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 GMD Visualize Spatial RelationshipsCreate a Physical Representation
Progression (8)
4-1 1. Even number of flips returns original 4.G.A.3
4-1 2. Flip across a line creates symmetry 4.G.A.3
4-1 3. Flipping or turning digits forms new digits 4.G.A.3
4-1 4. Four 90-degree turns return original 4.MD.C.5
4-1 5. Center of rotation stays fixed 4.MD.C.5
4-2 6. Folded angles are equal; chain to the unknown 4.MD.C.7
4-2 7. Rotation preserves side lengths and angle measures 4.MD.C.7
4-2 8. Folding makes congruent corresponding angles 4.G.A.1