Math · MeasurementVISUAL DISCOVERY 11 OF 1,100

Same Fence, Different Garden

Explorer · about 8 minutes · a little curiosity goes a long way

For grown-ups
Today’s little discovery

With fixed perimeter P, a rectangle has length P/2 − width. Its area changes as the sides rebalance and is largest when the rectangle becomes a square.

Record perimeter and area in separate columns.

This is a learning model. Try the take-home activity together.
Voice settings

Using Heart (en-US).

Your selected voice and opening narration get ready when the page opens with Sound on. The first visit downloads a voice model (about 92 MB), which your browser can cache. No lesson text is sent to a speech service.The sample plays once and does not change the Sound on/off setting.
  1. Wonder
  2. Guess
  3. Try it
  4. Discover
  5. Celebrate
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fixed fence reshapesPerimeter20Sides5 × 5Area25
HERE’S A LITTLE WONDER…

Can one fence length enclose different amounts of ground?

A gardener reshapes a fixed loop of fencing without cutting it.

No rush. Try an idea and see.