CCSS.Math.Content.8.G.A.1a
The standard
Lines are taken to lines, and line segments to line segments of the same length.
Common Core State Standards for Mathematics
What this standard means
Students need to understand what happens to lines and line segments under rigid transformations, like translations, rotations, and reflections. A line stays a line. A segment stays a segment. The segment also keeps the same length after the move.
Mastery looks like students checking an image after a transformation and explaining that straightness and distance were preserved. Common sticking points are thinking a tilted or moved segment has changed length, confusing a segment with its image, or relying only on how it looks instead of measuring or reasoning.
Ways to teach it
- Use string and grid paper to slide, flip, and turn a segment, then measure before and after with a ruler.
- Ask students to explain why a rotated segment may look different but still has the same length.
- Show two transformed segments on a coordinate grid and have students answer: same length or not, and how do you know?
- Connect to moving a couch across a room, where the couch changes position and direction but not its length.
Plan a lesson for CCSS.Math.Content.8.G.A.1a
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Related standards
- CCSS.Math.Content.HSG-SRT.A.1b
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
- CCSS.Math.Content.8.G.A.1c
Parallel lines are taken to parallel lines.
- CCSS.Math.Content.8.G.A.1b
Angles are taken to angles of the same measure.
- CCSS.Math.Content.HSG-SRT.A.1a
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.