3A · Chapter 3 · Lesson 4
Estimating Sums and Differences — Part 1
Round addends to a useful place for a quick estimate and assess plausibility.
Today's challenge
Estimate 2,144 + 992 by rounding BOTH numbers to the nearest 100. Try your own method, then compare it with a model.
What you'll learn
- Round addends to a useful place for a quick estimate and assess plausibility.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Rounding to tens and hundreds.
Prerequisite competency: MATH-3A-C01-PV-09
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Round 5,512 to the nearest 10.
Show answer and reasoning
Answer: 5,510
Find the neighboring multiples of 10; compare with their midpoint. This is a Chapter 1 rounding skill.
- E2
Round 5,535 to the nearest 100.
Show answer and reasoning
Answer: 5,500
Find the neighboring multiples of 100; compare with their midpoint. This is a Chapter 1 rounding skill.
Learn the concept
Words to know
- estimate
- an approximate answer
- round
- replace with a nearby number at a chosen place value
Round addends to a useful place for a quick estimate and assess plausibility.
Round the addends to tens or hundreds appropriate to the question, then add the rounded numbers. Compare the estimate with the exact result when accuracy matters.
Why this works
An estimate tells us about the size of an answer. To estimate 1,489 + 2,515 to the nearest hundred, round each number first: 1,500 + 2,500 = 4,000. The exact sum is 4,004. The estimate is useful for checking reasonableness, but it is not the exact answer.
Check the meaning
An estimate is useful for checking magnitude; it is not interchangeable with an exact count.
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
Estimate 2,144 + 992 by rounding BOTH numbers to the nearest 100.
- Round the addends to tens or hundreds appropriate to the question, then add the rounded numbers. Compare the estimate with the exact result when accuracy matters.
- Round 2,144 to 2,100 and 992 to 1,000. Estimate 2,100 + 1,000 = 3,100; it need not equal the exact answer.
- An estimate is useful for checking magnitude; it is not interchangeable with an exact count.
Result: 3,100
Understanding check 1 — your turn
Estimate 4,302 + 1,330 by rounding BOTH numbers to the nearest 100.
Reveal reasoning
Answer: 5,600 — Round 4,302 to 4,300 and 1,330 to 1,300. Estimate 4,300 + 1,300 = 5,600; it need not equal the exact answer.
Worked example 2
Reason and verify
Estimate 2,475 + 1,183 by rounding BOTH numbers to the nearest 10.
- Round the addends to tens or hundreds appropriate to the question, then add the rounded numbers. Compare the estimate with the exact result when accuracy matters.
- Round 2,475 to 2,480 and 1,183 to 1,180. Estimate 2,480 + 1,180 = 3,660; it need not equal the exact answer.
- An estimate is useful for checking magnitude; it is not interchangeable with an exact count.
Result: 3,660
Understanding check 2 — your turn
Estimate 4,633 + 1,521 by rounding BOTH numbers to the nearest 10.
Reveal reasoning
Answer: 6,150 — Round 4,633 to 4,630 and 1,521 to 1,520. Estimate 4,630 + 1,520 = 6,150; it need not equal the exact answer.
Worked example 3
Reason and verify
Estimate 2,806 + 1,374 by rounding BOTH numbers to the nearest 100.
- Round the addends to tens or hundreds appropriate to the question, then add the rounded numbers. Compare the estimate with the exact result when accuracy matters.
- Round 2,806 to 2,800 and 1,374 to 1,400. Estimate 2,800 + 1,400 = 4,200; it need not equal the exact answer.
- An estimate is useful for checking magnitude; it is not interchangeable with an exact count.
Result: 4,200
Understanding check 3 — your turn
Estimate 4,964 + 1,712 by rounding BOTH numbers to the nearest 100.
Reveal reasoning
Answer: 6,700 — Round 4,964 to 5,000 and 1,712 to 1,700. Estimate 5,000 + 1,700 = 6,700; it need not equal the exact answer.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Estimate 7,753 + 1,141 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 8,890
Round 7,753 to 7,750 and 1,141 to 1,140. Estimate 7,750 + 1,140 = 8,890; it need not equal the exact answer.
- G2
Estimate 1,184 + 1,332 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 2,500
Round 1,184 to 1,200 and 1,332 to 1,300. Estimate 1,200 + 1,300 = 2,500; it need not equal the exact answer.
- G3
Estimate 1,515 + 1,523 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 3,040
Round 1,515 to 1,520 and 1,523 to 1,520. Estimate 1,520 + 1,520 = 3,040; it need not equal the exact answer.
- G4
Estimate 1,846 + 1,714 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 3,500
Round 1,846 to 1,800 and 1,714 to 1,700. Estimate 1,800 + 1,700 = 3,500; it need not equal the exact answer.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Estimate 7,353 + 641 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 7,990
Round 7,353 to 7,350 and 641 to 640. Estimate 7,350 + 640 = 7,990; it need not equal the exact answer.
- I2
Estimate 7,684 + 832 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 8,500
Round 7,684 to 7,700 and 832 to 800. Estimate 7,700 + 800 = 8,500; it need not equal the exact answer.
- I3
Estimate 1,115 + 1,023 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 2,140
Round 1,115 to 1,120 and 1,023 to 1,020. Estimate 1,120 + 1,020 = 2,140; it need not equal the exact answer.
- I4
Estimate 1,446 + 1,214 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 2,600
Round 1,446 to 1,400 and 1,214 to 1,200. Estimate 1,400 + 1,200 = 2,600; it need not equal the exact answer.
- I5
Estimate 1,777 + 1,405 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 3,190
Round 1,777 to 1,780 and 1,405 to 1,410. Estimate 1,780 + 1,410 = 3,190; it need not equal the exact answer.
- I6
Estimate 2,108 + 1,596 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 3,700
Round 2,108 to 2,100 and 1,596 to 1,600. Estimate 2,100 + 1,600 = 3,700; it need not equal the exact answer.
- I7
Estimate 2,439 + 1,787 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 4,230
Round 2,439 to 2,440 and 1,787 to 1,790. Estimate 2,440 + 1,790 = 4,230; it need not equal the exact answer.
- I8
Estimate 2,770 + 278 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 3,100
Round 2,770 to 2,800 and 278 to 300. Estimate 2,800 + 300 = 3,100; it need not equal the exact answer.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Both positive addends were rounded UP. Can their rounded sum be smaller than the exact sum?
Show answer and reasoning
Answer: No
When both addends are replaced by numbers at least as large, their combined total cannot decrease.
- C2
A class needs roughly 200 seats. It has 96 seats in one room and 112 in another. Explain why rounding to tens can help and whether the estimate is adequate.
Show answer and reasoning
Answer: About 210; yes
96≈100 and 112≈110 so approximately 210. Exact total is 208, also enough.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Estimate 6,553 + 1,341 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 7,890
Round 6,553 to 6,550 and 1,341 to 1,340. Estimate 6,550 + 1,340 = 7,890; it need not equal the exact answer.
- E2
Estimate 6,884 + 1,532 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 8,400
Round 6,884 to 6,900 and 1,532 to 1,500. Estimate 6,900 + 1,500 = 8,400; it need not equal the exact answer.
- E3
Estimate 7,215 + 1,723 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 8,940
Round 7,215 to 7,220 and 1,723 to 1,720. Estimate 7,220 + 1,720 = 8,940; it need not equal the exact answer.