Grade 1 · Mathematical Practice · MAT-01-MATHPRACTICE-002
Check Whether an Answer Is Reasonable
Use estimation, inverse operations, counting, or models to check an answer.
Learning objectives
What you should be able to do
- Use estimation, inverse operations, counting, or models to check an answer.
- Identify answers that do not fit the size or meaning of a problem.
- Explain why a result is reasonable or unreasonable.
Prerequisite check
Make sure the foundation is ready.
Provides a result that can be checked in multiple ways.
Learn
Build the idea from meaning, not memorization.
Reasonable means the answer fits the problem
An answer can be a number but still make no sense. If five birds are joined by two more birds, an answer of 1 is unreasonable because the amount should increase, not shrink.
Estimate the size before exact calculation
You can often predict whether the result should be bigger, smaller, or near a certain number. This expectation helps catch operation mistakes and misplaced quantities.
Use an inverse or another method
Addition and subtraction can check each other. If 8−3=5, then 5+3 should return to 8. A second strategy gives independent evidence that the result is sensible.
Models make hidden errors visible
Number lines, ten-frames, base-ten blocks, drawings, and measurement tools can all verify whether a numerical answer matches the situation.
Interactive math lab
Change it. See what stays true.
Number Line Explorer
Move along the number line.
4 is one less. 5 and 6 is one more.
- predict direction
- estimate range
- verify with inverse
- spot impossible result
Worked examples
Twenty different ways to see the concept work.
5+2=7. Reasonable?
YesJoining 2 to 5 should give a number larger than 5, and counting confirms 7.
5+2=1. Reasonable?
NoAddition of positive counts should not make the total smaller.
8−3=5. Check it.
5+3=8The inverse operation returns to the starting amount.
8−3=11. Reasonable?
NoRemoving 3 from 8 cannot produce more than the starting amount.
9 objects plus 1 more gives 10.
ReasonableOne-more reasoning confirms the result.
10−1=9.
ReasonableOne-less reasoning confirms the result.
23+10=33.
ReasonableAdding one ten should increase the tens digit by one while ones stay 3.
23+10=24.
UnreasonableAdding ten should not behave like adding one.
15 compared with 12; answer says 12 is greater.
UnreasonableEqual tens, then 5 ones is greater than 2 ones.
A pencil measures about 6 cubes, answer says 60 cubes.
Likely unreasonableThe scale is far too large for the visible model.
4:00 shown on a clock, answer says 9:00.
UnreasonableThe hour hand position does not match.
Graph has 7 cats and 4 dogs; difference reported as 3.
Reasonable7−4=3.
Graph has 7 cats and 4 dogs; difference reported as 11.
Unreasonable11 is the sum, not the difference.
Two fourths said to equal one half.
ReasonableA four-part model confirms two shares cover half.
One fourth said to be larger than one half of same whole.
UnreasonableThe whole split into more equal shares creates smaller pieces.
6+7 estimated near 10, exact answer 13.
Reasonable13 is plausibly a bit above 10.
6+7 exact answer 30.
Unreasonable30 is far outside the expected size.
12−5 answer 7; count back five steps from 12.
12→11→10→9→8→7The number line verifies 7.
A student checks 4+3 using 3+4.
Both give 7Commutative reasoning is a valid check for addition.
Why use more than one check?
Different methods catch different mistakesAgreement increases confidence in the result.
Practice
Guided practice with hints
01Is 7+2=3 reasonable?
Hint: Should adding a positive amount make the total larger or smaller?
Answer: No
02Check 9−4=5 using addition.
Hint: Add the difference and removed amount.
Answer: 5+4=9
03Is 34+10=44 reasonable?
Hint: Adding 10 should change which place?
Answer: Yes
04A ruler-like model shows about 5 units, answer says 50. Reasonable?
Hint: Compare the scale of the model to the result.
Answer: No
05Which is a good second method for checking 6+3?
Hint: Try counting on or reversing the addends.
Answer: For example, count on three from 6 or compute 3+6.
06Why might an answer be mathematically computed but still unreasonable?
Hint: Think about whether the chosen operation or quantities match the situation.
Answer: The calculation can be based on a wrong interpretation or operation.
Practice
Independent practice
01Is 4+5=9 reasonable?
Answer: Yes
02Is 4+5=2 reasonable?
Answer: No
03Check 10−3=7.
Answer: 7+3=10
04Is 21+10=31 reasonable?
Answer: Yes
05Is 21+10=22 reasonable?
Answer: No
06A graph difference 8−5 is reported as 3. Reasonable?
Answer: Yes
07One half is reported smaller than one fourth of same whole. Reasonable?
Answer: No
08Name one checking strategy.
Answer: Inverse operation, estimate, model, recount, number line, or second method.
Common mistakes
Learn to catch the error, not just the answer.
Use a different method when possible, such as a model or inverse operation.
Compare the answer with the size and direction expected from the problem.
Support the judgment with mathematical evidence such as magnitude, inverse operations, or a model.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Estimate a grocery-item count before recounting to see whether the exact answer is plausible.
- Check change in a simple money situation by adding the change back to the amount spent.
Challenge problems
A student says 18+10=19. Diagnose the likely misunderstanding.
They treated +10 like +1 rather than adding one ten.
Why can an inverse check catch an arithmetic error?
A correct inverse should return to the original quantity.
Give an example where the exact answer is correct but the explanation is unreasonable.
Any case where a correct number is reached by unrelated or invalid reasoning.
Explain why estimation is useful even when you will still calculate exactly.
It creates an expected range or direction that can flag major mistakes.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Reasonable or Ridiculous?
Judge whether proposed answers fit the problem, then choose a valid checking strategy.
Practice
Mastery check
01What does reasonable mean in mathematics?
Answer: The answer fits the size, direction, and meaning of the problem.
02How can addition check subtraction?
Answer: Add the difference and removed amount to see whether you recover the starting amount.
03Why estimate before exact calculation?
Answer: To predict an expected answer size or direction.
04Is 7−2=12 reasonable?
Answer: No
05Is 18+10=28 reasonable?
Answer: Yes
06What should you do if two checking methods disagree?
Answer: Recheck the original work and assumptions.
07Name two checking methods.
Answer: For example inverse operation and model/number line.
08Why use a different checking method?
Answer: It is more likely to reveal a mistake that the original method repeated.
Terminology
Words to know
- reasonable
- Consistent with the size, direction, and meaning expected from the problem.
- estimate
- A close, useful approximation used to judge size or plausibility.
- inverse operation
- An operation that undoes another, such as subtraction undoing addition.
- verify
- Check using evidence that a result or method is correct.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematical Practice — MP1, MP2, MP3, MP6
Perseverance, quantitative reasoning, critique, and precision.