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Washington Standards

Washington 6th Grade Math Standards

All 33 Washington math standards for 6th grade, each explained in plain English. The official wording is one click away under each one.

33 standards

Data Analysis

9 standards
Formulate statistical investigative questions.
M.6.DA.DS.1
Write and recognize statistical questions students care about that can be answered with data from websites, phones, sensors or government sources.
Official wording
Formulate and recognize statistical investigative questions that are of interest to students to collect data from online sources and websites, smartphones, sensors, publicly available government agencies, and other modern devices.
Collect and consider data.
M.6.DA.DS.2
Collect and record data with technology to describe a data set, and tell apart data gathered firsthand, called primary, from existing data, called secondary.
Official wording
Collect and record data with technology to identify and describe the characteristics of data sets. Understand that data can be collected (primary data) or existing data can be obtained from other sources (secondary data).
Analyze the data.
M.6.DA.DS.3
Analyze dot plots and box plots to describe a distribution's center, spread and shape, like noting that most scores cluster near 80 with a few low ones.
Official wording
Analyze data visualizations and describe measures of center and variability of quantitative data using appropriate displays (dot plots, boxplots). Describe key features of distributions for the variables including center, variability, and shape.
Interpret results.
M.6.DA.DS.4
Answer the investigative question with evidence from the analysis and share full conclusions, with some help from the teacher.
Official wording
Use statistical evidence from analyses to answer the statistical investigative question and communicate results with comprehensive answers with some teacher guidance.
Develop understanding of statistical variability.
M.6.DA.SP.1
Tell a statistical question, one with varied answers like how old are the students in my school, from one with a single answer.
Official wording
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.
Common Core 6.SP.1
M.6.DA.SP.2
Describe a set of data by its center, its spread and its overall shape.
Official wording
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.
Common Core 6.SP.2
M.6.DA.SP.3
Know that a measure of center, like the mean or median, sums up a data set in one number, while a measure of spread tells how much the values vary.
Official wording
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.
Common Core 6.SP.3
Summarize and describe distributions.
M.6.DA.SP.4
Show numerical data on a number line as a dot plot, histogram or box plot.
Official wording
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Common Core 6.SP.4
M.6.DA.SP.5
Summarize a data set by its count, units and method, find the mean or median and a measure of spread, note outliers and explain which measures fit the data's shape.
Official wording
Summarize numerical data sets in relation to their context.aReporting data points as the set of a number of observations.bDescribe what's being measured including how it was measured and its units of measurement.cCalculate measures of center (mean and/or median) and variability (interquartile range and/or mean absolute deviation) of the data. Understand the shape of the data and identify any striking deviations (outliers) and connect these features to the context where the data came from.dCommunicate choice for selecting a given measure of center and variability and the connection to the shape of the data distribution related to the context in which the data were gathered.

Quantity

5 standards
Compute efficiently, flexibly, and accurately with multi-digit numbers and find common factors and multiples.
M.6.Q.NS.2
Divide multi-digit numbers quickly and correctly with a strategy or the standard method, like 8,736 ÷ 24 = 364.
Official wording
Efficiently, flexibly, and accurately divide multi-digit numbers using strategies or algorithms.
M.6.Q.NS.3
Add, subtract, multiply and divide multi-digit decimals quickly and correctly with a strategy or method for each, like 12.6 x 3.25.
Official wording
Efficiently, flexibly, and accurately add, subtract, multiply, and divide multi-digit decimals using strategies or algorithms for each operation.
Apply and extend previous understandings of numbers to the system of rational numbers.
M.6.Q.NS.5
Explain how positive and negative numbers describe opposites, like above and below sea level or deposits and withdrawals, and what 0 means in each case.
Official wording
Explain how 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.
M.6.Q.NS.6
Place positive and negative numbers on number lines and coordinate grids, see that the opposite of an opposite is the number itself, and that sign changes mirror points.
Official wording
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to place any number (integer or rational, positive or negative) on the line (horizontal or vertical), and in the plane.aUnderstand opposite signs of numbers as indicating locations on opposite sides of 0 on the number line, and recognize that, in situations like -(-3), the opposite of the opposite of a number is the number itself (in this example, 3).bUnderstand 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.cFind 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.
M.6.Q.NS.7
Order positive and negative numbers, read inequalities as number line positions, and treat absolute value as distance from 0, like -25 dollars meaning 25 dollars owed.
Official wording
Understand ordering and absolute value of positive and negative rational numbers.aInterpret statements of inequality as statements about the relative position of two numbers on a number line diagram.bWrite, interpret, and explain order for rational numbers on a number line in real-world contexts, including the use of inequalities.cInterpret absolute value as the distance a number is from zero on a number line, and understand the magnitude of absolute value in real world contexts like comparing temperatures, or understanding the size of a debt. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.dDistinguish comparisons of absolute value from statements about order.

Relationships

14 standards
Understand ratio concepts and use ratio reasoning to solve problems.
M.6.R.RP.1
Explain what a ratio is and use ratio language to describe how two amounts relate, like 3 cups of flour for every 2 cups of sugar.
Official wording
Explain the concept of a ratio and efficiently, flexibly, and accurately use ratio language to describe a ratio relationship between two quantities.
M.6.R.RP.2
Find the unit rate that goes with a ratio and describe it with rate language, like 12 dollars for 4 pounds is 3 dollars per pound.
Official wording
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.
M.6.R.RP.3
Solve ratio and rate problems with tables, tape diagrams and double number lines, including unit price, speed, percents of a quantity and converting measurement units.
Official wording
Efficiently, flexibly, and accurately demonstrate understanding of ratio and rate reasoning by solving real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations to find different ways to express the same ratio.aMake 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.bSolve unit rate problems (like price per item and constant speed)cFind percent of a quantity as a rate per 100 (a special ratio out of 100), including finding the whole, a part, and the percent as appropriate for a given context.dUse ratios to convert between different measurement units, like inches to feet, considering when it is appropriate to multiply or divide quantities.
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
M.6.R.NS.1
Divide fractions by fractions and solve story problems with them using models and equations, like how many 3/8 cup scoops fit in 3/4 cup.
Official wording
Interpret and efficiently, flexibly, and accurately determine 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.
Compute efficiently, flexibly, and accurately with multi-digit numbers and find common factors and multiples.
M.6.R.NS.4
Find greatest common factors up to 100 and least common multiples up to 12, and factor sums with the distributive property, like 24 + 36 as 12 times the sum of 2 and 3.
Official wording
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.
Apply and extend previous understandings of arithmetic to algebraic expressions.
M.6.R.EE.1
Write and evaluate number expressions with whole-number exponents, like 2^4 + 3 = 19.
Official wording
Efficiently, flexibly, and accurately write and evaluate numerical expressions involving whole-number exponents.
M.6.R.EE.2
Write expressions with letters for numbers, like n + 7 for 7 more than a number, name parts like terms and coefficients, and evaluate them using order of operations.
Official wording
Read, and evaluate expressions efficiently, flexibly, and accurately.aWrite expressions in which letters stand for numbers to write general instructions like "subtract y from 5" as a mathematical expression (5 - y).bBreak down expressions into smaller parts using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.cReplace values for the variables (evaluating the expression) and use the Order of Operations where appropriate to solve problems including using real-world formulas, and formulas with whole-number exponents.
M.6.R.EE.3
Use properties of operations, including the distributive property, to write equivalent expressions, like 3 times the sum of 2 and x equals 6 + 3x.
Official wording
Apply the properties of operations (including the distributive property) efficiently, flexibly, and accurately to generate equivalent expressions.
M.6.R.EE.4
Decide whether two expressions are equivalent by checking that they give the same value for any number, like y + y + y and 3y.
Official wording
Identify whether two expressions are equivalent (including expressions with one or more variables) as both expressions will always yield the same outcome for any value of a given variable.
Reason about and solve one-variable equations and inequalities.
M.6.R.EE.5
Check whether a given number makes an equation or inequality true by substituting it in.
Official wording
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.
Common Core 6.EE.5
M.6.R.EE.6
Use a letter for an unknown or changing number when writing an expression for a real problem.
Official wording
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.
Common Core 6.EE.6
M.6.R.EE.7
Solve real problems with one-step equations like x + 3 = 7 or 4x = 20, using positive whole numbers, fractions and decimals.
Official wording
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.
Common Core 6.EE.7
M.6.R.EE.8
Write an inequality like x > 5 for a real condition, know it has infinitely many solutions, and show them on a number line.
Official wording
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.
Common Core 6.EE.8
Represent and analyze quantitative relationships between dependent and independent variables.
M.6.R.EE.9
Use variables for two related real-world quantities, write an equation giving the dependent one from the independent one, and link it to tables and graphs, like d = 60t.
Official wording
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.

Spatial Reasoning

5 standards
Solve real-world and mathematical problems involving area, surface area, and volume.
M.6.SR.G.1
Find areas of triangles, special quadrilaterals and other polygons by rearranging them into rectangles or cutting them into triangles, including in real-world problems.
Official wording
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by efficiently, flexibly, and accurately composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
M.6.SR.G.2
Find the volume of a rectangular prism with fractional edge lengths, both by packing it with small cubes and with the formula V = l w h.
Official wording
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.
Common Core 6.G.2
M.6.SR.G.3
Draw polygons from the coordinates of their corners and use the coordinates to find side lengths.
Official wording
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.
Common Core 6.G.3
M.6.SR.G.4
Unfold a 3D shape into a net of rectangles and triangles and use the net to find its surface area.
Official wording
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.
Common Core 6.G.4
Apply and extend previous understandings of numbers to the system of rational numbers.
M.6.SR.NS.8
Solve problems by graphing points in all four quadrants and find the distance between two points that line up horizontally or vertically.
Official wording
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
Common Core 6.NS.8

The official Washington documents

Washington State Learning Standards for Mathematics by the Office of Superintendent of Public Instruction are available under a Creative Commons Attribution License (CC BY 4.0).

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.