You will learn
- Use estimation to test an answer.
- Check subtraction by addition.
- Check addition by subtraction.
- Spot an unreasonable answer.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Estimate to test an answer.
- Use the opposite operation to check.
- Add checks subtraction. Subtract checks addition.
- Spot answers that cannot be right.
Words to know
The opposite operation.
Makes sense.
Prove it is right.
A close answer.
1. Discover: is it right?
A pupil says 4,812 + 3,975 = 7,687. Without a full sum, how can we tell if that is reasonable?
2. Understand: checking
Two ways to check:
- Estimate: 4,812 + 3,975 ≈ 5,000 + 4,000 = 9,000. 7,687 is far from 9,000, so it is wrong. The exact sum is 8,787.
- Inverse: 7,000 − 2,568 = 4,432. Check 4,432 + 2,568 = 7,000 ✓.
Addition checks subtraction; subtraction checks addition.
Idea 1: Estimate check
Is 6,821 + 3,179 = 10,000 reasonable? 7,000 + 3,000 = 10,000, so yes.
Idea 2: Inverse check
Check 9,000 − 3,456 = 5,544 by adding: 5,544 + 3,456 = 9,000. It works.
Idea 3: Unreasonable
4,000 + 5,000 = 8,000? No. It is 9,000.
Why check? Every answer can have a slip.
3. Worked examples
Example 1 (I show you): Estimate
Estimate 8,950 − 3,010
- 9,000 − 3,000.
Answer: about 6,000
Example 2 (We do it together): Inverse
Check 9,000 − 3,456 = 5,544
- Add 5,544 + 3,456.
Answer: 9,000, so correct
Example 3 (You try): Reasonable?
4,000 + 5,000 = 8,000
Show the steps and answer
- Add the digits: 4 + 5 = 9.
Answer: Not reasonable
Did you know?
Subtraction and addition are inverse operations.
Why this matters
Checking saves us from costly mistakes.
4. Explore: catch the mistake
You need paper.
- Estimate 4,812 + 3,975.
- Compare with 7,687.
- Find the exact sum.
- Check with subtraction.
Think about it: what did you notice?
8,787 − 3,975 = 4,812.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- My estimate is ___.
- The answer is close to / far from it.
- I check by ___.
- So the answer is ___.
Guided practice
Question 1. Estimate 4,812 + 3,975?
9,000.
Question 2. Exact sum?
8,787.
Question 3. Check 7,000 − 2,568 = 4,432 by?
4,432 + 2,568 = 7,000.
Independent practice
Level 1: Start
- Is 6,821 + 3,179 = 10,000 reasonable?
- Estimate 8,950 − 3,010
- Check: 9,000 − 3,456 = 5,544 by addition
- Is 4,000 + 5,000 = 8,000 reasonable?
- Inverse of adding
Level 2: Grow
- Is 5,100 + 4,900 = 10,000 reasonable?
- Estimate 7,980 − 2,010
- Check 8,000 − 2,500 = 5,500
Level 3: Stretch
- Is 3,950 + 4,060 = 8,010 reasonable?
- Check 15,000 − 6,250 = 8,750 by adding
- Ben says 9,000 − 3,456 = 6,544. Check it.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A pupil gets 12,000 + 15,000 = 17,000. Is it reasonable?
Show a sample answer
No; it should be about 27,000.
Another one. Ola says 6,821 + 3,179 = 9,000. Use an estimate and a check to test it.
Show a sample answer
The estimate is 7,000 + 3,000 = 10,000, so 9,000 is too small. The exact sum is 10,000.
7. Common mistakes
Fix: Always estimate or use the inverse.
Fix: Use the inverse operation.
Fix: A quick estimate catches big slips.
8. Lesson summary and revision card
- I can use estimation to test an answer.
- I can check subtraction by adding.
- I can check addition by subtracting.
- I can spot an unreasonable answer.
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
- Estimate first.
- Use inverse operations.
- Does the answer make sense?
11. Next lesson
Next lesson: Multiplication fact review. 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.
- Is 6,821 + 3,179 = 10,000 reasonable? Explain. [2 marks]
- Estimate 8,950 − 3,010. [2 marks]
- Check 9,000 − 3,456 = 5,544 by adding. [2 marks]
- Is 4,000 + 5,000 = 8,000 reasonable? [1 mark]
- Kofi says 12,000 + 15,000 = 17,000. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 7,000 + 3,000 [1]; yes [1]
- 9,000 − 3,000 [1]; 6,000 [1]
- 5,544 + 3,456 [1]; = 9,000 [1]
- No, it is 9,000 [1]
- No [1]. The estimate is 27,000 [1]. 17,000 is far too small [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 6,821 + 3,179
- Estimate 8,950 − 3,010
- Inverse of adding
- 4,000 + 5,000 = 8,000? (reasonable/no)
- 12,000 + 15,000 is about
- 4,812 + 3,975 is about
- Check 9,000 − 3,456 = 5,544 by…
- The exact sum of 4,812 + 3,975 is
- 12,000 + 15,000 = 17,000 is…
- 6,821 + 3,179 is exactly
Homework
Check three of your earlier answers using estimation and the inverse.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 6,821 + 3,179 | 10,000 | 2 |
| Estimate 8,950 − 3,010 | 6,000 | 2 |
| Inverse of adding | subtracting | 2 |
| 4,000 + 5,000 = 8,000? (reasonable/no) | no | 2 |
| 12,000 + 15,000 is about | 27,000 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 10,000; 2 6,000; 3 subtracting; 4 no; 5 27,000.
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 9,000; 7 5,544 + 3,456 = 9,000; 8 8,787; 9 not reasonable; 10 10,000.
Independent practice answers. Level 1: 1 yes, 7,000 + 3,000 = 10,000; 2 6,000; 3 5,544 + 3,456 = 9,000; 4 no, the sum is 9,000; 5 subtraction. Level 2: 1 Yes, 5,000 + 5,000 = 10,000.; 2 6,000; 3 5,500 + 2,500 = 8,000, so correct. Level 3: 1 Yes, 4,000 + 4,000 = 8,000.; 2 8,750 + 6,250 = 15,000, so correct; 3 6,544 + 3,456 = 10,000, not 9,000. The answer is 5,544..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use estimation to test an 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 |
| O2 Check subtraction by addition | 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 Check addition by subtraction | 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 Spot an unreasonable 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Trusting an answer without checking. Always estimate or use the inverse.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise checking 3-digit sums.
- 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 answers with estimates and inverse operations. You do not need to be good at mathematics to help.
- Ask: does that answer sound right?
- Estimate before using a calculator.
- Show how to check with the inverse.
- 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: use estimation to test an answer; check subtraction by addition; check addition by subtraction; spot an unreasonable answer.
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. 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. Is it close to my estimate? Does the inverse work?
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. Trusting an answer without checking. Always estimate or use the inverse.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. Practise checking 3-digit sums. 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
Alignment is pending verification and no external 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. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.OA.A.3 (assess reasonableness); Cambridge Primary Mathematics Stage 4 (checking results). These sources informed the lesson; no official alignment is claimed.