Addition and Subtraction of Whole Numbers to 1,000,000
Adding and subtracting numbers up to one million uses the same place value strategies as smaller numbers, extended one digit further. The annex-zeros strategy is powerful: 800 + 700 = 1,500 because 8 + 7 = 15, with two zeros annexed. This meta-strategy generalizes: any addition or subtraction can be simplified by identifying the core fact and applying it at the appropriate place value level.
Annex-zeros mental math
800 + 700: I know 8 + 7 = 15. Annex two zeros: 800 + 700 = 1,500. 60,000 + 40,000: I know 6 + 4 = 10. Annex four zeros: 100,000. This technique uses known single-digit facts to solve multi-digit additions mentally. It works because our place value system is base 10: the positional structure scales the fact by powers of 10.
Front-end estimation
To estimate 347,862 + 289,541: use the leading digits. 300,000 + 200,000 = 500,000. The actual sum is around 637,000: substantially higher because we only used the leading digits. A better estimate: 350,000 + 290,000 = 640,000 (round to nearest 10,000). Front-end estimation is fast; rounding to a smaller place value is more accurate.
Real-world large-number contexts
Fundraising for a community project: donated 189,043 in Year 2. Total? 234,567 + 189,043 = 423,610. Remaining to goal of $500,000? 500,000 - 423,610 = 76,390. These multi-step problems connect addition, subtraction, and financial reasoning to community goals.