L5 · Percent problems: finding the part and the whole

Learning goal

“I can solve percent problems in BOTH directions: find the part when I know the whole (L4), and find the whole when I know the part - by first finding what 10% or 1% of the whole must be, then scaling up to 100%.”

Whole — the full amount, the 100% (from L4).

Part — the amount a percent picks out (from L4).

Unit chunk — the value of a small friendly percent (usually 10% or 1%) of the unknown whole, found first and then scaled.

Scale up — multiply a unit chunk to reach 100%: if 10% is worth 8, then 100% is worth 10 x 8 = 80.

Worked example

Two problems, same skeleton: (P1) "15% of 80" - the whole (80) is given; the PART is unknown. L4 chunking: 10% = 8, 5% = 4, part = 12. (P2) "A number's 15% is 12" - the PART (12) is given; the WHOLE is unknown. Chunking in reverse does not directly work, because the chunks must be built from the whole we do not have. Step 1 of every percent problem: ask "is the 100% amount given, or is it the mystery?" Step 2: If the whole is given - L4 direction. If the whole is the mystery - unit-chunk method (Chunk B). Say it plainly: most percent errors are direction errors. Label the given percent, the given amount, and the unknown BEFORE any arithmetic.

Check yourself — explain it

"24 students is 60% of the class" - the unknown is...

Paired problem — example still visible

"45% of 200" - direction? -> Part unknown (whole 200 given) -> part = 90.

Faded completion — last step is yours

"'8 is 20% of a number': given percent = ___%, given amount = ___ (the part), unknown = the ___" -> 20; 8; whole

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz