3A · Chapter 2 · Lesson 6
Strategies for Numbers Close to Hundreds
Turn numbers near a multiple of 100 into easier calculations.
Today's challenge
Calculate 440 + 199 by using a nearby hundred. Try your own method, then compare it with a model.
What you'll learn
- Turn numbers near a multiple of 100 into easier calculations.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Adding and subtracting with round hundreds.
Prerequisite competency: 3A-C02-L02
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Find 99 + 185 using compensation.
Show answer and reasoning
Answer: 284
Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 284.
- E2
Find 198 + 30 using compensation.
Show answer and reasoning
Answer: 228
Increase 198 by 2 to get a multiple of 100; then subtract that same adjustment from the total. Result: 228.
Learn the concept
Words to know
- benchmark number
- a friendly multiple of ten or one hundred
- compensation
- reversing a temporary adjustment
Turn numbers near a multiple of 100 into easier calculations.
Think of 199 as 200 − 1 and 302 as 300 + 2. Replace a difficult addend or subtrahend with the round hundred, then repair the difference.
Why this works
A number close to a hundred can be rewritten as that hundred plus or minus a small amount. Since 199 = 200 − 1, we can calculate 199 + 243 as 200 + 243 − 1 = 442. In a subtraction such as 602 − 299, subtract 300 first, then add one back.
Check the meaning
Test the strategy against an estimate so an incorrect sign on the correction is caught.
Concrete → Pictorial → Abstract
- Build: Use counters, grid paper, or labeled bundles to represent the story or quantity.
- Draw: Sketch an array, place-value exchange, or equal-unit bar; label what is known.
- Calculate: Write an equation matching the representation and solve.
- Verify: Use an inverse operation or a second strategy to check.
For advanced students: if you can already explain this concept, start with the independent or challenge set.
Worked examples and immediate checks
Explain each step aloud or in writing. Work the fresh question before revealing its solution.
Worked example 1
Reason and verify
Calculate 440 + 199 by using a nearby hundred.
- Think of 199 as 200 − 1 and 302 as 300 + 2. Replace a difficult addend or subtrahend with the round hundred, then repair the difference.
- Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 440 and check the exact answer 639.
- Test the strategy against an estimate so an incorrect sign on the correction is caught.
Result: 639
Understanding check 1 — your turn
Calculate 464 + 402 by using a nearby hundred.
Reveal reasoning
Answer: 866 — Rewrite 402 as the nearby multiple of 100 with a small correction. Apply the correction to 464 and check the exact answer 866.
Worked example 2
Reason and verify
Calculate 477 − 301 by using a nearby hundred.
- Think of 199 as 200 − 1 and 302 as 300 + 2. Replace a difficult addend or subtrahend with the round hundred, then repair the difference.
- Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 477 and check the exact answer 176.
- Test the strategy against an estimate so an incorrect sign on the correction is caught.
Result: 176
Understanding check 2 — your turn
Calculate 251 + 503 by using a nearby hundred.
Reveal reasoning
Answer: 754 — Rewrite 503 as the nearby multiple of 100 with a small correction. Apply the correction to 251 and check the exact answer 754.
Worked example 3
Reason and verify
Calculate 264 + 402 by using a nearby hundred.
- Think of 199 as 200 − 1 and 302 as 300 + 2. Replace a difficult addend or subtrahend with the round hundred, then repair the difference.
- Rewrite 402 as the nearby multiple of 100 with a small correction. Apply the correction to 264 and check the exact answer 666.
- Test the strategy against an estimate so an incorrect sign on the correction is caught.
Result: 666
Understanding check 3 — your turn
Calculate 288 + 98 by using a nearby hundred.
Reveal reasoning
Answer: 386 — Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 288 and check the exact answer 386.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Calculate 373 − 98 by using a nearby hundred.
Show answer and reasoning
Answer: 275
Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 373 and check the exact answer 275.
- G2
Calculate 410 + 199 by using a nearby hundred.
Show answer and reasoning
Answer: 609
Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 410 and check the exact answer 609.
- G3
Calculate 447 − 301 by using a nearby hundred.
Show answer and reasoning
Answer: 146
Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 447 and check the exact answer 146.
- G4
Calculate 234 + 402 by using a nearby hundred.
Show answer and reasoning
Answer: 636
Rewrite 402 as the nearby multiple of 100 with a small correction. Apply the correction to 234 and check the exact answer 636.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Calculate 1,953 − 98 by using a nearby hundred.
Show answer and reasoning
Answer: 1855
Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 1,953 and check the exact answer 1,855.
- I2
Calculate 2,079 + 199 by using a nearby hundred.
Show answer and reasoning
Answer: 2278
Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 2,079 and check the exact answer 2,278.
- I3
Calculate 2,205 − 301 by using a nearby hundred.
Show answer and reasoning
Answer: 1904
Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 2,205 and check the exact answer 1,904.
- I4
Calculate 2,081 + 402 by using a nearby hundred.
Show answer and reasoning
Answer: 2483
Rewrite 402 as the nearby multiple of 100 with a small correction. Apply the correction to 2,081 and check the exact answer 2,483.
- I5
Calculate 2,207 − 503 by using a nearby hundred.
Show answer and reasoning
Answer: 1704
Rewrite 503 as the nearby multiple of 100 with a small correction. Apply the correction to 2,207 and check the exact answer 1,704.
- I6
Calculate 2,333 + 98 by using a nearby hundred.
Show answer and reasoning
Answer: 2431
Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 2,333 and check the exact answer 2,431.
- I7
Calculate 2,459 − 199 by using a nearby hundred.
Show answer and reasoning
Answer: 2260
Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 2,459 and check the exact answer 2,260.
- I8
Calculate 785 + 301 by using a nearby hundred.
Show answer and reasoning
Answer: 1086
Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 785 and check the exact answer 1,086.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Explain mentally why 602 − 299 is 303 without column subtraction.
Show answer and reasoning
Answer: 303
602−300=302; since 299 is one less than 300, add one back: 303.
- C2
Is 799 + 243 closer to 1,000 or 1,100? Use compensation rather than column addition.
Show answer and reasoning
Answer: 1,000
800+243−1=1,042. It is 42 from 1,000 and 58 from 1,100.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 1,553 − 98 by using a nearby hundred.
Show answer and reasoning
Answer: 1455
Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 1,553 and check the exact answer 1,455.
- E2
Calculate 1,679 + 199 by using a nearby hundred.
Show answer and reasoning
Answer: 1878
Rewrite 199 as the nearby multiple of 100 with a small correction. Apply the correction to 1,679 and check the exact answer 1,878.
- E3
Calculate 1,805 − 301 by using a nearby hundred.
Show answer and reasoning
Answer: 1504
Rewrite 301 as the nearby multiple of 100 with a small correction. Apply the correction to 1,805 and check the exact answer 1,504.