Test Item Specifications - Stretching and Shrinking and Comparing and Scaling
2004-2005 Washington State

GS03 (Symmetry, Congruence, and Similarity) Demonstrate an understanding of symmetry, congruence, and similarity (1.3.3 Understand symmetry, congruence, and similarity)

Item Characteristics:

  1. Identify, describe, or compare congruent, symmetrical, or similar figures in illustrations of either geometric figures or real-world objects.
  2. Draw congruent, symmetrical, or similar figures.
  3. Identify and/or draw one or more lines of symmetry in given geometric figures.
  4. Complete a picture or design given the line of symmetry.

NS06 (Ratio and Proportion) Demonstrate an understanding of and apply the concepts of ratio and direct proportion (1.1.4 Understand and apply the concepts of ratio and direct proportion.)

Item Characteristics:

  1. Identify a ratio or proportion in a given situation.
  2. Explain the meaning of a ratio or proportion.
  3. Use ratio and/or proportion to determine an unknown value for a dimension or a number of events or objects.
  4. Complete a proportion.
  5. Example:
    NS06 b A journal article says that 3 out of 4 doctors recommend daily exercise. Suppose you met two doctors who did not recommend daily exercise. Does this mean that the journal article is wrong?
    • Explain whether the journal article is right or wrong.
    • Support your explanation using words, numbers and/or pictures.

GS02 (Location) Identify and describe location of objects on a coordinate grid in any of the four quadrants (1.3.5 Identify and describe location of objects on coordinate grids in any of the four quadrants.)

Item Characteristics:

  1. Use ordered pairs or letter and number combinations to identify or describe the location of points or objects on a two-dimensional coordinate grid.
  2. Plot and label points or shapes on a coordinate grid using ordered pairs.
  3. Identify objects or the location of objects on a number line using coordinates and/or labels.

GS04 (Transformations) Demonstrate an understanding of and apply simple geometric transformations using combinations of including translations (slides) or reflections (flips) or rotations (turns) (1.3.6 Understand and apply simple geometric transformations using combinations of translations (slides), or reflections (flips), or rotations (turns).)

Item Characteristics:

  1. Use ordered pairs to identify or describe the location of given transformed objects on a 2-dimensional coordinate grid.
  2. Identify or describe the relative location of objects to one another on a 2-dimensional coordinate or location grid (map), using ordered pairs or map coordinates (e.g., letter and number combinations) and in terms of mathematical transformations.
  3. Identify, describe, or classify whether an object has been translated (slid), reflected (flipped), or rotated (turned), with or without a grid.
  4. Plot/draw one or two transformations of a simple geometric figure on a grid.
  5. Identify a picture or diagram of a particular transformation of a figure, with or without a grid.

ME01 (Attributes and Dimensions) Demonstrate an understanding of the concepts of and relationships among linear dimensions, perimeter, area, and volume (1.2.1)

Item Characteristics:

  1. Items may ask students to describe and compare the impact that a change in one dimension has on perimeter, area, and/or volume.
  2. Items may ask students to describe the relationships among linear dimensions, perimeter, circumference, area, and volume.
  3. Items may ask students to assess the impact of a simple contraction (e.g., one-half) or expansion on the dimensions, perimeter, area, or volume of an object or figure.
  4. Items may ask students to describe and compare perimeter, area, and volume and label measurements to show an understanding that perimeter is measured in linear units, area in square units, and volume in cubic units.
  5. Items may ask students to draw a diagram or figure based on given dimensions.
  6. Items may ask students to determine the change in one dimension of a figure based on a given change in perimeter, area, or volume.
Note: Students are expected to determine and label units.

Content Strand 2: Measurement

ME02 (Measuring and Calculating) Measure directly and indirectly and use measurements to describe and compare objects; demonstrate an understanding of the concept of rate, calculate rates and other derived measurements, and determine units (1.2.2, 1.2.3)

Item Characteristics:
  1. Items may ask students to select and/or use procedures for measuring and/or comparing length, perimeter, circumference, area, volume, angle measure, weight, temperature, time and rate, labeling units appropriately.
  2. Items may ask students to use or calculate rate and determine and label units.
  3. Items may ask students to calculate perimeter, area, or volume.
  4. Items may ask students to determine linear dimensions of a shape or figure based on a given perimeter, circumference, or area.

Note: Students are expected to determine and label units.

ME03 (Approximation and Precision) Demonstrate an understanding of how precision is affected by the unit of measurement; know when estimating is appropriate and estimate to obtain reasonable approximations (1.2.4, 1.2.5)

Item Characteristics:

  1. Items may ask students to obtain reasonable approximations using estimation in a context.
  2. Items may ask students to determine when or whether estimation is appropriate for finding reasonable approximations of a measure.
  3. Items may ask students to identify a process that would be an appropriate way to estimate.
  4. Items may ask students to explain how they would obtain an estimated measurement.
  5. Items may ask students to explain why they would use estimation rather than an exact measurement.
  6. Items may ask students to identify or describe how the selection of units affect precision.

Note: Students may not receive full credit in estimation items for computing and then rounding. Students are expected to determine and label units.

ME04 (Systems and Tools) Demonstrate an understanding of the appropriate uses of standard units of measurement; demonstrate an understanding of the relationships among units within the U.S. system and within the metric system; select and use units and tools that will provide an appropriate degree of precision (1.2.6, 1.2.7, 1.2.8, 1.2.4)

Item Characteristics:

  1. Items may ask students to select and use appropriate instruments (tools) and units (standard or nonstandard) for measuring length, perimeter, area, volume, capacity, and rate.
  2. Items may ask students to identify or describe the benefits of standard and/or nonstandard units of measure and identify or describe appropriate times to use standard and/or nonstandard units of measure.
  3. Items may ask students to identify or describe examples of the approximate nature of measurement.
  4. Items may as students to explain how the selection and use of units and/or tools affect precision and accuracy.
  5. Items may ask students to explain the relationship among units within the same system.

MC01 (Connect within Mathematics) Use concepts and procedures from a variety of the mathematics content strands in a given problem or situation; relate and use equivalent mathematical models and representations (5.1.1, 5.1.2)

Item Characteristics:

  1. Items may ask students to use concepts and procedures from two or more mathematics concept strands - number sense, measurement, geometric sense, probability and statistics, and algebraic sense.
  2. Items may ask students to create two equivalent mathematical models or representations.
  3. Items may ask students to identify which of several mathematical models or representations is equivalent to a given mathematical model or representation.
  4. Items may ask students to create a model or representation that is equivalent to a given model or representation, including graphical, numerical, pictorial, geometric, and/or written descriptions.
  5. Items may ask students to describe how two mathematical models or representations are equivalent.

AS02 (Symbols and Notations) Symbolically write simple expressions, equations, and inequalities to represent situations that involve variable quantities (1.5.3, 1.5.4)

Item Characteristics

  1. Items may ask students to identify or write an equation or inequality with variables to represent a given situation, using =, <, >, =, or =.
  2. Items may ask students to identify or write an expression, using variables to represent a given situation.
  3. Items may ask students to explain the meaning of a variable in a formula, expression, or equation.
  4. Items may ask students to identify or write a situation that corresponds to a given equation or expression.

AS03 (Evaluating and Solving) Evaluate expressions and formulas; solve single-variable equations (1.5.5, 1.5.6)

Item Characteristics:

  1. Items may ask students to write and evaluate an expression given the values for the variables.
  2. Items may ask students to evaluate an expression or formula given the values for the variables.
  3. Items may ask students to solve single-variable equations.
  4. Items may ask students to write and solve single-variable equations.

Example:
AS02b: · Given r = 10; and Area of a Circle (A) = ?rē, find A.