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 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 – d A-REI.1 Student gave a short incorrect answer or left the question blank. Student showed at least one correct step, but the solution was incorrect. Student solved the equation correctly (every step that was shown was correct) but did not express the answer as a solution set. Student solved the equation correctly step that was shown was correct) and expressed the answer as a solution set. e A-SSE.1b A-REI.3 Student did not answer or answered incorrectly with something other than b and d. Student answered b and d but did not demonstrate reasoning in the explanation. Student answered b and d but made misstatements in the explanation. Student answered b and d and articulated solid reasoning in the explanation. 2 a – b A-CED.3 Student responded incorrectly or left the question blank. Student responded correctly that c must be greater but did not use solid reasoning to explain the answer. Student responded correctly that c must be greater but gave an incomplete or slightly incorrect explanation of why. Student responded correctly that c must be greater and supported the statement with well-expressed reasoning. 3 a Student responded incorrectly or left the Student responded correctly by circling Student responded correctly by circling Student responded correctly by circling
A-SSE.1b question the expression on the left but did not use reasoning to explain the answer. the expression on the left but gave limited explanation or did not use the properties of inequality in the explanation. the expression on the left and gave a complete explanation that used the properties of inequality. b A-SSE.1b Student was unable to respond to question or left items blank. Part (b) was answered incorrectly. Student provided limited expression of the reasoning. Student provided solid reasoning with examples. 4 a – h A-REI.1 A-REI.3 Student answered incorrectly with no correct shown. Student answered incorrectly but had one or more correct steps. Student answered correctly but did not express the answer as a solution set. Student answered correctly and expressed the answer as a solution set. 5 a A-REI.1 Student did not answer or demonstrated incorrect reasoning throughout. Student demonstrated only limited reasoning. Student demonstrated solid reasoning but fell short of a complete answer or made a minor misstatement in the answer. Student answer was complete and demonstrated solid reasoning throughout. b A-REI.1 Student did not answer or did not demonstrate understanding of what the question was asking. Student made more than one misstatement in the definition. Student provided a mostly correct definition with a minor misstatement. Student answered completely and used a correct definition without error or c A-REI.1 Student made mistakes in both verifications and demonstrated incorrect reasoning or left the question blank. Student conducted both verifications but fell short of articulating reasoning to answer the question. Student conducted both verifications and articulated reasoning to answer the question but made a minor error in the verification or a minor misstatement in the explanation. Student conducted both verifications without error and articulated valid reasoning to answer the question.
d A-REI.1 Student answered incorrectly or does not answer. Student identified one or both solutions but was unable to convey how the solutions could be found using the fact that 4 is a solution to the original equation. Student identified only one solution correctly but articulated the reasoning of using the solution to the original equation to find the solution to the new equation. Student identified both solutions correctly and articulated the reasoning of using the solution to the original equation to find the solution to the new equation. 6 A-CED.4 Student did not answer or showed no evidence of reasoning. Student made more than one error in the solution process but showed some evidence of reasoning. Student answer showed steps but with one minor error. Student answered correctly. 7 a – c A-CED.3 Student was unable to answer any portion correctly. Student answered one part correctly or showed some evidence of reasoning in more than one part. Student showed evidence of reasoning in every part but may have made minor errors. Student answered every part correctly AND demonstrated and expressed valid reasoning throughout. 8 a A-CED.2 Student provided no or a table with multiple incorrect entries. Data table is incomplete OR has more than one minor error. Data table is complete but may have one error OR slightly inaccurate headings. Data table is complete and correct with correct headings. b A-CED.2 Student provided no equation or an equation that did not represent exponential growth. Student provided an incorrect equation but one that modeled exponential growth. Student provided a correct answer in the form of . Student provided a correct answer in the form of or in more than one form such as and . c A-CED.2 Student provided no graph or a grossly inaccurate graph. Student provided a with an inaccurate shape but provided some evidence of reasoning in labeling the axes and/or data points. Student created a with correct general shape but may have left off OR made an error on one or two axes or data points. Student created complete graph with correctly labeled axes and correctly labeled data points (or a data table) showing the values for h = 0, 1, 2, 3, 4.
d A-CED.2 Student provided no answer or an incorrect answer with no evidence of reasoning in arriving at the answer. Student provided limited evidence of reasoning AND an incorrect answer. Student answered that 409.6 bacteria would be alive. Student answered that 410 or about 410 bacteria would be alive. 9 a A-CED.1 Student wrote incorrect equations or did not provide equations. Student answers were incorrect, but at least one of the equations was correct. Student may have made a gross error in the solution, made more than one minor error in the solution process, or may have had one of the two equations incorrect. Both equations were correct, but student made a minor mistake in finding the solution. Both equations were correct and student solved them correctly to arrive at the answer that Jack is 31 and Susan is 4. b A-REI.3 Student did not answer or gave a completely incorrect answer. Student articulated only one of the calculations correctly. Student articulated the two calculations but with a in one of the descriptions. Student articulated both calculations correctly. 10 a-b A-APR.1 Student work is blank or demonstrates no understanding of multiplication of polynomials, nor how to apply part (a) to arrive at an answer for part (b). Student made more than one error in the multiplication but demonstrated some understanding of multiplication of polynomials. Student may not have been able to garner or apply information from part a to use in answering part b correctly. Student demonstrated the ability to multiply the polynomials (expressing the product as a sum of monomials with like combined) and to apply the structure from part a to solve part b. There may be minor errors. Student demonstrated the ability to multiply the polynomials (expressing the product as a sum of monomials with like combined) and to apply the structure from part a to solve part b as: . 11 a A-REI.6 Student was unable to demonstrate the understanding that two equations with (3, 4) as a solution are needed. Student provided two equations that have (3, 4) as a solution (or attempted to provide such equations) but made one or more errors. Student may Student showed one minor error in the answer but attempted to provide two equations both containing (3, 4) as a Student provided two equations both containing (3, 4) as a solution and both with positive slope.
b A-CED.2 A-REI.10 A-REI.12 Student was unable to communicate a relevant requirement of the solution set. Student provided a verbal description that lacked precision and accuracy but demonstrated some reasoning about the solution within the context of the problem. Student made minor errors in communicating the idea that both (a) and (b) must be whole numbers whose sum is less than or equal to 160. Student communicated effectively that both (a) and (b) must be whole numbers whose sum is less than or equal to 160. c A-CED.2 A-REI.6 Student was unable to demonstrate any substantive understanding in how to create the equations and the system of equations. Student made multiple errors in the equations and/or solving process but demonstrated some understanding of how to create equations to represent a context and/or solve the system of equations. Student made minor errors in the equations but solved the system accurately, or the student created the correct equations but made a minor error in solving the system of equations. Student correctly wrote the equations to represent the system. Student solved the system accurately and summarized by defining or describing the values of the variable in the context of the problem: that there were 100 adult tickets and 44 child tickets sold. Name Date Solve the following equations for. Write your answer in set notation.