NY Next Generation Math GEO-G.CO.2
The Standard
Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students represent transformations as functions from input points to output points. They compare rigid motions with transformations such as dilations that do not preserve both distance and angle measure.
What Mastery Looks Like
- The student maps several points under a transformation and describes its rule. The student correctly identifies preserved and changed properties with evidence.
Common Misconceptions
- Students may treat a transformation as moving only a drawn figure rather than every plane point. They may assume every transformation preserves distance because the shape looks similar.
How to Assess It
- Give coordinate rules for two transformations and one triangle. Ask students to map the vertices and compare which distances and angles are preserved.
Lesson moves
Ways to Teach It
Transform a point-grid transparency and record each input-output pair as a function table.
Ask which properties distinguish a rigid motion from a dilation.
Play property sort with transformation rules, mapped figures, and preserved-measure cards.
Compare image resizing and sliding in a graphics program as geometric functions.
Keep exploring
Related Standards
- GEO-G.SRT.5.b
Prove relationships in geometric figures.
- GEO-G.SRT.2
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformatio...
- GEO-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...
- GEO-G.CO.4
Develop definitions of rotations, reflections, and translations in terms of points, angles, circles, perpendicular lines, parallel lines, and line segments.
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