Addition and Subtraction to 10,000
Warm-up
Number talk: 3,994 + 2,008. Students solve mentally. Strategies: 4,000 + 2,000 = 6,000, subtract 6 = 5,994, then add 8 = 6,002. Or decompose: 3000+2000=5000, 900+0=900, 90+0=90, 4+8=12. 5000+900+90+12=6002. Compare strategies.
Explore
Fish stock scenario: a lake has 7,340 rainbow trout. 1,852 are caught in spring and 2,106 in fall. How many remain? Students solve with two strategies each, show an estimate, and verify with the inverse. Discuss: which strategy was most efficient?
Formalize
Regrouping with four digits: 4,387 + 2,845. Work through by place value, showing where regrouping occurs. Ones: 7+5=12 (regroup 1 ten). Tens: 8+4+1=13 (regroup 1 hundred). Hundreds: 3+8+1=12 (regroup 1 thousand). Thousands: 4+2+1=7. Result: 7,232.
Addition and Subtraction to 10,000
Inverse verification: computed 9,150 - 3,427 = 5,723. Check: 5,723 + 3,427 = 9,150? Work it through. 3+7=10, carry 1. 2+2+1=5. 7+4=11, carry 1. 5+3+1=9. Yes: 9,150. The answer is verified.
Practice
Students solve 6 four-digit computation problems using at least two strategies each, recording estimates. Exit ticket: estimate then compute 4,892 + 3,641.
Exit ticket
Students solve 6 four-digit computation problems using at least two strategies each, recording estimates. Exit ticket: estimate then compute 4,892 + 3,641.
Step 1: Estimate first: 3,500 + 2,800 ≈ 6,300. Guard posted.
Step 2: Ones: 8 + 7 = 15 → write 5, trade 10 ones for 1 ten (the little 1 above the tens column IS that traded ten — say so every time).
Step 3: Tens: 5 + 6 + 1 = 12 tens → write 2, trade 10 tens for a hundred.
Step 4: Hundreds: 4 + 7 + 1 = 12 hundreds → write 2, trade for a thousand.
Step 5: Thousands: 3 + 2 + 1 = 6. Answer: 6,225. Compare with the estimate 6,300 ✓ close.
The narration rule: every "carry" must be SAID as a trade ("ten tens make a hundred") at least until it's boring. Students who chant "put down the 2, carry the 1" without the trade-talk are running a ritual, and rituals break under pressure (watch what they do with 3 addends).
Strategy 1 — count up (recommended here): from 2,876 climb to 5,002: +124 reaches 3,000; +2,000 reaches 5,000; +2 arrives. Total: 124 + 2,000 + 2 = 2,126.
Strategy 2 — shift both: slide both numbers down 3: 4,999 − 2,873. No zeros left, no borrowing at all: 4,999 − 2,873 = 2,126.
Strategy 3 — the algorithm (for comparison): borrowing across the two zeros of 5,002 — the 2 becomes 12, the 0s become 9s, the 5 becomes 4 — arrives, after careful bookkeeping, at 2,126.
Step 4: Debrief: all three agree. Rank them for THIS problem: counting up and shifting were fast and safe; the algorithm was the accident-prone route (those cascading 9s). For 8,435 − 2,113 the ranking flips — the algorithm sails through with no borrows.
The skill of the year: reading a problem BEFORE choosing a weapon.
The story: an arena holds 9,500. On Friday 6,748 tickets sold; on Saturday 8,209. How many MORE seats were empty on Friday than on Saturday?
Step 1: Untangle what's asked: not tickets sold, not total empties — the DIFFERENCE between the two nights' empty seats. Plan before computing: find each night's empties, then compare.
Step 2: Friday's empties: 9,500 − 6,748. Count up: 6,748 + 252 → 7,000; + 2,500 → 9,500. Empty: 2,752.
Step 3: Saturday's empties: 9,500 − 8,209. Count up: +791 → 9,000; +500 → 9,500. Empty: 1,291.
Step 4: Compare: 2,752 − 1,291 = 1,461 more empty seats on Friday.
Step 5: The shortcut worth discussing afterward: the difference in empties equals the difference in SALES — 8,209 − 6,748 = 1,461 — because both nights share the same arena. Seeing that identity is optional; checking that both routes agree is delightful.