Grade 11 - Claim 1 - Target I
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Claim 1
Concepts and Procedures
Standards
REI-3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
REI-4
Solve quadratic equations in one variable.
REI-4a
Use the method of completing the square to transform any quadratic equation in x into an equation of the form ${(x – p)}^{2}$ = $q$ that has the same solutions. Derive the quadratic formula from this...
REI-4b
Solve quadratic equations 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. Recognize when the quadratic...
Clarifications
Tasks for this target will require students to solve linear equations and inequalities in one variable and solve quadratic equations in one variable. Tasks asking students to choose the appropriate method will contribute evidence...
Range Achievement Level Descriptors
Evidence Required
1
The student solves linear equations in one variable with numeric coefficients.
2
The student solves linear inequalities in one variable with numeric coefficients.
3
The student solves linear inequalities in one variable with letter coefficients or identifies appropriate value(s) of a letter coefficient given specific information about a variable in a linear equation or inequality.
4
The student solves quadratic equations in one variable by taking square roots, completing the square, using the quadratic formula, or by factoring.
5
The student recognizes when the quadratic formula gives complex solutions (no real solutions).
6
The student writes complex solutions for the quadratic formula in the form where a and b are real numbers.
7
The student recognizes equivalent equations to given linear or quadratic equations in one variable.
Item Guidelines
Depth of Knowledge
M-DOK1
Recall includes the recall of information such as fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one-step, well-defined, and straight algorithmic procedure should be...
M-DOK2
Skill/Concept includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a...
Allowable Item Types
- Equation/Numeric
- Multiple Choice, single correct response
Allowable Stimulus Materials
linear equation with one variable, linear inequality with one variable, number line solution to a linear inequality, quadratic equation in one variable
Key/Construct Relevant Vocabulary
quadratic equation, square root, completing the square, quadratic formula
Allowable Tools
None
Target-Specific Attributes
quadratic formula, factoring quadratic equations, completing the square
Accessibility
Item writers should consider the following Language and Visual Element/Design guidelines [1] when developing items. Language Key Considerations: Use simple, clear, and easy-to-understand language needed to assess the construct or aid in the understanding of the...
Development Notes
None
Task Models
Task Model 1
Item Types
Equation/NumericDepth of Knowledge
M-DOK1Standards
REI-3
Target Evidence Statement
The student solves linear equations in one variable with numeric coefficients.
Allowable Tools
None
Task Description
Prompt Features: The student is prompted to solve a linear equation in one variable. Stimulus Guidelines: The student is presented with a linear equation in one variable with rational coefficients. The solution must be rational. If the...
Stimulus
The student is presented with a one-variable, linear equation with a rational solution and rational coefficients.
Example 1
Example Stem 1: Enter the value for t that makes the given equation true.
Rubric: (1 point) The student enters the correct value for the variable x (e.g., 51).
Example 2
Example Stem 2: Enter the value for x that makes the given equation true.
Rubric: (1 point) The student enters the correct value for the variable x (e.g., -1).