Addition and subtraction: change, comparison, and the way back

Where we are on the map

With place value in place, we study how quantities change.

Begin with a familiar image

Combining two boxes of objects suggests addition; removing one part from a whole suggests subtraction. The same three numbers form a family of related facts.

Precise meaning

Addition finds a whole from parts or a value after an increase. Subtraction finds a remainder, a difference, or the original value.

The lesson’s support signal

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

part + part = whole; whole − part = other part; addition ↔ subtraction

Worked example

268 + 157 = 425. Check: 425 − 157 = 268; the inverse operation returns the starting number.

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

In 217 + 185 = 392, the ones were handled but a regrouped ten was lost. Recalculating by place gives 402.

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. Solve 487 + 368 and 700 − 456, check each with the inverse operation, and write one joining problem and one comparison problem.

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

The next lesson turns repeated equal additions into multiplication and equal sharing into division.

Course contents