Math Released Item Algebra 1. Solve the Equation VH046614

Transcription

1 Math Released Item 2017 Algebra 1 Solve the Equation VH046614

2 Anchor Set A1 A8 With Annotations

3 Prompt

4 Rubric VH Rubric Score Description 3 Student response includes the following 3 elements. Reasoning component = 2 points o Two valid methods for solving the quadratic equation (at least one method must be algebraic) Computation component = 1 point o Correct solution of x = 3 Sample Student Response: One method could be factoring: 2x = 12x 2x 2-12x + 18 = 0 (2x - 6)(x - 3) = 0 2(x - 3)(x - 3) = 0 x - 3 = 0 x = 3 A second method could be graphing the equation. If I change the equation into a system: y 1 = 2x , I can y 2 = 12x graph this on my calculator. These two equations intersect at (3,36), so the equation has a solution at x = 3. Note: The student earns 1 reasoning point for each of the two methods used to solve the equation. 2 Student response includes 2 of the 3 elements. 1 Student response includes 1 of the 3 elements. 0 Student response is incorrect or irrelevant.

5 A1 Score Point 3

6 Annotation Anchor Paper 1 Score Point 3 This response receives full credit. It includes each of the three required elements. The response includes an algebraic method of solving the quadratic equation, using the quadratic formula (a=2, b=-12, c=18; ( 12)± (2)(18) 2(+2) ). The response provides the correct solution of x=3 (+3 and +3). The response includes a description of an alternate method of solving the equation, graphing (put it into your calculator. Under y1=2x and y2=12x. When you graph it, you will get one parabola and one straight line. Then, find the int. and x=3). Note: An algebraic solution comprises factoring, quadratic formula, or completing the square. Substitution of possible values (guess-and-check) and graphing are not algebraic solution methods.

7 A2 Score Point 3

8 Annotation Anchor Paper 2 Score Point 3 This response receives full credit. It includes each of the three required elements. The response includes an algebraic method of solving the quadratic equation, factoring. The response provides the correct solution of x=3. The response includes a description of an alternate method of solving the equation, graphing. Providing a table of values and drawing the graph provides a complete description of the method.

9 A3 Score Point 2

10 Annotation Anchor Paper 3 Score Point 2 This response receives partial credit. It includes two of the three required elements. The response includes an algebraic method of solving the quadratic equation, factoring. The response provides the correct solution of x=3. This response does not receive credit for the alternate method. In this response, the student does not give any indication of how the formula is used. The quadratic formula is provided to students on the math reference sheet they receive when they take the exam, and therefore the formula does not count as student work. At minimum, the response needs to indicate which values are being used for variables a, b, and c in the quadratic formula in order to receive credit for a description of an alternate method.

11 A4 Score Point 2

12 Annotation Anchor Paper 4 Score Point 2 This response receives partial credit. It includes two of the three required elements. The response includes an algebraic method of solving the quadratic equation, factoring by grouping [2x(x-3)+(-6)(x-3)]. The response provides the correct solution of x=3. The description of the solution method does not receive credit because it is not specific enough. The student does not indicate either that the line is intersecting with the parabola or that the parabola is intersecting with the x- axis or provide specific information about how to graph the equation.

13 A5 Score Point 1

14 Annotation Anchor Paper 5 Score Point 1 This response receives partial credit. It includes one of the three required elements. The response provides the correct solution of x=3. The response does not provide an algebraic method of solving the equation. The alternate method, guess-and-check, does not receive credit. A scoring decision was made that states that students must show at least one incorrect guess, in addition to the correct guess, to receive credit.

15 A6 Score Point 1

16 Annotation Anchor Paper 6 Score Point 1 This response receives partial credit. It includes one of the three required elements. The response includes an algebraic method of solving the quadratic equation, factoring by grouping [2x(x-3)+6(x-3)]. The response does not, however, include the interpretation of the factors to arrive at the solution of x=3. Also, no alternate method is included.

17 A7 Part A: Score Point 0

18 Annotation Anchor Paper 7 Score Point 0 This response receives no credit. It includes none of the three required elements. No correct work is shown, since 18 is not divided by 2. No solution is given. The description of the alternate method is not specific enough (use a graph).

19 A8 Score Point 0

20 Annotation Anchor Paper 8 Score Point 0 This response receives no credit. It includes none of the three required elements. Although the correct solution of x=3 is shown, the work used to obtain the answer is entirely incorrect. A scoring decision was made that states that a correct answer resulting from clearly incorrect work will not receive credit.

21 Practice Set P101 - P105 No Annotations Included

22 P101

23 P102

24 P103

25 P104

26 P105

27 Practice Set Paper Score P101 1 P102 2 P103 0 P104 3 P105 2