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Grade 3 - Claim 1 - Target I

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Mathematics

Target I

Geometric measurement: Area

Sample Item

Grade 3

Test

Claim 1

Concepts and Procedures

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

Grade

Grade 3

Content Domain

Measurement and Data

Standards

MD-5MD-5aMD-5bMD-6MD-7MD-7aMD-7bMD-7cMD-7d
Major

Standards

  • MD-5

    Recognize area as an attribute of plane figures and understand concepts of area measurement.

  • MD-5a

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

  • MD-5b

    A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

  • MD-6

    Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

  • MD-7

    Relate area to the operations of multiplication and addition.

  • MD-7a

    Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

  • MD-7b

    Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning....

  • MD-7c

    Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning....

  • MD-7d

    Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Clarifications

Some tasks associated with this target should assess conceptual understanding of area as a measurable attribute of plane figures. All figures in such problems should be rectilinear and coverable without gaps or overlaps by...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student measures areas by counting unit squares.

  • 2

    The student finds areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts.

  • 3

    The student finds the area of a rectangle with whole-number side lengths by tiling it, and shows that the area is the same as would be found by multiplying the side lengths....

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

None

Key/Construct Relevant Vocabulary

unit square, area, square unit, plane figure, square centimeter, square meter, square inch, square feet

Allowable Tools

None

Target-Specific Attributes

All figures in such problems should be rectilinear and coverable without gaps or overlaps by unit squares.

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

Some of the expectations in 3.MD.C.7 (such as using tiling to show that area of a rectangle with whole number side lengths is the same as would be found by multiplying the side lengths)...

Task Models

Task Model 1

  • Item Types

    Equation/Numeric

  • Depth of Knowledge

    M-DOK2

  • Standards

    MD-6

Target Evidence Statement

  • The student measures areas by counting unit squares.

  • Allowable Tools

    None

Task Description

Prompt Features: The student is prompted to find the area of a figure by counting whole and/or half unit squares. Stimulus Guidelines: Item difficulty can be adjusted via these example methods: Student counts whole unit squares on...

Stimulus

The student is presented with a shaded figure in a grid and determines the total area, in square units, of the figure.

Example 1

Example Stem 1: Use this diagram to solve the problem.

A diagram shows a shaded figure in a grid. The figure has 6 rows of shaded squares. First row: 5 squares. Second row: 3 squares. Third row: 2 squares. Fourth row: 2 squares. Fifth row: 3 squares. Sixth row: 3 squares.

The Key shows each square represents 1 square unit.

Enter the area, in square units, of the shaded figure in the response box.

Rubric: (1 point) The student correctly enters the area, in square units, of the shaded figure (e.g., 18).

Example 2

Example Stem 2: Use this diagram to solve the problem.

A diagram shows a shaded figure in a grid. The figure has 4 rows of shaded squares. First row: one-half square, one-half square. Second row: one-half square, one-half square, one-half square, one-half square. Third row: one-half square, one-half square, one-half square, one-half square. Fourth row: one-half square, one-half square.

The Key shows each square represents 1 square unit.

Enter the area, in square units, of the shaded figure in the response box.

Rubric: (1 point) The student correctly enters the area, in square units, of the shaded figure (e.g., 6).