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Grade 8 - Claim 1 - Target G

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Mathematics

Target G

Understand congruence and similarity using physical models, transparencies, or geometry software

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-1G-1aG-1bG-1cG-2G-3G-4G-5
Major

Standards

  • G-1

    Verify experimentally the properties of rotations, reflections, and translations.

  • G-1a

    Lines are taken to lines, and line segments to line segments of the same length.

  • G-1b

    Angles are taken to angles of the same measure.

  • G-1c

    Parallel lines are taken to parallel lines.

  • G-2

    Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a...

  • G-3

    Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

  • G-4

    Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures,...

  • G-5

    Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for...

Clarifications

Technology enhanced items will be used to allow students to “draw” lines, line segments, angles, and parallel lines after undergoing rotations, reflections, and translations. Similar technology enhanced items will ask students to produce a...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student verifies that rigid transformations preserve distance and angle measures.

  • 2

    The student describes sequences of rotations, reflections, translations, and dilations that can verify whether two-dimensional figures are similar or congruent to each other.

  • 3

    The student constructs a new figure after the original figure is dilated, rotated, reflected, or translated.

  • 4

    The student describes the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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
  • Graphing
  • Hot Spot

Allowable Stimulus Materials

two-dimensional geometric figures, the coordinate plane, two-dimensional geometric figures in the coordinate plane

Key/Construct Relevant Vocabulary

angle, transformation, translation, translate, rotation, rotate, reflection, reflect, dilation, dilate, line segment, similar, congruent, parallel, transversal, exterior angle, interior angle, angle-angle criterion, scale factor, vertical angles, adjacent angle, supplementary angles, complementary angles

Allowable Tools

Calculator

Target-Specific Attributes

Rotations are only multiples of 90 degrees about the origin. Reflections are only over the x- and y-axes. Dilations are only with the origin as the center. There are at most three transformations in a sequence of...

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

Much of the evidence for 8.G.A will be assessed in Claim 3.

Task Models

Task Model 1a

  • Item Types

    Equation/Numeric

  • Depth of Knowledge

    M-DOK1

  • Standards

    G-1

Target Evidence Statement

  • The student verifies that rigid transformations preserve distance and angle measures.

  • Allowable Tools

    Calculator

Task Description

Prompt Features: The student is prompted to give a length or angle measure in a geometric figure after one rigid transformation. Stimulus Guidelines: The distance formula should not be needed to find the length of the...

Stimulus

The student is presented with an image or description of a geometric object and one rigid transformation.

Example 1

Example Stem 1: Line segment DE is translated left 3 units and down 2 units to form line segment D’E’.

A coordinate grid is shown with x and y axes ranging from negative 8 to 8 in increments of 2. Line D E starts at (negative 4, 7) and ends at (6, 7).

Enter the distance, in units, between point D’ and point E’.

Rubric: (1 point) The student gives the correct measure (e.g., 10).

Example 2

Example Stem 2: Line segment FG begins at (–2, 4) and ends at (–2, –3). The segment is translated left 3 units and up 2 units to form line segment F′G′.

Enter the length, in units, of line segment F′G′.

Rubric: (1 point) The student gives the correct measure (e.g., 7).