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Grade 11 - Claim 1 - Target O

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Mathematics

Target O

Define trigonometric ratios and solve problems involving right triangles

Sample Item

Grade 11

Test

Claim 1

Concepts and Procedures

Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

Grade

Grade 11

Content Domain

Geometry

Standards

SRT-6SRT-7SRT-8
Supporting

Standards

  • SRT-6

    Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

  • SRT-7

    Explain and use the relationship between the sine and cosine of complementary angles.

  • SRT-8

    Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Clarifications

Tasks for this target will be posed to elicit student understanding of the relationship between similar triangles and their side ratios. Other tasks will ask students to explain and use the relationship between the...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student uses the definitions of trigonometric ratios for acute angles in a right triangle.

  • 2

    The student uses similar triangles to define and determine trigonometric ratios in right triangles.

  • 3

    The student explains and uses the relationship between the sine and cosine of complementary angles.

  • 4

    The student uses the Pythagorean Theorem and trigonometric ratios to solve problems involving right triangles in mathematical or real-world context.

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

  • Multiple Choice, single correct response
  • Matching Tables
  • Equation/Numeric
  • Multi-Select, multiple correct response

Allowable Stimulus Materials

right triangles, coordinate plane

Key/Construct Relevant Vocabulary

trigonometry, trigonometric ratio, right triangle, sine, cosine, tangent, side, Pythagorean Theorem

Allowable Tools

Calculator (varies by task model)

Target-Specific Attributes

None

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 1a

  • Item Types

    Multiple Choice, single correct response

  • Depth of Knowledge

    M-DOK1

  • Standards

    SRT-6

Target Evidence Statement

  • The student uses the definitions of trigonometric ratios for acute angles in a right triangle.

  • Allowable Tools

    None

Task Description

Prompt Features: The student is prompted to identify the value of sine, cosine, or tangent for a given angle. Stimulus Guidelines: Stimuli may include right triangles or descriptions of the features (angles, side lengths, sine, cosine,...

Stimulus

The student is presented with a right triangle that has given side lengths.

Example 1

Example Stem: Consider this right triangle.

Right triangle A B C is shown. The hypotenuse line segment A B is 5. Line segment B C is 4. Line segment C A is 3.

What is the value of sin(B)?

A) 45\frac{4}{5}

B) 53\frac{5}{3}

C) 35\frac{3}{5}

D) 34\frac{3}{4}

Rubric: (1 Point) The student selects the correct number (C).