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Grade 5 - Claim 1 - Target I

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Mathematics

Target I

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Sample Item

Grade 5

Test

Claim 1

Concepts and Procedures

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

Grade

Grade 5

Content Domain

Measurement and Data

Standards

MD-3MD-3aMD-3bMD-4MD-5MD-5aMD-5bMD-5c
Major

Standards

  • MD-3

    Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

  • MD-3a

    A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

  • MD-3b

    A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

  • MD-4

    Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

  • MD-5

    Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

  • MD-5a

    Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying...

  • MD-5b

    Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

  • MD-5c

    Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems....

Clarifications

Tasks for this target will ask students to find the volume of right rectangular prisms with whole-number edge lengths using unit cubes and formulas. Some tasks should ask students to consider the effect of...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student determines the volume of a right rectangular prism with whole-number side lengths by counting...

  • 2

    The student applies the formulas V = l × w × h and V = b...

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
  • Matching Tables

Allowable Stimulus Materials

right rectangular prism models

Key/Construct Relevant Vocabulary

area array, right rectangular prism, associative property, cube, volume, length, width

Allowable Tools

None

Target-Specific Attributes

Items are limited to right rectangular prisms with whole-number edge lengths.

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

Other tasks will ask students to find the volume of two non-overlapping right rectangular prisms, often together with targets from Claim 2 or Claim 4. Tasks that ask students to show that the volume of...

Task Models

Task Model 1a

  • Item Types

    Equation/Numeric

  • Depth of Knowledge

    M-DOK2

  • Standards

    MD-3

Target Evidence Statement

  • The student determines the volume of a right rectangular prism with whole-number side lengths by counting or packing unit cubes.

  • Allowable Tools

    None

  • Accessibility Note

    Care should be given to make sure the dimensions of the prism and layers can be...

Task Description

Prompt Features: The student is prompted to determine the volume of a right rectangular prism with whole-number side lengths by counting unit cubes. Stimulus Guidelines: Items are limited to right rectangular prisms with whole-number edge lengths. Right...

Stimulus

The student is presented with a model of a completed right rectangular prism and a diagram of the individual layers of the prism.

Example 1

Example Stem: The layers of a rectangular prism are shown to the right of the prism.

A rectangular prism is shown with the key showing one block represents 1 cubic centimeter. The rectangular prism has a length of three blocks and width of two blocks and a height of four blocks. The figure is then split into 4 sections each one with a length of three blocks, a width of two blocks, and a height of one block.

Enter the volume, in cubic centimeters, of the rectangular prism.

Rubric: (1 point) The student correctly enters the volume of the completed rectangular prism (e.g., 24).