Percent of What?

Mathematics 7 · Term 1 · Week 7
Name: Section: Date:
Teacher: one page per learner, printed A4. Sections A, B and C count toward Written Works; see assessment.md §1. No calculators — every problem here is one keystroke to a calculator, and that keystroke hides the base. The answer key at the foot is screen-only and will not print.

A The two-column ledger — fill in every blank, including the base

1. ₱100, up 20%, then down 20%
Up
20% of ₱ = ₱
new price = ₱
Down
20% of ₱ = ₱
final price = ₱
2. ₱500, up 10%, then down 10%
Up
10% of ₱ = ₱
new price = ₱
Down
10% of ₱ = ₱
final price = ₱
3. ₱240, up 50%, then down 50%
Up
50% of ₱ = ₱
new price = ₱
Down
50% of ₱ = ₱
final price = ₱

B Build it from 10% and 1%

FindAnswer
10% of ₱600
1% of ₱600
15% of ₱600
12% of ₱250
35% of ₱800

C Increase or decrease

ProblemAnswer
₱400  +  15%
₱800  −  25%
₱250  +  12%
₱1 200  −  35%
multiplier for −8%

D One discount instead of two

  1. 50% off, then 20% off %
  2. 30% off, then 10% off %
  3. 20% off, then 20% off %

E True or false?

  1. Up 20% then down 20% returns to the start.
  2. The multiplier for a 15% increase is 1.15.
  3. 30% off then 10% off is 40% off.
  4. A percentage is always a percentage of something.

★ The challenge

What would bring it back exactly?
  1. A price goes up 25%. By what percentage must it come down to return exactly to the start? %
  2. A price goes up 100%. By what percentage must it come down? %
  3. A price rises from ₱40 to ₱50 — that is a 25% increase. It then falls from ₱50 back to ₱40 — that is a 20% decrease. In one sentence, explain why the two percentages are different.
Answer key — screen only, not printed.
A1 · 20% of ₱100 = ₱20 → ₱120  |  20% of ₱120 = ₱24 → ₱96
A2 · 10% of ₱500 = ₱50 → ₱550  |  10% of ₱550 = ₱55 → ₱495
A3 · 50% of ₱240 = ₱120 → ₱360  |  50% of ₱360 = ₱180 → ₱180
B · ₱60 · ₱6 · ₱90 · ₱30 · ₱280  |  C · ₱460 · ₱600 · ₱280 · ₱780 · 0.92
D · 60% · 37% · 36%  |  E · false · true · false · true
★ · 1. 20% (₱125 must lose ₱25) · 2. 50% (₱200 must lose ₱100) · 3. any wording carrying "the base is different — ₱40 one way, ₱50 the other".
Item ★3 is the diagnostic. A learner can fill in every blank above it and still believe the two percentages ought to match. Read the sentences first.
Watch the second base in every row of §A. A learner who writes the original amount in both boxes has produced the right shape and the wrong idea, and the ledger is designed to make that visible at a glance rather than hidden inside a final answer.