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Grade 8 - Claim 1 - Target I

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Mathematics

Target I

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

Sample Item

Grade 8

Test

Claim 1

Concepts and Procedures

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

Grade

Grade 8

Content Domain

Geometry

Standards

G-9
Major

Standards

  • G-9

    Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student solves real-world problems by applying the formulas for the volumes of cylinders, cones, and...

  • 2

    The student solves mathematical problems by applying the formulas for the volumes of cylinders, cones, and...

Item Guidelines

Depth of Knowledge

  • 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

Three-dimensional representations of cylinders, cones, and spheres

Key/Construct Relevant Vocabulary

Volume, cylinder, cone, sphere, radius, diameter, area, base, pi

Allowable Tools

Calculator

Target-Specific Attributes

It is expected that students will know and use the formulas for the volumes of cylinders, cones, and spheres.

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

Tasks for this target will ask students to apply the formulas for volume of cylinders, cones and spheres to solve problems. Many of these tasks will contribute evidence to Claims 2 and 4.

Task Models

Task Model 1a

  • Item Types

    Equation/Numeric

  • Depth of Knowledge

    M-DOK2

  • Standards

    G-9

Target Evidence Statement

  • The student solves real-world problems by applying the formulas for the volumes of cylinders, cones, and spheres.

  • Allowable Tools

    Calculator

Task Description

Prompt Features: The student is prompted to find the volumes or dimensions of cylinders, cones, or spheres in real-world scenarios. Stimulus Guidelines: Context should be familiar to students 13 to 15 years old. Use rational numbers in...

Stimulus

The student is presented with a situation that includes sufficient measurements of a cylinder, cone, or sphere.

Example 1

Example Stem 1: This figure shows the dimensions of a tanker truck. The tank forms a cylinder with a length of 32 feet and radius of 4 feet.

A cylinder is shown with a radius of 4 feet and a length of 32 feet.

 

What is the volume, in cubic feet, of the tank? Round your answer to the nearest hundredth.

Enter your answer in the response box.

Rubric: (1 point) The student gives the correct volume within a range to accommodate different acceptable values of pi (e.g., 1608.50).

Example 2

Example Stem 2: A spherical baseball has a radius of 2 inches, as shown in the diagram.

A sphere is shown with a radius of 2 inches

What is the volume, in cubic inches, of the baseball? Round your answer to the nearest hundredth.

Enter your answer in the response box.

Rubric: (1 point) The student gives the correct volume within a range to accommodate different acceptable values of pi (e.g., 33.51).