Fold it. Flip it. Does it fit?

SparkClass

Move the fold line, reflect one half, and use the real overlap to test for symmetry.

CCSS 4.G.A.3
Fold Test
Stationary partMoving part
A shape folding across a movable lineA square is unfolded across the vertical line x equals 360.
Test

One side will fold onto the other. Fold to 100%, then check the actual overlap.

Ready
Fold Linex = 360 · right side reflects left
0% folded
Your Investigation
  1. 1Predict first. Before folding, point to where a corner of the moving part will land.
  2. 2Test the challenge line. Some overlap is not enough. Look for edges or corners that do not coincide.
  3. 3Try another direction. The square works with vertical, horizontal, and diagonal lines. Does every shape?
Quick Challenge

Make a new symmetric figure

Start with the irregular polygon. Move the line off-center, then complete the other half. Explain why the new outline must be symmetric—even though it is different from the original.

Teacher notes · from folding to evidence

Ask students to predict the landing position of one vertex before they fold. After checking, have them point to a pair of corresponding vertices and compare their distances from the fold line.

1

Separate overlap from symmetry

The Challenge preset gives a non-symmetry line for every shape. At 100%, the checker measures the reflected polygon’s actual intersection with the stationary polygon. Partial coverage can look convincing, so ask which edges or vertices still fail to coincide.

2

Use the presets flexibly

Symmetry preset loads a valid line for the selected figure; Challenge preset loads a clearly invalid one. For the square, also test y = 280 and y = x − 80. The triangle, irregular polygon, heart, and house each have a vertical symmetry preset.

3

Complete a half

In mirror-completion mode, only the source half and its reflected copy are shown. The resulting outline is symmetric by construction, even when the original figure was not symmetric about that line. Return to Fold Test to investigate the original again.

CCSS 4.G.A.3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Model note: Intermediate frames use a simple orthographic paper-fold projection. At 100%, the moving half is an exact 2-D reflection; matching is based on polygon overlap, not animation appearance.