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Common Core Standards
Converted/Unpacked Standards
Standards Code: OA=Operations and Algebraic Thinking, NBT=Number and Operations in Base 10, MD=Measurements and Data, G=Geometry, NF=Number and Operations-Fractions, RP=Rations and Proportional Relationships, NS= Number System, EE=Expressions and Equations, SP=Statistics and Probability, A=Algebra.
CC.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. 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 apply the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (CCSS: 6.RP.1)
I can explain the relationship that a ratio represents. (CCSS: 6.RP.1)CC.6.RP.2 Understand ratio concepts and use ratio reasoning to solve problems. 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 non-complex fractions.)I can apply 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. (CCSS: 6.RP.2)
I can convert a given ratio (a/b) to a unit rate (a:b). (CCSS: 6.RP.2) I can describe the ratio relationship represented by a unit rate. (CCSS: 6.RP.2)
CC.6.RP.3 Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
I can use ratio and rate reasoning to solve real-world and mathematical problems. (CCSS: 6.RP.3)
I can create a table of equivalent ratios, tape diagrams, double number line diagrams, and equations. (CCSS: 6.RP.3a)
I can use the proportional relationship to find missing values in a table of equivalent ratios. (CCSS: 6.RP.3a) I can plot corresponding values from an equivalent ratio table on a coordinate grid or other visual represtations. (CCSS: 6.RP.3b)
I can write a percent as a rate per one-hundred and find percent of a given number.(CCSS: 6.RP.3c) I can use ratio reasoning to convert measurement units. (CCSS: 6.RP.3d)CC.6.RP.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.
Common Core Standards
Converted/Unpacked Standards
CC.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?CC.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.CC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 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 3/4-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?I can solve real world problems involving the division of fractions and interpret the quotient in the context of the problem. (CCSS: 6.NS.1)I can compute quotients of fractions. (CCSS: 6.NS.1)I can solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. (CCSS: 6.NS.1)
CC.6.NS.2 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently divide multi-digit numbers using the standard algorithm. I can use the standard algorithm to fluently divide multi-digit numbers. (CCSS: 6.NS.2)CC.6.NS.3 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.I can fluently add, subtract, multiply, and divide multi-digit decimals using standard algorithms for each operation. (CCSS: 6.NS.3)CC.6.NS.4 Compute fluently with multi-digit numbers and find common factors and multiples. 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 1100 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 find the greatest common factor of two whole numbers less than or equal to 100. (CCSS: 6.NS.4)I can find the least common multiple of two whole numbers less than or equal to 12. (CCSS: 6.NS.4)I can use the distributive property to express a simple addition problem when the addends have a common factor. (CCSS: 6.NS.4)
Common Core Standards
Converted/Unpacked Standards
CC.6.NS.5 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, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.I can explain why positive and negative numbers are used together to describe quantities having opposite directions or values. (CCSS: 6.NS.5)I can use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. (CCSS: 6.NS.5)CC.6.NS.6 Apply and extend previous understandings of numbers to the system of rational numbers. 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 use number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates. (CCSS: 6.NS.6)I can describe a rational number as a point on the number line. (CCSS: 6.NS.6)
I can use opposite signs of numbers to indicate locations on opposite sides of 0 on the number line. (CCSS: 6.NS.6a)
I can explain when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. (CCSS: 6.NS.6b)I can identify that the opposite of the opposite of a number is the number itself. (CCSS: 6.NS.6a)
I can find and position integers and other rational numbers on a horizontal or vertical number line diagram. (CCSS: 6.NS.6c)I can find and position pairs of integers and other rational numbers on a coordinate plane. (CCSS: 6.NS.6c)CC.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.CC.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. CC.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.
Common Core Standards
Converted/Unpacked Standards
CC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers.
I can order and find absolute value of rational numbers. (CCSS: 6.NS.7)
I can interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (CCSS: 6.NS.7a)
I can write, interpret, and explain statements of order for rational numbers in real-world contexts. (CCSS: 6.NS.7b)
I can define the absolute value of a rational number as its distance from 0 on the number line and interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (CCSS: 6.NS.7c)
I can distinguish comparisons of absolute value from statements about order. (CCSS: 6.NS.7d)CC.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.CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3C > 7C to express the fact that 3C is warmer than 7C.CC.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 real-world situation. For example, for an account balance of 30 dollars, write |30| = 30 to describe the size of the debt in dollars.CC.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.CC.6.NS.8 Apply and extend previous understandings of numbers to the system of rational numbers. 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.I can graph points in any quadrant of the coordinate plane to solve real world problems. (CCSS: 6.NS.8)
I can use absolute value to find distances between two points with the same x or y coordinate. (CCSS: 6.NS.8)
CC.6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Write and evaluate numerical expressions involving whole-number exponents.
I can write and evaluate expressions involving whole-number exponents. (CCSS: 6.EE.1)
Common Core Standards
Converted/Unpacked Standards
CC.6.EE.2 Apply and extend previous understandings of arithmetic to algebraic expressions. Write, read, and evaluate expressions in which letters stand for numbers.
I can write, read, and evaluate expressions in which letters stand for numbers. (CCSS: 6.EE.2)
I can write expressions that record operations with numbers and with letters standing for numbers. (CCSS: 6.EE.2a)
I can identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) and describe one or more parts of an expression as a single entity. (CCSS: 6.EE.2b)
I can evaluate expressions at specific values of their variables including expressions that arise from formulas used in real-world problems. (CCSS: 6.EE.2c)I can apply the order of operations when evaluating both arithmetic and algebraic expressions. (CCSS: 6.EE.2c)CC.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. CC.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. CC.6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world 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). 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. CC.6.EE.3 Apply and extend previous understandings of arithmetic to algebraic expressions. Apply the properties of operations to generate equivalent expressions. 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.
I can apply the properties of operations, especially the distributive property, to generate equivalent expressions. (CCSS: 6.EE.3)
I can create a visual model to show equality between two expressions or equations. (CCSS: 6.EE.3)
Common Core Standards
Converted/Unpacked Standards
CC.6.EE.4 Apply and extend previous understandings of arithmetic to algebraic expressions. 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 identify when two expressions are equivalent by using the same value to evaluate both expressions. (CCSS: 6.EE.4)
CC.6.EE.5 Reason about and solve one-variable equations and inequalities. 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 describe solving an equation or inequality leads to finding the value or values of the variables. (CCSS: 6.EE.5)I can use substitution to determine whether a given number in a specified set makes an equation or inequality true. (CCSS: 6.EE.5)CC.6.EE.6 Reason about and solve one-variable equations and inequalities. 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.I can use variables to represent numbers and write expressions when solving a real-world or mathematical problem. (CCSS: 6.EE.6)I can recognize that a variable can represent an unknown number or any number in a specified set. (CCSS: 6.EE.6)CC.6.EE.7 Reason about and solve one-variable equations and inequalities. 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.I can 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. (CCSS: 6.EE.7)CC.6.EE.8 Reason about and solve one-variable equations and inequalities. 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.I can write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. (CCSS: 6.EE.8)I can show that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. (CCSS: 6.EE.8)CC.6.EE.9 Represent and analyze quantitative relationships between dependent and independent variables. 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.
I can use variables to represent two quantities in a real-world problem that change in relationship to one another. (CCSS: 6.EE.9)I can 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. (CCSS: 6.EE.9)I can analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (CCSS: 6.EE.9)
Common Core Standards
Converted/Unpacked Standards
CC.6.G.1 Solve real-world and mathematical problems involving area, surface area, and volume. 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.
I can develop and apply formulas and procedures for area of plane figures. I can find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. (CCSS: 6.G.1)I can apply these techniques in the context of solving real-world and mathematical problems. (CCSS: 6.G.1)
CC.6.G.2 Solve real-world and mathematical problems involving area, surface area, and volume. 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.
I can develop and apply formulas and procedures for volume of regular prisms. I can 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. (CCSS: 6.G.2)I can show that volume is the same as multiplying the edge lengths of a rectangular prism. (CCSS: 6.G.2)I can 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. (CCSS: 6.G.2)CC.6.G.3 Solve real-world and mathematical problems involving area, surface area, and volume. 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.I can plot polygons in the coordinate plan to solve real-world and mathematical problems. (CCSS: 6.G.3)I can plot polygons in the coordinate plane given coordinates for the vertices. (CCSS: 6.G.3)I can use coordinates to find the length of a side joining points. (CCSS: 6.G.3)CC.6.G.4 Solve real-world and mathematical problems involving area, surface area, and volume. 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.I can develop and apply formulas and procedures for the surface area. I can represent three-dimensional figures using nets made up of rectangles and triangles. (CCSS: 6.G.4)I can use nets to find the surface area of figures. (CCSS: 6.G.4)I can apply techniques for finding surface area in the context of solving real-world and mathematical problems. (CCSS: 6.G.4)CC.6.SP.1 Develop understanding of statistical variability. 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 explain what makes a good statistical question.(CCSS: 6.SP.1) I can develop a question that can be used to collect statistical information. (CCSS: 6.SP.1)
Common Core Standards
Converted/Unpacked Standards
CC.6.SP.2 Develop understanding of statistical variability. 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 demonstrate 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. (CCSS: 6.SP.2)
I can describe mean, median, and mode. (CCSS: 6.SP.2) I can describe extremes, clusters, gaps, and outliers.(CCSS: 6.SP.2)
I can describe the overall shape of the set of data in terms of its symmetry or skewness. (CCSS: 6.SP.2)
CC.6.SP.3 Develop understanding of statistical variability. 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 explain that a measure of center for a numerical data set summarizes all of its values with a single number. (CCSS: 6.SP.3) I can measure how variations describe its values with a single number. (CCSS: 6.SP.3)CC.6.SP.4 Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. I can display numerical data in plots on a number line, including dot plots, histograms, and box plots. (CCSS: 6.SP.4)CC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by: -- a. Reporting the number of observations. -- b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. -- c. 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. -- d. 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 summarize numerical data sets in relation to their context. (CCSS: 6.SP.5)I can report the number of observations. (CCSS: 6.SP.5a)I can describe the nature of the attribute under investigation, including how it was measured and its units of measurement. (CCSS: 6.SP.5b)I can give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation). (CCSS: 6.SP.5c) I can describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (CCSS: 6.SP.5c)I can relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. (CCSS: 6.SP.5d)
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Converted/Unpacked Standards
Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
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Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Common Core Math Standards
Grade 6
PAGE
PAGE 1
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