# Grade 6 Mathematics Common Core State Standards

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1 Grade 6 Mathematics Common Core State Standards Standards for Mathematical Practice HOW make sense of problems, persevere in solving them, and check the reasonableness of answers. reason with and flexibly use math symbols, numbers, and operations. construct mathematical arguments (using stated assumptions, definitions, previously established results, and logical progressions) and critique the math reasoning of others. recognize math in everyday life and use math to solve real problems. use tools (e.g., protractor, calculator) strategically to solve problems and deepen understanding. calculate accurately, use precise math definitions and vocabulary, and express math ideas clearly. look for and make use of patterns and structure in math. discern when calculations are repeated, and look both for general methods and for shortcuts. Math Content Standards WHAT Ratios and Proportional Relationships understand ratios and use ratio language to describe the relationship between two amounts. 6.RP.1 understand how to find a rate when given a specific ratio. For example, We paid \$75 for 15 hamburgers, which is a rate of \$5 per hamburger. 6.RP.2 solve real-world and mathematical word problems related to ratios and rates. 6.RP.3 make tables of equivalent ratios, find missing values in the tables, plot those values on a coordinate plane, and use the tables to compare ratios. 6.RP.3a solve unit rate problems including unit pricing & constant speed (e.g., 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?). 6.RP.3b

2 find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity). 6.RP.3c solve problems to find the whole, given a part and the percent. 6.RP.3c use what is known about ratios to convert/manipulate units of measurement when multiplying & dividing. 6.RP.3d The Number System divide two fractions; solve word problems involving the division of fractions by fractions. 6.NS.1 quickly and easily divide multi-digit numbers. 6.NS.2 fluently add, subtract, multiply and divide multi-digit numbers involving decimals. 6.NS.3 find the greatest common factor of two whole numbers less than or equal to NS.4 find the least common multiple of two whole numbers less than or equal to NS.4 use the distributive property to show the sum of two whole numbers with a common factor as a multiple of a sum. For example, show as 4 (9+2). 6.NS.4 understand that positive & negative numbers are used to describe amounts having opposite values or directions. 6.NS.5 use positive and negative numbers to represent amounts in real-world situations; explain the meaning of 0 in each situation. 6.NS.5 understand that a rational number is a point on a number line. 6.NS.6 extend number line diagrams and axes to show positive and negative numbers on the line and in the plane. 6.NS.6 recognize opposite signs of numbers as showing points on opposite sides of 0 on the number line. 6.NS.6a understand signs of numbers in ordered pairs as showing locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the points are related by reflections across one or both axes. 6.NS.6b place integers and other rational numbers on a horizontal or vertical number line diagram. 6.NS.6c place ordered pairs of integers on a coordinate plane. 6.NS.6c order positive and negative numbers; understand absolute value of rational numbers. 6.NS.7 interpret statements of inequality as statements about the relative position of two numbers (positive or negative) on a number line (e.g., interpret -3 > -7 to mean that -3 is located to the right of -7 on a horizontal number line). 6.NS.7a

3 write and explain statements that show the order of rational numbers in real-world situations (e.g., write -3 C > -7 C to show that -3 C is warmer than -7 C). 6.NS.7b understand the absolute value of a rational number as the number s distance from 0 on the number line. 6.NS.7c understand absolute values as they apply to real-world situations (e.g., for an account balance of -30 dollars, write -30 = 30 to describe the size of the debt in dollars). 6.NC.7c tell the difference between comparing absolute values and ordering positive and negative numbers. 6.NS.7d graph in all four quadrants of the coordinate plane to help solve real-world and mathematical problems. 6.NS.8 find the distance between points with the same first coordinate or the same second coordinate. 6.NS.8 Expressions and Equations write and understand numerical expressions involving whole-number exponents. 6.EE.1 write, read and evaluate expressions in which letters stand for numbers (e.g., express subtract y from 5 as 5-y). 6.EE.2 identify the parts of an expression using mathematical words (sum, term, product, factor, quotient, coefficient). 6.EE.2b view one or more parts of an expression as a single unit (e.g., describe 2(8 + 7) as a product of two factors; view (8 + 7) as a sum of two terms or as the single quantity 15). 6.EE.2b determine the answer to expressions when given the specific value of a variable. 6.EE.2c use order of operations to solve problems in the conventional order when there are no parentheses. 6.EE.2c use properties of operations to create equivalent expressions (e.g., apply properties to y+y+y to produce 3y). 6.EE.3 identify when two expressions are equivalent (e.g., when two expressions name the same number regardless of the value substituted for the letter: y+y+y = 3y or 3(2+x) = 6+3x). 6.EE.4 understand that solving an equation or inequality is like answering a question: which values makes the equation or inequality true? Use substitution to determine whether a given number makes an equation or inequality true. 6.EE.5 use variables to represent numbers and write expressions when solving real-world problems. 6.EE.6 understand that a variable can represent an unknown number or a number in a specified set. 6.EE.6

4 write and solve equations in the form x+p=q and px=q when p, q, and x are all nonnegative rational numbers. 6.EE.7 write an inequality in the form x>c or x<c; represent the infinite solutions of these inequalities on a number line. 6.EE.8 write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable (e.g., write d=65t to represent the relationship between distance and time). 6.EE.9 use graphs and tables to show the relationship between dependent and independent variables. 6.EE.9 Geometry put together and take apart shapes to find the area of right triangles, other triangles, special quadrilaterals, and polygons; apply these techniques to solve real-world and mathematical problems. 6.G.1 use unit cubes to find the volume of a right rectangular prism with fractional edge lengths; show that the volume is the same as found by multiplying the edge lengths of the prism. 6.G.2 use the formulas V = l w h or V = b h to find volumes of right rectangular prisms in real-world problems. 6.G.2 draw polygons in the coordinate plane when given the coordinates for the vertices. 6.G.3 use coordinates to find the length of a polygon s side in a coordinate plane. 6.G.3 show how three-dimensional figures can be represented with twodimensional nets (a net is the pattern made when the surface of a three-dimensional figure is laid out flat) made of rectangles and triangles. 6.G.4 figure out the surface area of 3-D shapes by using nets; apply this technique to real-world & math problems. 6.G.4 Statistics and Probability understand that a statistical question expects responses/data to be varied (e.g., How old are the students at the school? is a statistical question because one anticipates variation in students ages). 6.SP.1 understand that a set of statistical data has a distribution that can be described by its center, spread, & shape. 6.SP.2 understand that a set of numerical data has a measure of center (median and/or mode) that summarizes all of its values with one number. 6.SP.3

5 understand that the measure of variation in a set of data describes with one number how values vary. 6.SP.3 show numerical data in plots on a number line, including dot plots, histograms, and boxplots. 6.SP.4 summarize numerical data sets by reporting the number of observations. 6.SP.5a summarize data by describing the attribute under investigation, including how it was measured. 6.SP.5b summarize data by giving numerical measures of center and variability as well as describing overall pattern. 6.SP.5c describe deviations from the overall pattern of a data set, referring to the context of data collection. 6.SP.5c describe the relationship between the measures of center & variability and the shape of the data distribution. 6.SP.5.d

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