Expressions: simplify notation without changing value

Where we are on the map

A variable now joins operations to form an expression.

Begin with a familiar image

The same collection can be regrouped without changing its quantity. Algebraic rewriting does the same when its properties are respected.

Precise meaning

Like terms have the same variable part. Distribution a(b+c)=ab+ac sends the outside factor to every term inside.

The lesson’s support signal

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

read structure → distribute → combine like terms → check one value

Worked example

3(2x + 5) − 4x = 6x + 15 − 4x = 2x + 15; both forms equal 23 at x=4.

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

Writing 3(2x+5)=6x+5 is wrong: 3 multiplies both terms, so the constant becomes 15.

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. Simplify 5(2a−3)+4a−7 and verify the original and new forms at a=2.

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

An equation asks for an unknown quantity when the value of an expression is known.

Course contents