School Improvement in Maryland

Using the State Curriculum: Mathematics, Grade 4

Algebra | Geometry | Measurement | Statistics | Probability | Number | Processes
Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 2.0 Knowledge of Geometry

Topic E. Transformations

Indicator 1. Analyze a transformation

Objective a. Identify and describe the results of translations, reflections, and rotations

  • Use a horizontal line translation, reflection over a vertical line, or rotation of 90° clockwise around a given point of a geometric figure or picture

Clarification

A transformation is the movement of a plane figure to a new location. At this level, the transformations students will investigate are translations, reflections and rotations, which do not change the size or shape (congruency) of the figure.

A translation or slide, (as identified in Grade 3), is a horizontal, vertical, or diagonal movement of a figure. A translation provides a change in the location of the figure, but not its orientation, size, or shape.

geometric image

A reflection, or flip (as identified in Grade 3), is the process of reflecting a figure across a line of symmetry creating a mirror or reflected image on the opposite side of the line. A reflection is not the same as a coin flip or pancake flip, but is instead a mirror reflection of the original image. A reflection changes the location and the orientation of the figure, but not it's size or shape.

geometric image

A rotation, or turn (as identified in Grade 3), is the process of turning a figure about a single point of rotation. At this grade level, the point of rotation is always a vertex of the figure. A rotation changes the location and the orientation of the figure, but not it's size or shape.

geometric image
Rotation ( rotation or 90 degrees clockwise)

Classroom Example 1

Identify the transformation performed.

geometric image Answer: 90° clockwise rotation
geometric image NOTE: The arrow may be helpful during instruction, but will not appear on an assessment item.
Answer: Translation
geometric image Answer: Reflection

Classroom Example 2

Describe which transformation(s) have taken place to get from the start figure to the end figure. Also draw the stages of the figure in between start and end with how it looked after each transformation.

Example:

geometric image

Possible Answer:
The arrow was rotated clockwise three times (three 90° turns/270°). It also was translated down and to the right.

geometric image

Students may not transform the figure in this exact manner. For example, they may translate it first and then rotate it counter-clockwise.
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