# Evidence Statement Tables Grade 6 Mathematics. Evidence Statements Grade 6 Mathematics 1

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4 Listing by Type 1, Type II, and Type III The PR s for Grade 6 Mathematics are provided starting on the next page. The list has been organized to indicate whether items designed are aligned to an used for Type I items, Type II items (reasoning), or Type III items (modeling). s are presented in the order shown below and are color coded: Peach is applicable to Type I items. Lavender is applicable to Type II items. qua is applicable to the Type III items. s Grade 6 Mathematics 4

7 6.NS.33 Fluently multiply multidigit decimals using the standard algorithm. ii) Only the product is required. iii) The given factors require an efficient/standard algorithm (e.g., ). iv) For purposes of assessment, the possibilities are 1digit x 2digit, 1digit x 3 digit, 2digit x 3digit, 2digit x 4digit, or 2digit x 5digit. 6.NS.34 Fluently divide multidigit decimals using the standard algorithm. ii) Only the quotient is required. iii) The given dividend and divisor require an efficient/standard algorithm (e.g., ). iv) Tasks are either 4digit 2digit or 3digit 3digit. (For example, or ). v) Every quotient is a whole number or a decimal terminating at the tenths, hundredths, or thousandths place. 6.NS.41 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 NS.42 Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4(9 + 2). ii) Tasks require writing or finding the equivalent expression with the greatest common factor. 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, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. i) Tasks do not require students to perform any computations. ii) Students may be asked to recognize the meaning of 0 in the situation, but will not be asked to explain. 6.NS.6a 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. a 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) Tasks have thin context 2 or no context. s Grade 6 Mathematics 7

9 6.NS.7b Understand ordering and absolute value of rational numbers. b. Write, interpret, and explain statements of order for rational numbers in realworld contexts. For example, write 3 o > 7 o to express the fact that 3 o is warmer than 7 o. i) Tasks are not limited to integers. ii) For the explain aspect of 6.NS.7b, see NS.7c1 Understand ordering and absolute value of rational numbers. c. Understand the absolute value of a rational number as its distance from 0 on the number line. ii) Tasks are not limited to integers. 6.NS.7c2 Understand ordering and absolute value of rational numbers. c. 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) Tasks have a context. ii) Tasks are not limited to integers. 6.NS.7d Understand ordering and absolute value of rational numbers. d. 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) Tasks may or may not contain context. ii) Tasks are not limited to integers. iii) Prompts do not present students with a number line diagram, but students may draw a number line diagram as a strategy. 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) Tasks may or may not contain context. ii) Finding distances is limited to points with integer coordinates. s Grade 6 Mathematics 9

12 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. nalyze 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) Tasks that involve writing an equation should not go beyond the equation types described in 6.EE.7 (x+p =q and px = q where p, q, and x are all nonnegative rational numbers). 6.G.1 Find the 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. 6.G.21 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. ii) Tasks require focusing on the connection between packing the solid figure and computing the volume. 6.G.22 pply the formulas V = l w h and V = h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. i) Tasks focus on using the formulas in problemsolving contexts. 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. pply these techniques in the context of solving realworld and mathematical problems. 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. pply these techniques in the context of solving realworld and mathematical problems. s Grade 6 Mathematics 12

14 ase explanations/reasoning on the properties of operations. ontent Scope: Knowledge and skills articulated in 6.EE.3, 6.EE.4 ase explanations/reasoning on the relationship between addition and subtraction or the relationship between multiplication and division. ontent Scope: Knowledge and skills articulated in 6.NS.1 ase arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. ontent Scope: Knowledge and skills articulated in 6.NS.1 i) Tasks should not require students to identify or name properties 6..4 ase explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response). ontent Scope: Knowledge and skills articulated in 6.NS.6, 6.NS ase explanations/reasoning on a coordinate plane diagram (whether provided in the prompt or constructed by the student in her response). ontent Scope: Knowledge and skills articulated in 6.NS.6, 6.NS Given an equation, present the solution steps as a logical argument that concludes with a solution. ontent Scope: Knowledge and skills articulated in 6.EE. i) Tasks do not require students to write an equation or inequality onstruct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. ontent Scope: Knowledge and skills articulated in 6.EE Present solutions to multistep problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as = = 12, even if the final answer is correct), or identify or describe errors in solutions to multistep problems and present corrected solutions. i) Expectations for ratios in this grade are limited to ratios of noncomplex fractions. The initial numerator and denominator should be whole numbers. ontent Scope: Knowledge and skills articulated in 6.RP. s Grade 6 Mathematics 14

15 Relationsh ip Present solutions to multistep problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as = = 12, even if the final answer is correct), or identify or describe errors in solutions to multistep problems and present corrected solutions. i) Tasks that involve writing an equation should not go beyond the equation types described in 6.EE.7 (x+p =q and px = q where p, q, and x are all nonnegative rational numbers). ontent Scope: Knowledge and skills articulated in 6.EE Distinguish correct explanation/reasoning from that which is flawed, and if there is a flaw in the argument present corrected reasoning. (For example, some flawed student reasoning is presented and the task is to correct and improve it.) i) Tasks may have scaffolding 1, if necessary, in order to yield a degree of difficulty appropriate to Grade 6. ontent Scope: Knowledge and skills articulated in 5.NT, 5.MD.. s Grade 6 Mathematics 15

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