Variables: a letter holds the value of a changing quantity

Where we are on the map

We move from particular numbers to algebraic language that records a general relationship.

Begin with a familiar image

A taxi fare combines a fixed 700 tenge charge with 120 tenge for every kilometre. As distance changes, total cost changes.

Precise meaning

A variable represents a quantity whose value may change. Always state its meaning, units, and allowed values.

The lesson’s support signal

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

name quantity → letter and unit → relationship → substitute → check meaning

Worked example

C = 700 + 120d; for d = 5 km, C = 700 + 120 × 5 = 1300 tenge.

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

Replacing d with 5 as 700 + 120 + 5 is wrong: 120 is charged for each kilometre, so 120d is a product.

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. Use the model to find costs for 0, 3, and 12 km; state every variable’s meaning and unit.

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

Next we simplify expressions made from variables without changing their value.

Course contents