CCSS.Math.Content.8.G.A.3
The standard
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to track how a shape changes on the coordinate plane after a slide, flip, turn, or resize. They should describe the rule, apply it to each vertex, and compare the new figure to the original.
Mastery looks like moving from a graph to coordinate rules and back again. Students can say what changed, what stayed the same, and whether side lengths or angle measures were preserved. Common stuck points are mixing up x and y, rotating around the wrong point, and treating dilation like a translation.
Ways to teach it
- Hands-on activity: Give students patty paper and grid paper to translate, reflect, rotate, and dilate a triangle, then record new coordinates.
- Discussion prompt: Show two graphed figures and ask, What move happened, and what evidence in the coordinates proves it?
- Quick assessment: Give three points of a triangle and one transformation rule, then ask students for the image coordinates.
- Real-world connection: Use a simple map grid to describe moving, turning, mirroring, or scaling a logo on a sign design.
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Related standards
- CCSS.Math.Content.HSG-CO.A.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
- CCSS.Math.Content.8.G.A.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 trans...
- CCSS.Math.Content.HSG-CO.A.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. ...
- CCSS.Math.Content.8.G.A.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, translation...