Transformations Preserve Measures
Flips, turns, and folds move a figure without changing its side lengths or angle measures, and repeated transformations can return it to start (two flips, four quarter-turns) or be undone in reverse. Learners reason about flip/turn identities, rotation centers, and folded figures whose matched parts are congruent. The invariance principle underlies all of congruence.
grade 4 GeometryMeasurement & data Visualize Spatial RelationshipsCreate a Physical Representation
Progression (15)
g4 1. Even number of flips returns original Geometry
g4 2. Flip across a line creates symmetry Geometry
g4 3. Flipping or turning digits forms new digits Geometry
g4 4. Four 90-degree turns return original Measurement & data
g4 5. Center of rotation stays fixed Measurement & data
g4 6. Folded angles are equal; chain to the unknown Measurement & data
g4 7. Rotation preserves side lengths and angle measures Measurement & data
g4 8. Folding makes congruent corresponding angles Geometry
g8 9. Congruent figures have equal corresponding sides GeometryMeasurement & data
g4 10. Symmetry axis splits figure into congruent halves Geometry
g6 11. Use congruence to find lengths for area GeometryMeasurement & data
g4 12. Draw axis to split into congruent halves GeometryMeasurement & data
g8 13. Fold or half-turn overlap reveals symmetry Geometry
g8 14. Symmetry axis or center bisects corresponding-point segment Geometry
g8 15. Overlapping congruent shapes leave congruent leftovers Geometry
Bridges to competition (3)
Reasoning problems that extend this idea toward competition:
Fold and cut paper, predict shapes Shape enumeration
Flipped digital clock readings Invariant
Clock seen in a mirror Invariant