3A · Chapter 3 · Lesson 6
Word Problems
Use exact addition or subtraction and a reasonableness estimate to solve an applied problem.
Today's challenge
An exhibit recorded 3,377 visitors in the morning and 796 more in the afternoon. How many altogether? Try your own method, then compare it with a model.
What you'll learn
- Use exact addition or subtraction and a reasonableness estimate to solve an applied problem.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Multidigit addition and subtraction.
Prerequisite competency: 3A-C03-L02
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Subtract 2,992 − 448; show any place-value exchange.
Show answer and reasoning
Answer: 2544
Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 2,544; add 448 to check.
- E2
Subtract 3,142 − 508; show any place-value exchange.
Show answer and reasoning
Answer: 2634
Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 2,634; add 508 to check.
Learn the concept
Words to know
- estimate
- an approximation used for checking
- exact value
- a quantity determined without rounding
Use exact addition or subtraction and a reasonableness estimate to solve an applied problem.
Read once for the story, again for the numerical relationship. Record what the given numbers measure, represent the whole and parts, and write an exact equation.
Why this works
Before calculating, decide what each number counts and what the question asks. If a museum had 2,005 tickets and used 968, the missing part is the tickets left. A whole-minus-part bar represents 2,005 − 968 = 1,037 tickets. Use an estimate to check that the result is sensible, and include the unit.
Check the meaning
Include the real-world unit and compare with a rounded estimate for a reasonableness check.
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
An exhibit recorded 3,377 visitors in the morning and 796 more in the afternoon. How many altogether?
- Read once for the story, again for the numerical relationship. Record what the given numbers measure, represent the whole and parts, and write an exact equation.
- Identify the whole and its parts, then compute 3,377 + 796 = 4,173. Estimate to hundreds to check size.
- Include the real-world unit and compare with a rounded estimate for a reasonableness check.
Result: 4173
Understanding check 1 — your turn
An exhibit recorded 4,373 visitors in the morning and 488 more in the afternoon. How many altogether?
Reveal reasoning
Answer: 4861 — Identify the whole and its parts, then compute 4,373 + 488 = 4,861. Estimate to hundreds to check size.
Worked example 2
Reason and verify
A museum had 3,600 tickets and sold 867. How many tickets remain?
- Read once for the story, again for the numerical relationship. Record what the given numbers measure, represent the whole and parts, and write an exact equation.
- Identify the whole and its parts, then compute 3,600 − 867 = 2,733. Estimate to hundreds to check size.
- Include the real-world unit and compare with a rounded estimate for a reasonableness check.
Result: 2733
Understanding check 2 — your turn
A museum had 4,596 tickets and sold 559. How many tickets remain?
Reveal reasoning
Answer: 4037 — Identify the whole and its parts, then compute 4,596 − 559 = 4,037. Estimate to hundreds to check size.
Worked example 3
Reason and verify
An exhibit recorded 3,823 visitors in the morning and 938 more in the afternoon. How many altogether?
- Read once for the story, again for the numerical relationship. Record what the given numbers measure, represent the whole and parts, and write an exact equation.
- Identify the whole and its parts, then compute 3,823 + 938 = 4,761. Estimate to hundreds to check size.
- Include the real-world unit and compare with a rounded estimate for a reasonableness check.
Result: 4761
Understanding check 3 — your turn
An exhibit recorded 4,819 visitors in the morning and 630 more in the afternoon. How many altogether?
Reveal reasoning
Answer: 5449 — Identify the whole and its parts, then compute 4,819 + 630 = 5,449. Estimate to hundreds to check size.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
A museum had 2,534 tickets and sold 285. How many tickets remain?
Show answer and reasoning
Answer: 2249
Identify the whole and its parts, then compute 2,534 − 285 = 2,249. Estimate to hundreds to check size.
- G2
An exhibit recorded 2,757 visitors in the morning and 356 more in the afternoon. How many altogether?
Show answer and reasoning
Answer: 3113
Identify the whole and its parts, then compute 2,757 + 356 = 3,113. Estimate to hundreds to check size.
- G3
A museum had 2,980 tickets and sold 427. How many tickets remain?
Show answer and reasoning
Answer: 2553
Identify the whole and its parts, then compute 2,980 − 427 = 2,553. Estimate to hundreds to check size.
- G4
An exhibit recorded 3,203 visitors in the morning and 498 more in the afternoon. How many altogether?
Show answer and reasoning
Answer: 3701
Identify the whole and its parts, then compute 3,203 + 498 = 3,701. Estimate to hundreds to check size.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
A museum had 3,534 tickets and sold 985. How many tickets remain?
Show answer and reasoning
Answer: 2549
Identify the whole and its parts, then compute 3,534 − 985 = 2,549. Estimate to hundreds to check size.
- I2
An exhibit recorded 3,757 visitors in the morning and 1,056 more in the afternoon. How many altogether?
Show answer and reasoning
Answer: 4813
Identify the whole and its parts, then compute 3,757 + 1,056 = 4,813. Estimate to hundreds to check size.
- I3
A museum had 3,980 tickets and sold 227. How many tickets remain?
Show answer and reasoning
Answer: 3753
Identify the whole and its parts, then compute 3,980 − 227 = 3,753. Estimate to hundreds to check size.
- I4
An exhibit recorded 4,203 visitors in the morning and 298 more in the afternoon. How many altogether?
Show answer and reasoning
Answer: 4501
Identify the whole and its parts, then compute 4,203 + 298 = 4,501. Estimate to hundreds to check size.
- I5
A museum had 4,426 tickets and sold 369. How many tickets remain?
Show answer and reasoning
Answer: 4057
Identify the whole and its parts, then compute 4,426 − 369 = 4,057. Estimate to hundreds to check size.
- I6
An exhibit recorded 4,649 visitors in the morning and 440 more in the afternoon. How many altogether?
Show answer and reasoning
Answer: 5089
Identify the whole and its parts, then compute 4,649 + 440 = 5,089. Estimate to hundreds to check size.
- I7
A museum had 4,872 tickets and sold 511. How many tickets remain?
Show answer and reasoning
Answer: 4361
Identify the whole and its parts, then compute 4,872 − 511 = 4,361. Estimate to hundreds to check size.
- I8
An exhibit recorded 5,095 visitors in the morning and 582 more in the afternoon. How many altogether?
Show answer and reasoning
Answer: 5677
Identify the whole and its parts, then compute 5,095 + 582 = 5,677. Estimate to hundreds to check size.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
What is wrong with reporting “about 1,200” when a story asks for the exact number of tickets left?
Show answer and reasoning
Answer: It is an estimate, not an exact count
Find the exact difference for the required answer; use 1,200 only as a reasonableness check.
- C2
A festival sold 1,275 tickets on Friday and 986 on Saturday, but 147 were refunded. How many valid tickets were sold?
Show answer and reasoning
Answer: 2,114 tickets
Add sold: 1,275+986=2,261. Remove refunds: 2,261−147=2,114. Check estimate ≈2,300−150≈2,150.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
A museum had 5,534 tickets and sold 585. How many tickets remain?
Show answer and reasoning
Answer: 4949
Identify the whole and its parts, then compute 5,534 − 585 = 4,949. Estimate to hundreds to check size.
- E2
An exhibit recorded 5,757 visitors in the morning and 656 more in the afternoon. How many altogether?
Show answer and reasoning
Answer: 6413
Identify the whole and its parts, then compute 5,757 + 656 = 6,413. Estimate to hundreds to check size.
- E3
A museum had 5,980 tickets and sold 727. How many tickets remain?
Show answer and reasoning
Answer: 5253
Identify the whole and its parts, then compute 5,980 − 727 = 5,253. Estimate to hundreds to check size.