Procedural
Find 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 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values
Conceptual, Application
Use positive and negative numbers to represent quantities in real-world contexts Explain the meaning of 0 in each situation Understand and recognize opposite signs of numbers as indicating locations on opposite sides of 0 on a number line
Conceptual
Understand and recognize that the opposite of the opposite of a number is the number itself Understand and recognize that 0 is its own opposite
6.NS.C.6b
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
6.NS.C.6c
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
Conceptual
Procedural
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane Understand and recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes Find and position integers and other rational numbers on a horizontal or vertical number line diagram Find and position pairs of integers and other rational numbers on a coordinate plane
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard
6.NS.C.7a
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
Conceptual
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram
Interpret and explain statements of order for rational numbers in real-world context 6.NS.C.7b
Write, interpret, and explain statements of order for Conceptual, rational numbers in real-world contexts. For example, write Application 3C > -7C to express the fact that -3C is warmer than -7C.
Compare and order rational numbers
6.NS.C (cont'd)
< The Number System
Major Apply and extend previous understandings of numbers to the system of rational numbers.
Write and explain statements of order for rational numbers in real-world context
6.NS.C.7c
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30
Understand the absolute value of a rational number as its distance from 0 on the number line Conceptual, Application
dollars, write |-30| = 30 to describe the size of the debt in dollars.
6.NS.C.7d
6.NS.C.8
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
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.
Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation Understand that rational numbers may be ordered by their value or by their absolute value
Conceptual Interpret and explain statements of absolute value in real-world contexts Solve mathematical problems by graphing points in all four quadrants of the coordinate plane Conceptual, Procedural, Application
Solve real-world problems by graphing points in all four quadrants of the coordinate plane Use coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Understand that a ratio is the comparison of two quantities or measures
6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."
Understand that and identify when a ratio can be part-to-whole or part-to-part Conceptual
Understand and use multiple written forms of ratios to express the relationship between the two quantities, including 6/9, 6 to 9, and 6:9 Use ratio language to describe a ratio relationship between two quantities
6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (6.RP.A.2 footnote: Expectations for unit rates in this grade are limited to non-complex fractions.)
Understand unit rates as a unique part-to-1 ratio that compares a quantity in terms of 1 unit of another quantity Understand unit rate a/b as associated with ratio a:b, where b does not equal 0 Conceptual Identify real-world ratios and determine unit rates from these Use rate language in the context of a ratio relationship Understand that ratios and rates can be represented using tools such as tables of equivalent ratios, tape diagrams, double number line diagrams, and equations
6.RP.A Ratios & Proportional Relationships
< Major Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.3a
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.
Conceptual, Procedural
Make tables of equivalent ratios relating quantities with whole-number measurements Find missing values in the tables using ratio reasoning and plot the pairs of values on the coordinate plane Use tables to compare ratios
6.RP.A.3b
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Solve unit rate problems including those involving unit pricing and constant speed Application Solve real-world problems by identifying real-world ratios and determining the unit rate Understand that percents are a type of ratio and that percentage-based rate problems compare two different units where one of the units is 100
6.RP.A.3c
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Conceptual, Procedural, Application
Find a percent of a quantity as a rate per 100 Solve problems involving finding the whole, given a part and the percent
6.RP.A.3d
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Conceptual, Procedural, Application
Understand ratios as conversion factors Use ratio reasoning and methods involving multiplication and division to convert measurement units
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
6.SP.A.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.
Aspect(s) of Rigor
Understand that a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers Conceptual Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers 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
6.SP.A
o Additional
Parts of the Standard
6.SP.A.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.
Conceptual
Develop understanding of statistical variability.
Describe the distribution of data using center, spread, and shape Recognize a data distribution that is symmetric, skewed left, or skewed right
6.SP.A.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.
Understand that a single number can be used to describe the distribution of a data set resulting from a statistical question Conceptual
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number Recognize that a measure of variation describes how its values vary with a single number
Statistics & Probability
6.SP.B
6.SP.B.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5a
Summarize numerical data sets in relation to their context by reporting the number of observations.
Conceptual, Application
Summarize numerical data sets in relation to their context by reporting the number of observations
6.SP.B.5b
Summarize numerical data sets in relation to their context by describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
Conceptual, Application
Summarize numerical data sets in relation to their context by describing the nature of the attribute under investigation, including how it was measured and its units of measurement
6.SP.B.5c
Summarize numerical data sets in relation to their context by 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.
o Additional Summarize and describe distributions.
Display numerical data in plots on a number line, including dot plots, histograms, and box plots
Conceptual, Procedural, Application
6.SP.B.5d
Summarize numerical data sets in relation to their context by 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.
Identify the data set that is being displayed in a number line, including dot plots, histograms, and box plots
Describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered Conceptual, Procedural, Application
Summarize numerical data sets in relation to their context by calculating quantitative measures of center (median and/or mean) Summarize numerical data sets in relation to their context by calculating quantitative measures of variability (interquartile range and/or mean absolute deviation)
Conceptual, Application
Summarize numerical data sets in relation to their context by relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered Summarize numerical data sets in relation to their context by relating the choice of measures of variability to the shape of the data distribution and the context in which the data were gathered
Table of Contents
Content Overview to the Math Standards Guide Expressions & Equations Geometry The Number System Ratios & Proportional Relationships Statistics & Probability
Page Number 2-3 4-5 6 7-8 9 10
1
Overview to the Math Standards Guide What is the Math Standards Guide?1 Teachers know the Common Core standard language is important, yet it can often be dense or confusing. The Math Standards Guide is designed to shed light on each Common Core standard, including the key parts of the standard and the aspect(s) of rigor (Conceptual, Procedural, or Application) to which each standard most appropriately aligns. How should I use the Math Standards Guide? Use the Standards Guide to deeply study the standards. We suggest using this document during annual and unit planning as it is designed to help you better understand the key components of each standard and see how standards fit together within their cluster and domain.
What is different about the Math Standards Guide in 2016-17? We have revised this document, as we do every year, to best reflect our deepening knowledge of the Common Core. We have updated the aspects of rigor for some standards to give you a better understanding of which standards call for conceptual understanding of key concepts, speed and accuracy in calculations (procedural rigor), and/or to use math flexibly for applications in problem-solving contexts. In addition, each standard code is now hyperlinked to their standard page on myANet. The revisions represent feedback from Achievement Network’s assessment and coaching teams, Student Achievement Partners, and our schools. When planning, be sure to consider how the parts fit together, representing the breadth of the standard, as well as how the standards fit within the appropriate cluster and domain. It’s important to note that fragmenting the standards may prevent you from recognizing the full scope and rigor of the standards, so avoid interpreting the parts of the standard as individual or daily objectives.
1
The content in this guide is an interpretation of the standards, and could differ from other sources. However, this guide represents feedback from Achievement Network’s assessment and coaching teams, Student Achievement Partners, and our schools.
For example: Domain
Cluster
4.NBT.A
CC Standard
CC Standard Language
4.NBT.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Major
Number & Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.2
4.NBT.3
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.(4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) Use place value understanding to round multi-digit whole numbers to any place. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Aspect(s) of Rigor
Parts of the Standard
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Conceptual
Recognize that 10 tens is 100, 10 hundreds is 1,000, so forth up to 1,000,000. Apply concepts of place value to recognize quotients and products in multiplication and division problems involving whole numbers and a factor of 10.
Conceptual Procedural
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6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
6.EE.A.1
CC Standard Language
Write and evaluate numerical expressions involving wholenumber exponents.
Aspect(s) of Rigor Conceptual, Procedural
Parts of the Standard Write numerical expressions involving whole-number exponents in the form a^b, where a and b are non-zero whole numbers Evaluate numerical expressions involving whole-number exponents in the form a^b, where a and b are non-zero whole numbers Identify or write an expression that records operations with numerical values (whole numbers, fractions, and/or decimals) and with letters standing for numbers for a given phrase
6.EE.A.2a
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.
Conceptual
Identify or write a phrase that describes a given expression with operations, numerical values (whole numbers, fractions, and/or decimals) and with letters standing for numbers Identify or write equivalent descriptions of a given expression with operations, numerical values (whole numbers, fractions, and/or decimals) and with letters standing for numbers
6.EE.A.2b 6.EE.A
< Expressions & Equations
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
Identify parts of an expression with numerical values (whole numbers, fractions, and decimals) and variables using mathematical terms (sum, term, product, factor, quotient, and coefficient) Conceptual
View one or more parts of an expression with numerical values (whole numbers, fractions, and decimals) and variables as a single entity
Major Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2c
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
Evaluate expressions at specific values of their variables in mathematical and real-world contexts, including formulas for volume or surface area of a geometric figure Procedural, Application
For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.
Apply the properties of operations to generate equivalent expressions. 6.EE.A.3
6.EE.A.4
For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Identify a combination of terms (ie. a term with a given coefficient)
Perform arithmetic operations, including those involving whole-number exponents and whole numbers, fractions, and/or decimals, in the conventional order when there are no parentheses to specify a particular order Apply the distributive property to expand and factor simple expressions
Conceptual, Procedural
Generate one or more equivalent expressions using the associative and commutative properties, including combining and separating like terms Explain whether expressions are equivalent using the properties of operations and substitution of the variable
Conceptual
Identify whether expressions are equivalent using the properties of operations to simplify or expand expressions to look the same Identify whether expressions are equivalent by substituting the same numerical values for the variables to see if they result in the same result
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Understand that an equation or inequality is true when the values on either side of the equal or inequality signs reflect the relationship being expressed
6.EE.B.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.
Conceptual, Procedural
Understand that the solution of an equation or inequality is the value of the variable that will make the equation or inequality true Understand that substituting a number in the expression or inequality is one way to determine what values that will solve an equation or inequality or make the equation or inequality true Use substitution to determine whether a number or a set of numbers makes an equation or inequality true
6.EE.B.6 6.EE.B
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.
Understand that variables are used in expressions to represent unknown numbers or any number in a set of numbers Conceptual, Application
Create a real-world situation to represent an expression using variables to represent numbers
< Major Reason about and solve onevariable equations and inequalities.
Solve a real world or math problem by writing an expression to represent the situation using variables to represent unknown numbers
Solve equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers 6.EE.B.7
Expressions & Equations
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.
Procedural, Application
Write equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers given a real-world context Write and solve equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers in the context of a real-world problem Recognize that an inequality represents a real world or math problem where there is a range of values that make the inequality true
6.EE.B.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.
Recognize that inequalities of the form x > c or x < c have infinitely many solutions that include not only whole numbers but also fractions and decimals Conceptual, Application
Write inequalities to represent real-world problems Write inequalities to represent mathematical problems Represent solutions of inequalities of the form x > c or x < c on number line diagrams using an open circle to represent solutions greater or less than
6.EE.C
< Major Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.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. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Use information about a real-world situation presented in a table or other form to write an equation using two different variables to represent two quantities where the dependent variable (y) is expressed in terms of the independent variable (x) Conceptual, Application
Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation Solve real-world problems by writing an equation to reflect the relationship between independent and dependent variables and graphing those to analyze the relationship between them
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Recognize that triangles, special quadrilaterals, and polygons can be decomposed into triangles and other shapes or composed into rectangles
6.G.A.1
Find 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.
Procedural, Application
Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles Find area of right triangles, other triangles, special quadrilaterals, and polygons by decomposing into triangles and other shapes Solve real-world and mathematical that involve finding the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes Understand that the volume of right rectangular prisms with fractional edge lengths can be determined by packing it with unit cubes of the appropriate unit fraction edge lengths
6.G.A.2 6.G.A
p Supporting Geometry
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 = 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.
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 Conceptual, Procedural, Application
Use the formula V=lwh to find volumes of right rectangular prism with fractional edge lengths in the context of solving real-world and mathematical problems Use the formula V=bh to find volumes of right rectangular prism with fractional edge lengths in the context of solving real-world and mathematical problems Demonstrate that the volume of a right rectangular prism with fractional edge lengths by packed with unit cubes of the appropriate unit fraction edge lengths is the is the same as it would be found by multiplying the fractional edge lengths or multiplying the area of the base by the height
Solve real-world and mathematical problems involving area, surface area, and volume.
Draw polygons in the coordinate plane given coordinates from any of the four quadrants for the vertices
6.G.A.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.
Identify the coordinates of missing vertices to to complete the construction of a polygon Procedural, Application
Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate Solve real-world and mathematical problems by drawing polygons in the coordinate plane given coordinates for vertices or by identifying the coordinates of missing vertices Solve real-world and mathematical problems by using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate Understand that the surface of a three-dimensional figure can be decomposed into a net made up of rectangles and triangles
6.G.A.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.
Conceptual, Procedural, Application
Represent three-dimensional figures using nets made up of rectangles and triangles Use nets to find the surface area of a three-dimensional figures Solve real-world and mathematical problems using nets to find the surface area of threedimensional figures
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
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. For example, create a story context for
6.NS.A
< Major Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.A.1
(2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. [In general, (a/b) ÷ (c/d) = ad/bc.] How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Aspect(s) of Rigor
Parts of the Standard Interpret quotients of fractions
Conceptual, Procedural, Application
Compute quotients of fractions
Solve word problems involving division of fractions by fractions
6.NS.B.2
Fluently divide multi-digit numbers using the standard algorithm.
Procedural
Fluently divide multi-digit whole numbers using the standard algorithm
6.NS.B.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Procedural
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation
6.NS.B.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. For example, express 36 + 8 as 4 (9 + 2).
6.NS.B
o
CC Standard Language
Additional Compute fluently with multidigit numbers and find common factors and multiples.
The Number System 6.NS.C.5
6.NS.C
< Major
6.NS.C.6a
Apply and extend previous understandings of numbers to the system of rational numbers.
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.
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
Find the greatest common factor of two whole numbers less than or equal to 100 Conceptual, Procedural
Find 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 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values
Conceptual, Application
Use positive and negative numbers to represent quantities in real-world contexts Explain the meaning of 0 in each situation Understand and recognize opposite signs of numbers as indicating locations on opposite sides of 0 on a number line
Conceptual
Understand and recognize that the opposite of the opposite of a number is the number itself Understand and recognize that 0 is its own opposite
6.NS.C.6b
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
6.NS.C.6c
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
Conceptual
Procedural
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane Understand and recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes Find and position integers and other rational numbers on a horizontal or vertical number line diagram Find and position pairs of integers and other rational numbers on a coordinate plane
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard
6.NS.C.7a
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
Conceptual
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram
Interpret and explain statements of order for rational numbers in real-world context 6.NS.C.7b
Write, interpret, and explain statements of order for Conceptual, rational numbers in real-world contexts. For example, write Application 3C > -7C to express the fact that -3C is warmer than -7C.
Compare and order rational numbers
6.NS.C (cont'd)
< The Number System
Major Apply and extend previous understandings of numbers to the system of rational numbers.
Write and explain statements of order for rational numbers in real-world context
6.NS.C.7c
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30
Understand the absolute value of a rational number as its distance from 0 on the number line Conceptual, Application
dollars, write |-30| = 30 to describe the size of the debt in dollars.
6.NS.C.7d
6.NS.C.8
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
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.
Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation Understand that rational numbers may be ordered by their value or by their absolute value
Conceptual Interpret and explain statements of absolute value in real-world contexts Solve mathematical problems by graphing points in all four quadrants of the coordinate plane Conceptual, Procedural, Application
Solve real-world problems by graphing points in all four quadrants of the coordinate plane Use coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Understand that a ratio is the comparison of two quantities or measures
6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."
Understand that and identify when a ratio can be part-to-whole or part-to-part Conceptual
Understand and use multiple written forms of ratios to express the relationship between the two quantities, including 6/9, 6 to 9, and 6:9 Use ratio language to describe a ratio relationship between two quantities
6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (6.RP.A.2 footnote: Expectations for unit rates in this grade are limited to non-complex fractions.)
Understand unit rates as a unique part-to-1 ratio that compares a quantity in terms of 1 unit of another quantity Understand unit rate a/b as associated with ratio a:b, where b does not equal 0 Conceptual Identify real-world ratios and determine unit rates from these Use rate language in the context of a ratio relationship Understand that ratios and rates can be represented using tools such as tables of equivalent ratios, tape diagrams, double number line diagrams, and equations
6.RP.A Ratios & Proportional Relationships
< Major Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.3a
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.
Conceptual, Procedural
Make tables of equivalent ratios relating quantities with whole-number measurements Find missing values in the tables using ratio reasoning and plot the pairs of values on the coordinate plane Use tables to compare ratios
6.RP.A.3b
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Solve unit rate problems including those involving unit pricing and constant speed Application Solve real-world problems by identifying real-world ratios and determining the unit rate Understand that percents are a type of ratio and that percentage-based rate problems compare two different units where one of the units is 100
6.RP.A.3c
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Conceptual, Procedural, Application
Find a percent of a quantity as a rate per 100 Solve problems involving finding the whole, given a part and the percent
6.RP.A.3d
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Conceptual, Procedural, Application
Understand ratios as conversion factors Use ratio reasoning and methods involving multiplication and division to convert measurement units
6th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
6.SP.A.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.
Aspect(s) of Rigor
Understand that a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers Conceptual Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers 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
6.SP.A
o Additional
Parts of the Standard
6.SP.A.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.
Conceptual
Develop understanding of statistical variability.
Describe the distribution of data using center, spread, and shape Recognize a data distribution that is symmetric, skewed left, or skewed right
6.SP.A.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.
Understand that a single number can be used to describe the distribution of a data set resulting from a statistical question Conceptual
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number Recognize that a measure of variation describes how its values vary with a single number
Statistics & Probability
6.SP.B
6.SP.B.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5a
Summarize numerical data sets in relation to their context by reporting the number of observations.
Conceptual, Application
Summarize numerical data sets in relation to their context by reporting the number of observations
6.SP.B.5b
Summarize numerical data sets in relation to their context by describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
Conceptual, Application
Summarize numerical data sets in relation to their context by describing the nature of the attribute under investigation, including how it was measured and its units of measurement
6.SP.B.5c
Summarize numerical data sets in relation to their context by 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.
o Additional Summarize and describe distributions.
Display numerical data in plots on a number line, including dot plots, histograms, and box plots
Conceptual, Procedural, Application
6.SP.B.5d
Summarize numerical data sets in relation to their context by 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.
Identify the data set that is being displayed in a number line, including dot plots, histograms, and box plots
Describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered Conceptual, Procedural, Application
Summarize numerical data sets in relation to their context by calculating quantitative measures of center (median and/or mean) Summarize numerical data sets in relation to their context by calculating quantitative measures of variability (interquartile range and/or mean absolute deviation)
Conceptual, Application
Summarize numerical data sets in relation to their context by relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered Summarize numerical data sets in relation to their context by relating the choice of measures of variability to the shape of the data distribution and the context in which the data were gathered
