Transformation Golf
Description
Practice your skills with translations, rotations, and reflections in this coordinate based game. Can you get a hole in one?
Levels
- Grades 6 through 12.
Preparation Time
5 minutes
Activity Time
15 to 60 minutes
Topics
- transformations
- rotations
- reflections
- translations
- rigid motions
- congruence
- lines
- coordinates
- angles
Goals
- Students will learn how translations, rotations, and reflections act on geometric objects.
- Students will learn to estimate the number of degrees needed to rotate an object to a given orientation.
- Students will learn to use coordinate clues to improve the efficiency of their transformation sequences.
- Students will explore the concept of congruence as being equivalent to the existence of a sequence of translations, rotations, and reflections that take one object to the other.
Materials
- laptops or computers
- paper for calculations and for recording moves
- pencil
- calculator (optional)
Prerequisites
- angles measured in degrees
- plotting ordered pairs
- slope-intercept form of a line
Advanced Prerequisites
- trigonometry
- matrices as transformations
- matrix multiplication
Authors
Game designed and coded by Anna Varvak with assistance from Prototyping Team members Ian Garner, Jeremy Mische-Gibson, and Tony Nguyen. Lesson plan by Amanda Serenevy.
National Common Core Standards
| 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations. |
| 8.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, give a sequence of transformations that exhibits the congruence. |
| 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. |
| 8.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 figures, give a sequence of transformations that exhibits the similarity. |
| HS.G-CO.4 | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. |
| HS.G-CO.5 | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. |
| HS.G-CO.6 | Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. |
| HS.G-SRT.1 | Verify experimentally the properties of dilations given by a center and a scale factor. |
| HS.G-SRT.2 | Given two figures, use similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. |
