3A · Chapter 2 · Lesson 3
Mental Subtraction — Part 1
Break the amount being subtracted into manageable place-value parts.
Today's challenge
Find 472 − 192 by breaking apart the amount subtracted. Try your own method, then compare it with a model.
What you'll learn
- Break the amount being subtracted into manageable place-value parts.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Number bonds and subtraction as taking away.
Prerequisite competency: MATH-3A-C01-PV-03
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Write 3,415 as thousands + hundreds + tens + ones.
Show answer and reasoning
Answer: 3000 + 400 + 10 + 5
Break the number into the value of each nonzero place. This is a Chapter 1 decomposition skill.
- E2
In 6,116, what is the value of the hundreds digit?
Show answer and reasoning
Answer: 100
The hundreds digit is 1; it represents 1 hundreds, or 100 ones. This is a Chapter 1 place-value skill.
Learn the concept
Words to know
- difference
- the result of subtraction
- decompose
- separate a number into parts
Break the amount being subtracted into manageable place-value parts.
Rename the subtrahend as hundreds + tens + ones. Subtract each part from the starting number, keeping a running total. Or count up from the smaller number to the larger.
Why this works
To find 743 − 258, you may subtract 200, then 50, then 8. The running amounts are 543, 493, and 485. Those three pieces add to 258, so you have removed exactly the intended quantity. Another method is to count upward from 258 to 743; both measure the same difference.
Check the meaning
A check by addition should restore the original amount. A number line illustrates the total distance between the two quantities.
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
Find 472 − 192 by breaking apart the amount subtracted.
- Rename the subtrahend as hundreds + tens + ones. Subtract each part from the starting number, keeping a running total. Or count up from the smaller number to the larger.
- Decompose 192 into tens and ones, subtract each part from 472, and check the difference 280.
- A check by addition should restore the original amount. A number line illustrates the total distance between the two quantities.
Result: 280
Understanding check 1 — your turn
Find 576 − 159 by breaking apart the amount subtracted.
Reveal reasoning
Answer: 417 — Decompose 159 into tens and ones, subtract each part from 576, and check the difference 417.
Worked example 2
Reason and verify
Find 354 − 37 by breaking apart the amount subtracted.
- Rename the subtrahend as hundreds + tens + ones. Subtract each part from the starting number, keeping a running total. Or count up from the smaller number to the larger.
- Decompose 37 into tens and ones, subtract each part from 354, and check the difference 317.
- A check by addition should restore the original amount. A number line illustrates the total distance between the two quantities.
Result: 317
Understanding check 2 — your turn
Find 386 − 182 by breaking apart the amount subtracted.
Reveal reasoning
Answer: 204 — Decompose 182 into tens and ones, subtract each part from 386, and check the difference 204.
Worked example 3
Reason and verify
Find 414 − 60 by breaking apart the amount subtracted.
- Rename the subtrahend as hundreds + tens + ones. Subtract each part from the starting number, keeping a running total. Or count up from the smaller number to the larger.
- Decompose 60 into tens and ones, subtract each part from 414, and check the difference 354.
- A check by addition should restore the original amount. A number line illustrates the total distance between the two quantities.
Result: 354
Understanding check 3 — your turn
Find 268 − 27 by breaking apart the amount subtracted.
Reveal reasoning
Answer: 241 — Decompose 27 into tens and ones, subtract each part from 268, and check the difference 241.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Find 398 − 45 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 353
Decompose 45 into tens and ones, subtract each part from 398, and check the difference 353.
- G2
Find 458 − 68 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 390
Decompose 68 into tens and ones, subtract each part from 458, and check the difference 390.
- G3
Find 518 − 91 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 427
Decompose 91 into tens and ones, subtract each part from 518, and check the difference 427.
- G4
Find 328 − 114 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 214
Decompose 114 into tens and ones, subtract each part from 328, and check the difference 214.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Find 2,304 − 311 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 1993
Decompose 311 into tens and ones, subtract each part from 2,304, and check the difference 1,993.
- I2
Find 2,482 − 363 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 2119
Decompose 363 into tens and ones, subtract each part from 2,482, and check the difference 2,119.
- I3
Find 2,660 − 415 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 2245
Decompose 415 into tens and ones, subtract each part from 2,660, and check the difference 2,245.
- I4
Find 2,588 − 467 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 2121
Decompose 467 into tens and ones, subtract each part from 2,588, and check the difference 2,121.
- I5
Find 2,588 − 341 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 2247
Decompose 341 into tens and ones, subtract each part from 2,588, and check the difference 2,247.
- I6
Find 2,766 − 393 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 2373
Decompose 393 into tens and ones, subtract each part from 2,766, and check the difference 2,373.
- I7
Find 2,944 − 445 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 2499
Decompose 445 into tens and ones, subtract each part from 2,944, and check the difference 2,499.
- I8
Find 1,322 − 497 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 825
Decompose 497 into tens and ones, subtract each part from 1,322, and check the difference 825.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Why does 500 − 197 equal 500 − 200 + 3?
Show answer and reasoning
Answer: 303
Subtracting 200 removes 3 too many. Return 3 to obtain 303.
- C2
A child finds 743 − 258 by subtracting 200, then 50, then 8. Write the three remaining amounts.
Show answer and reasoning
Answer: 543, 493, 485
743−200=543; 543−50=493; 493−8=485. Each subtraction is part of the same 258.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Find 2,228 − 635 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 1593
Decompose 635 into tens and ones, subtract each part from 2,228, and check the difference 1,593.
- E2
Find 2,406 − 687 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 1719
Decompose 687 into tens and ones, subtract each part from 2,406, and check the difference 1,719.
- E3
Find 2,584 − 739 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 1845
Decompose 739 into tens and ones, subtract each part from 2,584, and check the difference 1,845.