Foundations · Part–whole bars

Fractions

Parts of a whole, shown as bars you can grow and shrink.

Interactive visual

3/5

Equal slices of one whole. Drag the sliders — watch the meaning change before the symbols do.

Equal parts in the whole5Shaded parts3

Story: you took 3 equal pieces from a whole cut into 5.

Best ways to learn this

Concrete → Picture → Abstract
Touch or imagine real objects first, then draw them, then use symbols.
Your brain builds meaning before memorizing notation. Skipping straight to symbols is why algebra feels empty.
Dual coding
Pair every idea with a picture, diagram, or motion.
Words and visuals use different memory channels. Together they stick far longer than either alone.
Teach it out loud
Explain the picture in a sentence as if teaching a friend.
Gaps hide until you speak. If you can narrate the visual, you own the concept.

1Start with a real bar (chocolate, ribbon, pizza) cut into equal pieces.
2Draw the same bar and shade the pieces — equal size matters more than the number of pieces.
3Only then write a/b: a = shaded pieces, b = equal pieces in the whole.
4Compare fractions by redrawing both on bars of the same length.

Tip: Always ask: “Equal parts of what whole?” before computing.

Memory check

Due now

Which detail decides whether 2/5 is a fraction of something?

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