You know several ways to add and subtract (Adding Three-Digit Numbers, Subtracting Three-Digit Numbers). A good mathematician can also say why a way works.
Worked example: Split by place value
Find $356 + 231$.
- $300 + 200 = 500$, $50 + 30 = 80$, and $6 + 1 = 7$.
- $500 + 80 + 7 = 587$.
- Why it works: these are the same blocks, sorted by kind.
Answer: $587$
Worked example: Make a friendly number
Find $398 + 245$.
- Move 2 from 245 to 398: $398 + 2 = 400$ and $245 - 2 = 243$.
- $400 + 243 = 643$.
- Why it works: nothing was added or lost, just moved.
Answer: $643$
Worked example: Take too many, give some back
Find $503 - 198$.
- 198 is 2 less than 200. Take away 200: $503 - 200 = 303$.
- You took away 2 too many, so give 2 back: $303 + 2 = 305$.
- Check: $305 + 198 = 503$.
Answer: $305$
Why it works
Every fair strategy keeps the amount the same. Splitting by place value only sorts the blocks. Moving 2 from one number to the other doesn’t change the total. Counting up works because subtraction tells how far apart two numbers are.
Key idea
A strategy works when it keeps the total the same. You can show why with blocks or a number line, and check by doing the opposite operation.
Common mistake
Fixing up in the wrong direction. For $503 - 198$, some people take away 200 and then take away 2 more, getting 301. But you already took away too many, so you add 2 back: 305. Check: $305 + 198 = 503$.
Grown-up tip: Ask, “How do you know?” and let your child explain with blocks, coins or a drawing.