6th Grade Math Standards and “I Can Statements”
Ratios and Proportional Relationships (RP)
Standard 6.RP.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.”
· I can write ratio notation __:__, __ to __, __/__ · I can explain how order matters when writing a ratio. · I can demonstrate how ratios can be simplified. · I can demonstrate how ratios compare two quantities; the quantities do not have to be the same unit of measure. · I can recognize that ratios appear in a variety of different contexts; parttowhole, parttopart, and rates. · I can generalize that all ratios relate two quantities or measures within a given situation in a multiplicative relationship. · I can analyze context to determine which kind of ratio is represented.
Standard 6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), 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." (Expectations for unit rates in this grade are limited to noncomplex fractions.)
· I can identify and calculate a unit rate. · I can use appropriate math terminology as related to rate. · I can analyze the relationship between a ratio a:b and a unit rate a/b where b≠0.
Standard 6.RP.3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
· I can make a table of equivalent ratios using whole numbers. · I can find the missing values in a table of equivalent ratios. · I can solve realworld and mathematical problems involving ratio and rate, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Standard 6.RP.3a: Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
· I can make a table of equivalent ratios using whole numbers. · I can find the missing values in a table of equivalent ratios. · I can plot pairs of values that represent equivalent ratios on the coordinate plane. · I can use tables to compare proportional quantities.
Standard 6.RP.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?
· I can apply the concept of unit rate to solve realworld problems involving unit pricing. · I can apply the concept of unit rate to solve realworld problems involving constant speed.
Standard 6.RP.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.
· I can demonstrate how a percent is a ratio of a number to 100. · I can find a percent of a number as a rate per 100. · I can solve realworld problems involving finding the whole, given a part and a percent.
Standard 6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
· I can apply ratio reasoning to convert measurement units in realworld and mathematical problems. · I can apply ratio reasoning to convert measurement units by multiplying or dividing in realworld and mathematical problems.
The Number System (NS)
Standard 6.NS.1: 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 (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 3/4cup 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?
· I can compute quotients of fractions divided by fractions (including mixed numbers). · I can interpret quotients of fractions. · I can figure out how to solve division problems with fractions in a realworld situation. · I can solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
Standard 6.NS.2: Fluently divide multidigit numbers using the standard algorithm.
· I can divide multidigit numbers using the standard algorithm with speed and accuracy, without any math tools (i.e., calculator, multiplication chart).
Standard 6.NS.3: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.
· I can fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation with speed and accuracy, without math tools (i.e., calculator).
Standard 6.NS.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).
· I can identify the factors of two whole numbers less than or equal to 100 and determine the Greatest Common Multiple. · I can identify the multiples of two whole numbers less than or equal to 12 and determine the Least Common Multiple. · I can apply the Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor.
Standard 6.NS.5: 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, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation.
· I can identify an integer and its opposite. · I can use integers to represent quantities in real world situations (above/below sea level, etc). · I can explain where zero fits into a situation represented by integers.
Standard 6.NS.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
· I can identify a rational number as a point in the number line.
Standard 6.NS.6a: 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.
· I can identify the location of zero on a number line in relation to positive and negative numbers. · I can recognize opposite signs of numbers as locations on opposite sides of 0 on the number line. · I can reason that a double negative, e.g., (2) is the opposite of that number itself.
Standard 6.NS.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.
· I can recognize the signs of both numbers in an ordered pair indicate which quadrant of the coordinate plane the ordered pair will be located. · I can reason that when only the x value in a set of ordered pairs are opposites, it creates a reflection over the y axis, e.g., (x,y) and (x,y). · I can recognize that when only the y value in a set of ordered pairs are opposites, it creates a reflection over the x axis, e.g., (x,y) and (x,y). · I can reason that when two ordered pairs differ only by signs, the locations of the points are related by reflections across both axes, e.g., (x,y) and (x,y).
Standard 6.NS.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.
· I can find and position integers and other rational numbers on a horizontal or vertical number line diagram. · I can find a position pairs of integers and other rational numbers on a coordinate plane. Standard 6.NS.7: Understand ordering and absolute value of rational numbers. · I can order rational numbers on a number line. Standard 6.NS.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. · I can interpret statements of inequality as statements about relative position of two numbers on a number line diagram.
Standard 6.NS.7b: Write, interpret, and explain statements of order for rational numbers in realworld contexts. For example, write –3°C > –7°C to express the fact that 3°C is warmer than 7°C.
· I can write, interpret, and explain statements of order for rational numbers in realworld contexts.
Standard 6.NS.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 realworld situation. For example, for an account balance of –30 dollars, write –30 = 30 to describe the size of the debt in dollars.
· I can identify absolute value of rational numbers. · I can interpret absolute value as magnitude for a positive or negative quantity in a realworld situation.
Standard 6.NS.7d: 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.
· I can distinguish comparisons of absolute value from statements about order and apply to real world contexts.
Standard 6.NS.8: Solve realworld 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.
· I can calculate absolute value. · I can graph points in all four quadrants of the coordinate plane. · I can solve realworld problems by graphing points in all four quadrants of a coordinate plane. · I can calculate the distances between two points with the same first coordinate or the same second coordinate using absolute value, given only coordinates.
Expressions and Equations (EE)
Standard 6.EE.1: Write and evaluate numerical expressions involving wholenumber exponents.
· I can write numerical expressions involving whole number exponents. Ex. 34 = 3x3x3x3 · I can evaluate numerical expressions involving whole number exponents. Ex. 34 = 3x3x3x3 = 81 · I can solve order of operation problems that contain exponents. Ex. 3+22 – (2+3) = 2
Standard 6.EE.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.
· I can use numbers and variables to evaluate expressions. · I can translate written phrases into algebraic expressions. · I can translate algebraic expressions into written phrases.
Standard 6.EE.2b: 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.
· I can identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient). · I can identify parts of an expression as a single entity, even if not a monomial.
Standard 6.EE.2c: Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in realworld problems. Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 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.
· I can substitute specific values for variables. · I can evaluate algebraic expressions including those that arise from realworld problems. · I can apply order of operations when there are no parentheses for expressions that include whole number exponents.
Standard 6.EE.3: Apply the properties of operations to generate equivalent expressions.
· I can create equivalent expressions using the properties of operations (e.g. distributive property, associative property, adding like terms with the addition property or equality, etc.). · I can apply the properties of operations to create equivalent expressions.
Standard 6.EE.4: 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.
· I can recognize when two expressions are equivalent. · I can prove (using various strategies) that two expressions are equivalent no matter what number is substituted.
Standard 6.EE.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.
· I can recognize solving an equation or inequality as a process of answering “which values from a specified set, if any, make the equation or inequality true?”. · I can use the solution to an equation or inequality to prove that the answer is correct. · I can use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Standard 6.EE.6: Use variables to represent numbers and write expressions when solving a realworld 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.
· I can recognize that a variable can represent an unknown number, or, depending on the scenario/situation, any number in a specific set. · I can relate variables to a context. · I can write expressions when solving a realworld or mathematical problem.
Standard 6.EE.7: Solve realworld 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.
· I can define an inverse operation. · I can use inverse operations to solve one step variable equations. · I can apply rules of the form x + p = q and px = q, for cases in which p, q and x are all nonnegative rational numbers, to solve real world and mathematical problems. (There is only one unknown quantity). · I can develop a rule for solving onestep equations using inverse operations with nonnegative rational coefficients. · I can solve and write equations for realworld mathematical problems containing one unknown.
Standard 6.EE.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld 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.
· I can identify the constraint or condition in a realworld or mathematical problem in order to set up an inequality. · I can recognize that inequalities of the form x>c or x
· I can write an inequality of the form x>c or x
· I can represent solutions to inequalities or the form x>c or x<c, with infinitely many solutions, on the number line diagrams.
Standard 6.EE.9: Use variables to represent two quantities in a realworld 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.
· I can define independent and dependent variables . · I can use variables to represent two quantities in a realworld problem that change in relationship to one another. · I can write an equation to express one quantity (dependent) in terms of the other quantity (independent). · I can analyze the relationship between the dependent variable and independent variable using tables and graphs. · I can relate the data in a graph and table to the corresponding equation.
Geometry (G)
Standard 6.G.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 realworld and mathematical problems.
· I can recognize and know how to compose and decompose polygons into triangles and rectangles. · I can compare the area of a triangle to the area of the composed rectangle. · I can apply the techniques of composing and/or decomposing to find the area of triangles, special quadrilaterals and polygons to solve mathematical and real world problems. · I can discuss, develop and justify formulas for triangles and parallelograms (6th grade introduction).
Standard 6.G.2: 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 realworld and mathematical problems.
· I can calculate the volume of a right rectangular prism. · I can apply volume formulas for right rectangular prisms to solve realworld and mathematical problems involving rectangular prisms with fractional edge lengths. · I can model the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths.
Standard 6.G.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 realworld and mathematical problems.
· I can draw polygons in the coordinate plane. · I can use coordinates (with the same xcoordinate or the same ycoordinate) to find the length of a side of a polygon. · I can apply the technique of using coordinates to find the length of a side of a polygon drawn in the coordinate plane to solve realworld and mathematical problems.
Standard 6.G.4: Represent threedimensional 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 realworld and mathematical problems.
· I can recognize that 3D figures can be represented by nets. · I can represent threedimensional figures using nets made up of rectangles and triangles. · I can apply knowledge of calculating the area of rectangles and triangles to a net. · I can combine the areas for rectangles and triangles in the net to find the surface area of a 3dimensional figure. · I can solve realworld and mathematical problems involving surface area using nets.
Statistics and Probability (SP)
Standard 6.SP.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.
· I can recognize that data has variability. · I can recognize a statistical question (examples versus nonexamples).
Standard 6.SP.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.
· I can identify that a set of data has distribution. · I can describe a set of data by its center, e.g., mean and median. · I can describe a set of data by its spread and overall shape, e.g. by identifying data clusters, peaks, gaps and symmetry.
Standard 6.SP.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.
· I can recognize there are measures of central tendency for a data set, e.g., mean, median, mode. · I can recognize there are measures of variances for a data set , e.g., range, interquartile range, mean absolute deviation. · I can recognize that measure of central tendency for a data set summarizes the data with a single number. · I can recognize that measures of variation for a data set describe how its values vary with a single number.
Standard 6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
· I can identify the components of dot plots, histograms, and box plots. · I can find the median, quartile and interquartile range of a set of data. · I can analyze a set of data to determine its variance. · I can create a dot plot to display a set of numerical data. · I can create a histogram to display a set of numerical data. · I can create a box plot to display a set of numerical data.
Standard 6.SP.5a: Summarize numerical data sets in relation to their context by reporting the number of observations.
· I can report the number of observations in a data set or display.
Standard 6.SP.5b: Summarize numerical data sets in relation to their context describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
· I can organize and display data in tables and graphs. · I can describe the data being collected, including how it was measured and its units of measurement.
Standard 6.SP.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 was gathered.
· I can calculate quantitative measures of center, e.g., mean, median, mode. · I can calculate measures of variance, e.g., range interquartile range, mean absolute deviation. · I can choose the appropriate measure of central tendency to represent the data.
Standard 6.SP.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 was gathered.
· I can identify outliers. · I can determine the effect of outliers on quantitative measures of a set of data, e.g., mean, median, mode, range, interquartile range, mean absolute deviation. · I can analyze the shape of the data distribution and the context in which the data were gathered to choose the appropriate measures of central tendency and variability and justify why this measure is appropriate in terms of the context.
