You will learn
- Check addition by subtracting.
- Check subtraction by adding.
- Spot a wrong answer.
- Use estimation as a first check.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Check addition by subtracting.
- Check subtraction by adding.
- Estimate first to spot big mistakes.
- Correct any error you find.
Words to know
The opposite operation.
Test that an answer is right.
A close answer.
A mistake.
1. Discover: is it right?
A learner says 2,500 + 1,800 = 4,200. How can you check without trusting the answer?
2. Understand: checking calculations
Inverse check: 3,478 + 2,365 = 5,843, so 5,843 − 2,365 should be 3,478. For 5,432 − 2,764 = 2,668, check 2,668 + 2,764 = 5,432.
Swap: 2,500 + 1,800 = 1,800 + 2,500.
Estimate: 2,500 + 1,800 should be about 4,300.
For 2,500 + 1,800 = 4,200, check 4,200 − 1,800 = 2,400, not 2,500. The answer is wrong. It should be 4,300.
Idea 1: Inverse
Addition and subtraction are inverse operations. To check 4,567 + 2,134 = 6,701, subtract: 6,701 − 2,134 = 4,567. It works.
Idea 2: Check subtraction
To check 9,000 − 4,567 = 4,433, add: 4,433 + 4,567 = 9,000. It works.
Idea 3: Spot an error
2,500 + 1,800 = 4,200? Subtract: 4,200 − 1,800 = 2,400, not 2,500. The right answer is 4,300.
Why check? Everyone makes mistakes, and checking finds them.
3. Worked examples
Example 1 (I show you): Check +
Check 4,567 + 2,134 = 6,701.
- 6,701 − 2,134.
Answer: 4,567, so it is correct
Example 2 (We do it together): Check −
Check 9,000 − 4,567 = 4,433.
- 4,433 + 4,567.
Answer: 9,000, so it is correct
Example 3 (You try): Error
Check 2,500 + 1,800 = 4,200.
Show the steps and answer
- 4,200 − 1,800 = 2,400.
Answer: Wrong. It should be 4,300
Did you know?
Teachers, accountants and engineers always check their calculations.
Why this matters
Checking stops small errors from becoming big problems.
4. Explore: detective checks
You need paper and a pencil.
- Solve 3,478 + 2,365 and check by subtracting.
- Solve 5,432 − 2,764 and check by adding.
- Check 2,500 + 1,800 = 4,200.
- Correct any mistake you find.
Think about it: what did you notice?
5,843; 2,668; 4,200 is wrong, 4,300 is right.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- To check, I ___.
- I get ___.
- It matches, so ___.
- The correct answer is ___.
Guided practice
Question 1. Check 3,478 + 2,365 = 5,843.
5,843 − 2,365 = 3,478. Correct.
Question 2. Check 3,000 − 1,234 = 1,766.
1,766 + 1,234 = 3,000. Correct.
Question 3. Check 2,500 + 1,800 = 4,200.
4,200 − 1,800 = 2,400, wrong.
Independent practice
Level 1: Start
- Check 4,567 + 2,134 = 6,701 by subtracting.
- Check 9,000 − 4,567 = 4,433 by adding.
- Check 2,500 + 1,800 = 4,200.
- Estimate 5,980 + 3,020.
- Correct the wrong answer from the third item.
Level 2: Grow
- Check 3,215 + 1,478 = 4,693 by subtracting
- Check 6,000 − 2,345 = 3,655 by adding
- 1,200 + 3,400 = 4,500. Right?
Level 3: Stretch
- Estimate 7,980 + 2,020
- 5,000 − 1,234 = 3,766. Check it.
- Ana says 3,000 − 1,234 = 1,866. Check it.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A trader says 2,500 + 1,800 = 4,200. Is he right?
Show a sample answer
No. 4,300 is correct.
Another one. A learner says 8,000 − 3,456 = 4,644. Check by adding and correct the answer.
Show a sample answer
4,644 + 3,456 = 8,100, so it is wrong. The answer is 4,544.
7. Common mistakes
Fix: Check every answer with the opposite operation.
Fix: Use the inverse operation.
Fix: If it does not match, find the error.
8. Lesson summary and revision card
- I can check addition by subtracting.
- I can check subtraction by adding.
- I can spot a wrong answer.
- I can use an estimate as a first check.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Use the opposite operation.
- Estimate first.
- Neat is not the same as right.
11. Next lesson
Next lesson: Multistep word problems. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Check 4,567 + 2,134 = 6,701 by subtracting. [2 marks]
- Check 9,000 − 4,567 = 4,433 by adding. [2 marks]
- Check 2,500 + 1,800 = 4,200. Give the correct answer. [3 marks]
- Estimate 5,980 + 3,020. [1 mark]
- Name the inverse of subtraction. [1 mark]
Total: 9 marks.
Marking guide and model answers
- 6,701 − 2,134 [1] = 4,567, so correct [1]
- 4,433 + 4,567 [1] = 9,000, so correct [1]
- 4,200 − 1,800 = 2,400 [1], not 2,500 [1]. The answer is 4,300 [1].
- About 9,000 [1]
- Addition [1]
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Check 4,567 + 2,134 = 6,701 by subtracting: 6,701 − 2,134 =
- Check 9,000 − 4,567 = 4,433 by adding: 4,433 + 4,567 =
- Is 2,500 + 1,800 = 4,200 correct? (yes/no)
- Estimate 5,980 + 3,020
- Correct answer to 2,500 + 1,800
- To check 3,478 + 2,365 = 5,843, do 5,843 − ___.
- To check 5,432 − 2,764 = 2,668, do 2,668 + ___.
- 3,000 − 1,234 = 1,766. Right?
- 2,500 + 1,800 should be ___.
- A quick first check is to ___.
Homework
Make five sums and check each two ways. Ask someone to find a mistake you made on purpose.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Check 4,567 + 2,134 = 6,701 by subtracting: 6,701 − 2,134 = | 4,567 | 2 |
| Check 9,000 − 4,567 = 4,433 by adding: 4,433 + 4,567 = | 9,000 | 2 |
| Is 2,500 + 1,800 = 4,200 correct? (yes/no) | no | 2 |
| Estimate 5,980 + 3,020 | 9,000 | 2 |
| Correct answer to 2,500 + 1,800 | 4,300 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4,567; 2 9,000; 3 no; 4 9,000; 5 4,300.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 2,365; 7 2,764; 8 yes; 9 4,300; 10 estimate.
Independent practice answers. Level 1: 1 6,701 − 2,134 = 4,567, so it is correct; 2 4,433 + 4,567 = 9,000, so it is correct; 3 4,200 − 1,800 = 2,400 not 2,500, so it is wrong; 4 about 9,000; 5 4,300. Level 2: 1 4,693 − 1,478 = 3,215, correct; 2 3,655 + 2,345 = 6,000, correct; 3 No, it is 4,600. Level 3: 1 about 10,000; 2 3,766 + 1,234 = 5,000, correct; 3 1,866 + 1,234 = 3,100, not 3,000. The answer is 1,766..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Check addition by subtracting | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Check subtraction by adding | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Spot a wrong answer | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Use estimation as a first check | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Believing an answer is right because it looks neat. Check every answer with the opposite operation.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Check small sums with counters first.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child checks calculations using the inverse operation and estimates. You do not need to be good at mathematics to help.
- Ask your child to check homework with the inverse operation.
- Ask: does the check match?
- Make a deliberate mistake for them to find.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: check addition by subtracting; check subtraction by adding; spot a wrong answer; use estimation as a first check.
Prerequisite knowledge. Lessons 1 to 5.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper and a pencil. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. What is the inverse? Does the check match? What is the estimate?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Believing an answer is right because it looks neat. Check every answer with the opposite operation.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Check small sums with counters first. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 3 » Operations & Algebraic Thinking; Grade 3 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.OA.D.8 and 4.NBT.B.4; Cambridge Primary Mathematics Stage 3 (checking calculations). These sources informed the lesson.