Write and solve an equation that can be used to find the value of . Write and solve an equation that can be used to find the value of . 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 STEP 4 A correct answer supported by substantial evidence of solid reasoning or application of mathematics to solve the problem
reasoning or application of mathematics to solve the problem 1 a 7.EE.A.1 Student demonstrates a limited understanding of writing the expression in standard form. OR Student makes a conceptual error, such as dropping the parentheses or adding instead of multiplying. Student makes two or more computational errors. Student demonstrates a solid understanding but makes one computational error and completes the question by writing a correct equivalent expression in standard form. OR Student answers correctly, but no further correct work is shown. Student writes the expression correctly in standard form, . Student shows appropriate work, such as using the distributive property and collecting like terms. b 7.EE.A.1 Student demonstrates a limited understanding of writing the expression in factored form. Student writes the expression correctly in factored form but has part (a) incorrect. Student demonstrates a solid understanding by writing a correct equivalent expression in factored form based on the answer from part (a) but makes one computational error. Student uses the correct expression from part (a). Student writes an equivalent expression in factored form. 2 a 7.EE.B.3 7.EE.B.4a Student demonstrates a limited understanding of perimeter by finding three sides of a triangle whose sum is , but the sides are incorrect and do not satisfy the given conditions. For example, a student says the sides are , and because they add up to but does not satisfy the given conditions. Student makes a conceptual error and one computational error. OR Student makes a conceptual error but writes an equation of equal difficulty and solves it correctly but does not find the lengths of the sides of the triangle. Student demonstrates a solid understanding and finishes the problem correctly but makes one computational error with a value still resulting in a fractional value.. OR Student sets up and solves an equation correctly but does not substitute the value back into the expressions to determine the actual side lengths. OR Student defines the sides correctly and sets up an equation but makes one error in solving the equation and finding the corresponding side lengths. Student correctly defines the variable, sets up an equation to represent the perimeter, such as , solves the equation correctly, , and determines the lengths of the three sides to be ,, and. OR Student finds the correct lengths of the sides of a triangle to be ,, and, using arithmetic or a tape diagram, showing appropriate and correct work.
c 7.EE.B.3 7.EE.B.4a Student demonstrates some understanding between an arithmetic and algebraic approach. Student fully understands the similarities between both approaches. 4 a 7.EE.A.2 7.EE.B.4a Student demonstrates a limited understanding by writing an incorrect equation and solving it incorrectly. Student makes a conceptual error in solving the equation, such as subtracting by instead of multiplying by . OR Student makes a conceptual error in writing the equation, such as or , but further work is solved correctly. OR Student writes a correct equation, but no further correct work is shown. OR Student finds the correct answer without writing an equation, such as using a tape diagram or arithmetic. Student sets up a correct equation but makes one computational error. OR Student finds the correct value of the variable but does not state the cost of one pair of shoes. OR Student sets up a wrong equation of equal difficulty by writing a number from the problem incorrectly, but all further work is correct. Student clearly defines the variable, writes a correct equation, such as , and finds the correct cost of one pair of shoes as . b 7.EE.A.2 7.EE.B.4b Student demonstrates a limited understanding of discount price, inequality, and solution of inequality. OR Student finds the correct new price for the shoes of , but no further correct work is shown. OR Student writes an inequality representing the total cost as an inequality, but no further correct work is shown, nor is the new price for the shoes found correctly. Student makes a conceptual error such as not finding the new discount price of the shoes. OR Student makes a conceptual error in writing or solving the inequality. OR Student makes two or more computational or rounding errors. Student demonstrates a solid understanding but makes one computational error. OR Student calculates the discount on the shoes incorrectly but finishes the remaining problem correctly. For example, student uses the discount amount, , as the new price of shoes but writes a correct inequality and solution of based on the discount amount. OR Student determines the correct discount price for the shoes but uses instead of . OR Student determines the correct new price for the shoes including the off as , writes a correct inequality, solves the inequality correctly, , and determines by rounding correctly that the amount of socks that could be purchased is pairs.
Student determines the correct discount price for the shoes, writes and solves the inequality correctly, but does not round or rounds incorrectly. 5 a 7.EE.B.4b Student demonstrates some understanding of writing an inequality but makes an error, such as or subtracting instead of adding. Student writes a correct inequality, , to represent the situation. b 7.EE.B.4b Student demonstrates a limited understanding of solving the inequality and interpreting the solution. Student makes a conceptual error in solving the inequality. OR Student makes two or more computational or rounding errors. Student demonstrates a solid understanding of solving the inequality but makes one computational or one rounding error. Student solves the inequality written from part (a) correctly, , and determines the correct number of people by rounding correctly to . c 7.EE.B.4b Student demonstrates a limited understanding of graphing inequalities by only plotting the point correctly. Student graphs the inequality but makes two or more errors. OR Student makes a conceptual error such as graphing on a coordinate plane instead of a number line. Student demonstrates a solid understanding of graphing an inequality but makes one error such as an open circle, an incorrect scale, a circle placed in the wrong area, or an arrow drawn in the wrong direction. Student correctly graphs the solution of the inequality from part (b). An appropriate scale is provided, clearly showing and . A closed circle is shown at approximately , a little less than , and an arrow is pointing to the left. 6 a 7.EE.B.4 Student demonstrates a limited understanding, such as indicating a sum, but the variables are not clearly defined, and the expression is left without collecting like terms. Student makes a conceptual error such as finding the difference of all the costs of admissions. OR Student does not write an expression to find the total cost. Instead, the student leaves each admission as a separate expression, and . Student writes a correct expression but does not define the variables or does not define them correctly, such as represents the 3D admission and represents regular. The variables need to specifically indicate the cost. OR Student makes one computational error in collecting like terms. OR Student clearly defines the variables correctly but makes one mistake in the expression, such Student clearly defines the variables and writes an expression such as , with appropriate work shown. The definition of the variables must indicate the cost of each admission.
as leaving out one person. b 7.EE.B.4a Student demonstrates a limited understanding, such as times or , but the variables are reversed: ,. An expression is written, such as or , to demonstrate that the cost of 3D admission is double, or two times, the cost of a regular admission ticket. c 7.EE.B.4a Student demonstrates a limited understanding of writing an equation and solving the equation. Student writes a correct equation but no further correct work is shown. OR Student makes a conceptual error, such as solving the equation but disregarding the two variables and making them one, such as . OR Student writes a correct equation but makes two or more computational errors. Student writes a correct equation but makes one computational error. OR Student solves the equation correctly but does not indicate the final cost of admission as . Student writes a correct equation such as , and solves it correctly by substituting for resulting in , and writes the correct answer of the cost of regular admission, . 7 a 7.G.B.5 Student demonstrates a limited understanding of vertical angle relationships by writing an equation such as , but no further work is shown, or the work shown is incorrect. Student writes the correct equation, but no further correct work is shown, or two or more computational errors are made solving the equation. OR Student makes a conceptual error such as adding the angles to equal , and all further work shown is correct. OR Student makes a conceptual error writing the equation, such as , but solves the equation correctly, getting , and all work is shown. OR Student writes a correct Student writes the correct equation representing the vertical angle relationship but makes one computational error in solving the equation. Student correctly recognizes the vertical angle relationship, writes the equation and solves the equation correctly, showing all work, getting a value of for .