Grade 2 · Mathematical Practice · MAT-02-MATHPRACTICE-002
Find and Explain an Arithmetic Error
Identify arithmetic and place-value errors in worked solutions.
Learning objectives
What you should be able to do
- Identify arithmetic and place-value errors in worked solutions.
- Explain precisely what went wrong and how to correct it.
- Use estimation, inverse operations, and models to verify corrections.
Prerequisite check
Make sure the foundation is ready.
Provides procedures and representations to critique.
Learn
Build the idea from meaning, not memorization.
Error analysis studies reasoning, not just answers
A wrong result may come from a fact error, misaligned place values, incorrect regrouping, wrong operation, or misread problem. Naming the error type helps prevent repetition.
Use evidence to locate the first incorrect step
Check each step in order. The earliest step that breaks a mathematical rule usually explains later incorrect results.
Independent checks strengthen diagnosis
Estimate, use inverse operations, or rebuild the problem with a model. A second method can distinguish a calculation slip from a deeper misunderstanding.
Explain corrections respectfully and precisely
A useful critique says what rule was violated and demonstrates a correct step, rather than simply labeling an answer wrong.
Interactive math lab
Change it. See what stays true.
Equation Balance
Adjust both sides. Equality means both expressions have the same value.
Balanced: both sides have equal value.
- find first error
- classify error
- repair step
- choose independent check
Worked examples
Twenty different ways to see the concept work.
38+27:8+7=15,write15 ones then5T=515.
regrouping error15 ones must become1T5O; sum65.
52−27 student does7−2=5 and5−2=3 ->35.
order/regroup errorCannot reverse digits; regroup to25.
243+10=244.
place-value error+10 adds one ten, result253.
604−278=426.
regroup errorCorrect326.
8+7=14.
fact errorCorrect15.
15−8=8.
fact/inverse error8+7=15, so difference7.
34+25=59.
correctNo error.
68−24=44.
correctPlace-wise subtraction valid.
Graph8 vs5 says13 more.
operation errorHow many more uses8−5=3.
Pay100¢ for65¢ says165¢ change.
operation errorChange=100−65=35¢.
One fourth labeled in unequal4-piece model.
model errorShares must equal.
Bar graph value6 drawn to8.
representation errorBar endpoint must match6.
Clock3:25 read3:05.
minute-hand scale errorPosition5=25 minutes.
305 expanded300+50.
place-value error305=300+5.
Compare398>402 because98>2.
comparison errorCompare hundreds first;398<402.
Estimate40+30≈70, exact38+27=65.
reasonableCheck supports65.
52−27=25 checked25+27=52.
verifiedInverse supports answer.
Units20cm+3in=23cm.
unit errorConvert before combining.
Odd classification of50.
parity errorOnes digit0 -> even.
How explain correction well?
State rule,first wrong step,correct workPrecise critique.
Practice
Guided practice with hints
01Student47+36=713.
Hint: Look at regrouping.
Answer: Should83
02Student70−28=58.
Hint: Check inverse.
Answer: Correct42
03Student says4 rows3=7.
Hint: Use repeated addition.
Answer: 12
04Student calls3 unequal parts thirds.
Hint: Check equality.
Answer: Invalid
05Student compares507>570.
Hint: Compare tens.
Answer: False;507<570
06How find first wrong step?
Hint: Trace work in order.
Answer: Check each operation/rule sequentially.
Practice
Independent practice
0129+54=713 error
Answer: Regrouping/place-value; correct83
0280−35=55 error
Answer: Correct45
0323+10=24 error
Answer: Place-value; correct33
04Quarter value10¢ error
Answer: Coin value; quarter25¢
052 icons key5=7 error
Answer: Scale; correct10
06Circle called polygon error
Answer: Curved boundary
07Why inverse check
Answer: Tests whether operation result reconstructs original relationship.
08Good critique includes
Answer: Error type/rule and corrected work.
Common mistakes
Learn to catch the error, not just the answer.
Identify violated rule and corrected reasoning.
Use an independent strategy/model.
Locate earliest incorrect step.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Review your own homework before submitting.
- Compare two solution methods and diagnose disagreements.
Challenge problems
Can correct answer come from invalid reasoning?
Yes; critique method as well as result.
Why estimate catches some errors but not all?
It detects magnitude issues but may not expose small errors.
Which check for52−27?
Addition25+27=52 or base-ten model.
How does explaining an error improve learning?
It makes rules/misconceptions explicit and reusable.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Math Detective
Find the first incorrect step and repair the solution.
Practice
Mastery check
0138+27=515 error
Answer: Failed regrouping;65
0252−27=35 error
Answer: Reversed ones instead of regrouping;25
03243+10=244 error
Answer: Treated10 as1;253
04Graph8 vs5 total13 when asked more
Answer: Wrong operation;3
05Why first error matters
Answer: Later steps may simply follow from it.
06Why use second method
Answer: Independent verification.
07Can correct answer hide error
Answer: Yes
08Good explanation style
Answer: Specific,rule-based,respectful.
Terminology
Words to know
- error analysis
- Examining work to identify and explain mistakes.
- misconception
- An incorrect underlying idea, not just a slip.
- verify
- Check with evidence.
- critique
- Evaluate reasoning and explain strengths or errors.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
Standards for Mathematical Practice MP3,MP6
Critique reasoning and attend to precision.