A Progression Toward Mastery Assessment Task Item STEP 1 Missing or incorrect answer and little evidence of reasoning or application of mathematics to solve the problem. STEP 2 Missing or incorrect answer but evidence of some reasoning or application of mathematics to solve the problem. STEP 3 A correct answer with some evidence of reasoning or application of mathematics to solve the problem or an incorrect answer with substantial evidence of solid reasoning or application of mathematics to solve the problem. STEP 4 A correct answer supported by substantial evidence of solid reasoning or application of mathematics to solve the problem. 1 a N-Q.A.1 N-Q.A.2 Student was unable to respond to question. or Student provided a minimal attempt to create an incorrect graph. Student created a graph that reflects something related to the problem, but the axes did not depict the correct units of distance from the house on the -axis and a measurement of time on the -axis, or the graph indicated significant errors in calculations or reasoning. Student created axes that depict distance from the house on the -axis and some measurement of time on the -axis, and the graph represents a reflection of what occurred but with errors in calculations, missing or erroneous axis labels, or choice of units that makes the graph difficult to obtain information from. Student created and labeled the-axis to represent distance from the house in miles and an-axis to represent time (in minutes past 1:00 p.m.) and created a graph based on solid reasoning and correct calculations.
b N-Q.A.1 Student answered incorrectly with no evidence of reasoning to support the answer. OR Student left item Student answered incorrectly but demonstrated some reasoning in explaining the answer. Student answered 1:21 p.m. but did not either refer to a correct graph or provide sound reasoning to support the answer. OR Student answered incorrectly because either the graph in part (a) was incorrect and the graph was referenced or because a minor calculation error was made but sound reasoning was used. Student answered 1:21 p.m. and either referred to a correct graph from part (a) or provided reasoning and calculations to explain the answer. c N-Q.A.1 Student answered incorrectly with no evidence of reasoning to support the answer. OR Student left item blank. Student answered incorrectly but demonstrated some reasoning in explaining the answer. Student answered miles but did not either refer to the work in part (a) or provide sound reasoning in support of the answer. OR Student answered incorrectly because either the work in part (a) was referenced, but the work was incorrect or because a calculation error was made but sound reasoning was used. Student answered miles and either referenced correct work from part (a) or provided reasoning and calculations to support the answer. 2 a N-Q.A.3 Student left the question blank. or Student provided an answer that reflected no or very little reasoning. Student either began with an assumption that was not based on the evidence of water being used at a rate of approximately liters/second at noon. or Student answered beginning with the idea that water was being used at a rate of approximately liters/second at noon but made an error in the calculations to Student answered beginning with the idea that water was being used at a rate of approximately liters/second at noon and made correct calculations to extend
Student used poor reasoning in extending that reading to consider use across hours. extend and combine that rate to consider usage across hours. or Student did not defend the choice by explaining water usage across the hours and how it compares to the reading taken at noon. and combine that rate to consider usage across hours. and Student defended the choice by explaining water usage across the hours and how it compares to the reading taken at noon. b N-Q.A.3 Student left the question blank. or Student provided an answer that reflected no or very little reasoning. Student provided an answer that is outside of the range from “to the nearest ten” to “to the nearest hundred”. OR Student provided an answer that is within the range but is not supported by an explanation. Student answer ranged from “to the nearest ten” to “to the nearest hundred” but was not well supported by sound reasoning. or Student answer contained an error in the way the explanation was written, even if it was clear what the student meant to say. Student answer ranged from “to the nearest ten” to “to the nearest hundred” and was supported by correct reasoning that is expressed accurately. c N-Q.A.3 Student left the question blank. or Student provided an answer that reflected no or very little reasoning. Student answer was not in the range of to checks but provided some reasoning to justify the choice. OR Student answer was in that range, perhaps written in the form of “every minutes” or “every hours” but was not supported by an explanation with solid reasoning. Student answer was in the range of to checks but was only given in the form of checks per minute or checks per hour; the answer was well supported by a written explanation. OR Student answer was given in terms of number of checks but was not well supported by a written explanation. Student answer was in the range of 6 to 48 checks, and student provided solid reasoning to support the answer.
3 a A-SSE.A.1a A-SSE.A.1b Student either did not answer. or Student answered incorrectly for all expressions. Student answered one or two of the three correctly but left the other one blank or made a gross error in describing what it represented. Student answered two of the three correctly and made a reasonable attempt at describing what the other one represented. Student answered all three correctly. b A-SSE.A.1a A-SSE.A.1b Student either did not answer. or Student answered incorrectly for all three parts of the question. Student understood that the expressions represented a portion of the orders for each color but the colors and/or incorrectly determined which one would be larger. Student understood that the expressions represented a portion of the orders for each and correctly determined which one would be larger but had errors in the way the answer was worded OR did not provide support for why would be larger. Student understood that the expressions represented a portion of the orders for each color, correctly determined which one would be larger, and provided a well written explanation for why. 4 A-SSE.A.1b A-SSE.A.2 Student left the question or Student was unable to re-write the expression successfully, even by multiplying out the factors first. Student got to the correct re-written expression of but did so by multiplying out the factors or did not show the work needed to demonstrate how was determined. Student attempted to use structure to the expression as described, showing the process, but student made errors in the process. Student correctly used the process described to arrive at without multiplying out linear factors and demonstrated the for doing so. 5 a–b A-SSE.A.2 Student was unable to respond to many of the questions. or Student left several items blank. Student was only able to come up with one option for part (a) and, therefore, had only partial work for part (b). OR Student answered “Yes” for the question about equivalent expressions. Student successfully answered part (a) and identified that the expressions created in part (b) were not equivalent, but there were minor errors in the answering of the remaining questions. Student answered all four parts correctly and completely.
6 a A-SSE.A.2 Student left at least three items blank. or Student answered at least three items incorrectly. Student answered one or two items incorrectly or left one or more items blank. Student completed circling task correctly and provided a correct ordering of symbols in the box, but the answer did not use parentheses or multiplication dots. Student completed all four item correctly, including exact placement of parentheses and symbols for the box: . b A-SSE.A.2 Student did not complete either proof successfully. Student attempted both proofs but made minor errors in both. or Student only completed one proof, with or without errors. Student attempted both proofs but made an error in one of them. Student completed both proofs correctly, and the two proofs were different from one another. 7 a A-APR.A.1 Student left the question blank or demonstrated no understanding of multiplication of polynomials. Student made more than one error in his multiplication but demonstrated some understanding of multiplication of polynomials. Student made a minor error in the multiplication. Student multiplied correctly and expressed the resulting polynomial as a sum of monomials. b A-APR.A.1 Student left the question or did not demonstrate a level of thinking that was higher than what was given in the problem’s description of Ahmed’s thinking. Student used language that did not indicate an understanding of base and/or the place value system. Student may have used language such as shifting or moving. Student made only errors in the use of mathematically correct language to relate the new number to the old in terms of place value and/or the use of base . Student made no errors in the use of mathematically correct language to relate the new number to the old in terms of place value and/or the use of base . 8 a–c A-APR.A.1 Student showed limited or no understanding of polynomial multiplication and of evaluating a polynomial for the given value of . Student made multiple errors but showed some understanding of polynomial multiplication. Student may not have combined like terms to present the Student made one or two minor errors but demonstrated knowledge of polynomial multiplication and combining like terms to create the new polynomial. Student also showed Student completed all products correctly, expressing each as a sum of monomials with like terms collected, and evaluated correctly when is .
product as the sum of monomials. understanding of evaluating a polynomial for the given value of . d A-APR.A.1 Student showed limited or no understanding of polynomial multiplication and of evaluating a polynomial for the given value of . Student made multiple errors but showed some understanding of polynomial multiplication. Student may not have combined like terms to present the product as the sum of monomials. Student may have gotten an incorrect result when evaluating with . Student made one or two minor errors but demonstrated knowledge of polynomial multiplication and combining like terms to create the new polynomial. Student also showed understanding of evaluating a polynomial for the given value of . Student correctly multiplied the polynomials and expressed the product as a polynomial in standard form. Student correctly evaluated with a value of and answered “Yes”. e A-APR.A.1 Student was unable to demonstrate an understanding that part (iii) is “No” and/or demonstrated limited or no understanding of polynomial multiplication. Student may have made some errors as he multiplied the polynomials and expressed the product as a sum of monomials. Student may have made some errors in the calculation of the value of the polynomial whenis . Student incorrectly answered part (iii) or applied incorrect reasoning. Student may have made errors in multiplying the polynomials and expressing the product as a sum of monomials. Student may have made minor errors in calculating the value of the polynomial when is . Student explained that the hypothesized equation being true when does not make it true for all real and/or explained that the two expressions are not algebraically equivalent. Student correctly multiplied the polynomials and expressed the product as a sum of monomials with like terms collected. Student correctly calculated the value of the polynomial when is . Student explained that the hypothesized equation being true when does not make it true for all real and/or explained that the two expressions are not algebraically equivalent.