Percent: one hundredth instead of three formulas

Where we are on the map

We study a special ratio: comparison with one hundred.

Begin with a familiar image

If 37 of 100 equal cells are shaded, the amount is 37/100 = 0.37 = 37%.

Precise meaning

Percent means one hundredth. Every problem needs a named 100% base; when the base changes, the same amount represents a different percentage.

The lesson’s support signal

meaning → model → calculation → check → explain in your own words

name the 100% base → convert percent to a fraction → multiply → estimate the size

Worked example

15% of 80,000 tenge is 80,000 × 0.15 = 12,000; the discounted price is 68,000.

Example with a fading prompt

Change the numbers in the example and repeat the solution without copying its steps. Estimate first, calculate exactly, and check against the original condition.

Recall without a prompt

1. Define the main idea in one sentence.
2. Rebuild the support signal from memory.
3. Solve the example with different numbers and explain why every step is valid.

Find and correct the mistake

A 20% decrease followed by a 20% increase does not restore the original value because the second percentage uses a smaller new base.

Transfer to a new setting

Apply the same relationship to something you can measure yourself. Name the quantities, units, and the boundary within which the model is valid. Check the answer by a second representation or an inverse operation.

Exercise

Required. Apply a 15% discount to 80,000 tenge, then 10% to the new price, and find the total percentage decrease.

With your own data. Create one everyday example with the same structure and show it in words, a formula, and a check.

Optional. Seven days later, change the numbers and repeat without the support map.

Open perspective

Proportion makes the invariant relationship in percent and scale problems explicit.

Course contents