Teaching article
Same area, different perimeter: rearrange six squares
Build two regions from the same number of equal squares and compare their outside boundaries.
Keep the same six unit squares while changing their arrangement. Comparing a two-by-three rectangle with a one-by-six rectangle creates a visible reason to distinguish the amount of covered space from the boundary length.
Both use six square units; their perimeters are ten and fourteen unit lengths respectively.
Use the same number of unit squares for both designs. Rearrangement can preserve area while changing the length of the boundary.
Count what stayed, measure what changed
Make a two-by-three rectangle. Rearrange into a one-by-six rectangle. Compare the boundary lengths.
Equal covered area does not force equal perimeter. What stayed constant during rearrangement?
Use a drawn unit grid for tracing.
Resources
- Reflection Journal Template — Use the blank reflection space for observations; write the measurement units and setup separately.
Further reading
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