**Sub-claim:**A

The students solve problems involving the Major Content with connections to the Standards for Mathematical Practice

Y = Yes; Assessed on Calculator Section

X = Calculator is Specific to Item

N = No; Assessed on Non-Calculator Sections

Z = Calculator Neutral (Could be Calculator or Non-Calculator Sections)

Solve quadratic equations in one variable. b) Solve quadratic equations with rational number coefficients by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

1) Tasks should exhibit variety in initial forms. Examples of quadratic equations with real solutions: t^2= 49, 3a^2 = 4, 7 = x^2, r^2 = 0, 12y^2 = 15 , y^2- 8y + 15 = 0, 2x^2 - 16x + 30 = 0, 2p = p^2 + 1, t^2 = 4t, 7x^2 + 5x - 3 = 0, 34c(c - 1) = c, (3𝑐−2)2 =6𝑥−4

2) Methods are not explicitly assessed; strategy is assessed indirectly by presenting students with a variety of initial forms.

3) For rational solutions, exact values are required. For irrational solutions, exact or decimal approximations may be required. Simplifying or rewriting radicals is not required; however, students will not be penalized if they simplify the radicals correctly.

4) Prompts integrate mathematical practices by not indicating that the equation is quadratic. (e.g., "Find all real solutions of the equation 𝑡^2 = 4t" ... not, "Solve the quadratic equation 𝑡^2 = 4t.")

EOY Released Test Item 33

PBA Released Test Item 3

Practice Test, Unit 2, Item 7

Paper Test, Unit 2, Item 19

What is the sum of the roots of the equation

2x

**Type of items:**Type 1**Color Code:**Peach**Evidence Statement Key:**A-REI.4b-1**Calculator:**XY = Yes; Assessed on Calculator Section

X = Calculator is Specific to Item

N = No; Assessed on Non-Calculator Sections

Z = Calculator Neutral (Could be Calculator or Non-Calculator Sections)

**Point:**1 each (1:26)**Evidence Statement Text:**Solve quadratic equations in one variable. b) Solve quadratic equations with rational number coefficients by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

**Clarifications, limits, emphases, and other information intended to ensure appropriate variety in tasks:**1) Tasks should exhibit variety in initial forms. Examples of quadratic equations with real solutions: t^2= 49, 3a^2 = 4, 7 = x^2, r^2 = 0, 12y^2 = 15 , y^2- 8y + 15 = 0, 2x^2 - 16x + 30 = 0, 2p = p^2 + 1, t^2 = 4t, 7x^2 + 5x - 3 = 0, 34c(c - 1) = c, (3𝑐−2)2 =6𝑥−4

2) Methods are not explicitly assessed; strategy is assessed indirectly by presenting students with a variety of initial forms.

3) For rational solutions, exact values are required. For irrational solutions, exact or decimal approximations may be required. Simplifying or rewriting radicals is not required; however, students will not be penalized if they simplify the radicals correctly.

4) Prompts integrate mathematical practices by not indicating that the equation is quadratic. (e.g., "Find all real solutions of the equation 𝑡^2 = 4t" ... not, "Solve the quadratic equation 𝑡^2 = 4t.")

**Sample Questions (taken from PARCC’s Practice Tests and Released Items):**EOY Released Test Item 33

PBA Released Test Item 3

Practice Test, Unit 2, Item 7

Paper Test, Unit 2, Item 19

**1. EOY Released Test Item 33**What is the sum of the roots of the equation

2x

^{2}+ 5x - 3 = 0 ?
a. -3.5

b. -2.5

c. -1.5

d. 2.5

**2. PBA Released Test Item 3**

What are the solutions to the equation

(2x + 1)

^{2}- (x+13) = 3x^{2}- 2x +2 ?
Enter your answers in the spaces provided. Enter only your answers.

x = _______

y = _______

**3. Paper Test, Unit 2, Item 19**

Find the equation that is equivalent to the quadratic equation shown.

**x**

^{2}- 6x - 27 = 0
a. x(x - 3) = 27

b. (x - 6)

^{2}= 63
c. (x - 3)

^{2}= 36
d. (x - 3)

^{2}= 28

**Answers:**

*to be posted soon*

**Reference:**

PARCC. (n.d.). Retrieved December 20, 2017, from http://www.aps.edu/assessment/parcc