Addition and Subtraction to 1000
Adding three-digit numbers is place value applied to computation. 342 + 256 can be solved as (300+200) + (40+50) + (2+6) = 500+90+8 = 598. The decompose-by-place-value strategy makes the algorithm transparent: it shows WHY the standard algorithm works, not just that it does. Students who understand this connection can compute any multi-digit sum mentally and check answers by estimation.
Decomposing by place value
342 + 256: decompose into hundreds, tens, ones. 300+200=500. 40+50=90. 2+6=8. Combine: 500+90+8=598. This strategy works because place values operate independently: hundreds add to hundreds, tens to tens, ones to ones. The standard column algorithm is exactly this process, compressed into a vertical format.
Friendly numbers and compensation
548 + 197: 197 is close to 200. 548 + 200 = 748. But I added 3 too many: 748 - 3 = 745. This compensation strategy is powerful for numbers close to a hundred. 623 - 298: 623 - 300 = 323. But I subtracted 2 too many: 323 + 2 = 325. The compensation direction reverses for subtraction.
Estimation as a verification tool
Before computing 476 + 389, estimate: 500 + 400 = 900. The actual answer should be close to 900. Computing: 865. Close enough to be confident. This habit of estimating before computing is the most important self-monitoring skill in arithmetic. A computed answer wildly different from the estimate signals an error.