You will learn
- Check addition with subtraction.
- Check subtraction with addition.
- Estimate by rounding.
- Spot a wrong answer.
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 by rounding first.
- Spot answers that cannot be right.
Words to know
The opposite operation.
A close answer.
Change to the nearest ten or hundred.
Test that an answer is right.
1. Discover: is it right?
A learner says 100 − 37 = 73. How can you check without trusting the answer?
2. Understand: checking answers
Inverse check: addition and subtraction are opposites. 45 + 38 = 83, so 83 − 38 should be 45. For 72 − 29 = 43, check 43 + 29 = 72.
Estimate: round to the nearest ten. 48 + 31 ≈ 50 + 30 = 80. The real answer is 79, close to 80.
Swap: 24 + 35 = 35 + 24 = 59.
For 100 − 37 = 73, check 73 + 37 = 110, not 100. The answer is wrong. It should be 63.
Idea 1: Opposite operations
Addition and subtraction are inverse (opposite). If 45 + 38 = 83 then 83 − 38 = 45. If 72 − 29 = 43 then 43 + 29 = 72.
Idea 2: Estimate
To estimate, round each number. 48 + 31 is about 50 + 30 = 80. The exact answer should be close.
Idea 3: Spot a wrong answer
If 100 − 37 = 73, check: 73 + 37 = 110, not 100. So it is wrong. The right answer is 63.
Why check? Checking finds mistakes before they cost us.
3. Worked examples
Example 1 (I show you): Check an addition
Check 56 + 27 = 83 by subtracting.
- Subtract one part from the total.
- 83 − 27 = 56.
Answer: 56. It matches.
Example 2 (We do it together): Check a subtraction
Check 90 − 34 = 56 by adding.
- Add the answer and the number taken away.
- 56 + 34 = 90.
Answer: 90. It matches.
Example 3 (You try): Estimate
Estimate 49 + 51.
Show the steps and answer
- Round 49 to 50 and 51 to 50.
- 50 + 50 = 100.
Answer: About 100
Did you know?
Shopkeepers estimate the bill in their head before the till gives the exact amount.
Why this matters
Checking helps us trust our answers.
4. Explore: detective checks
You need paper and a pencil.
- Solve 45 + 38 and check by subtracting 38.
- Solve 72 − 29 and check by adding 29.
- Estimate 48 + 31 by rounding.
- Decide if 100 − 37 = 73 is correct.
Think about it: what did you notice?
45 + 38 = 83; 72 − 29 = 43; estimate 80; 100 − 37 = 63, not 73.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- To check ___ I do ___.
- The estimate is ___.
- The answer is close to my estimate, so ___.
- It is wrong because ___.
Guided practice
Question 1. Check 45 + 38 = 83.
83 − 38 = 45. Correct.
Question 2. Check 72 − 29 = 43.
43 + 29 = 72. Correct.
Question 3. Estimate 48 + 31.
50 + 30 = 80.
Independent practice
Level 1: Start
- Check 56 + 27 = 83 by subtracting.
- Check 90 − 34 = 56 by adding.
- Estimate 49 + 51.
- Is 64 + 19 = 83 correct?
- Write 30 + 25 in another order.
Level 2: Grow
- Check 72 + 18 = 90 by subtracting.
- Estimate 51 + 38 to the nearest ten.
- Is 100 − 46 = 64 right? Check.
Level 3: Stretch
- Check 250 + 135 = 385.
- Estimate 603 − 198 to the nearest hundred.
- Sade says 47 + 25 = 62. Show with an estimate that she is wrong.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A trader says 100 − 37 = 73. Is she right?
Show a sample answer
No. 73 + 37 = 110. The answer is 63.
Another one. A shop had 120 books and sold 48. The shopkeeper says 62 are left. Check the answer.
Show a sample answer
62 + 48 = 110, not 120. It is wrong. 120 − 48 = 72.
7. Common mistakes
Fix: Always check with the opposite operation.
Fix: Use the opposite operation to check.
Fix: Round each number first.
8. Lesson summary and revision card
- I can check an addition with subtraction.
- I can check a subtraction with addition.
- I can estimate by rounding.
- I can spot a wrong 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
- Use the opposite operation.
- Estimate by rounding.
- A neat answer can still be wrong.
11. Next lesson
Next lesson: Two-step 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 45 + 38 = 83 by subtracting. [2 marks]
- Check 72 − 29 = 43 by adding. [2 marks]
- Estimate 48 + 31 by rounding to the nearest ten. [2 marks]
- 100 − 37 = 73. Is this right? Show how you know. [3 marks]
- Write 24 + 35 in a different order and check they are equal. [2 marks]
Total: 11 marks.
Marking guide and model answers
- 83 − 38 [1] = 45, so it is correct [1]
- 43 + 29 [1] = 72, so it is correct [1]
- 50 + 30 [1] = 80 [1]
- 73 + 37 [1] = 110, not 100 [1]; wrong, the answer is 63 [1]
- 35 + 24 [1]; both are 59 [1]
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- 83 − 27 checks 56 + 27 = 83?
- 56 + 34 checks 90 − 34 = 56?
- Estimate 49 + 51
- 64 + 19 = 83 correct?
- 30 + 25 in another order
- Check 30 + 25 = 55 by subtracting.
- Check 80 − 35 = 45 by adding.
- Estimate 31 + 68 to the nearest ten.
- Is 50 − 18 = 22 right?
- Estimate 296 + 204 to the nearest hundred.
Homework
Make five sums and check each one two ways. Ask someone to find a deliberate mistake you made.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 83 − 27 checks 56 + 27 = 83? | yes | 2 |
| 56 + 34 checks 90 − 34 = 56? | yes | 2 |
| Estimate 49 + 51 | 100 | 2 |
| 64 + 19 = 83 correct? | yes | 2 |
| 30 + 25 in another order | 25 + 30 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 yes; 2 yes; 3 100; 4 yes; 5 25 + 30.
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 55 − 25 = 30; 7 45 + 35 = 80; 8 30 + 70 = 100; 9 No. 22 + 18 = 40. It is 32.; 10 300 + 200 = 500.
Independent practice answers. Level 1: 1 83 − 27 = 56, so it is right; 2 56 + 34 = 90, so it is right; 3 about 100; 4 yes, 83 − 19 = 64; 5 25 + 30 = 55. Level 2: 1 90 − 18 = 72, so it is right; 2 50 + 40 = 90; 3 No. 64 + 46 = 110. The answer is 54.. Level 3: 1 385 − 135 = 250, so it is right; 2 600 − 200 = 400; 3 50 + 25 = 75, so 62 is too small. 47 + 25 = 72..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Check addition with 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 |
| O2 Check subtraction with 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 Estimate by rounding | 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 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 |
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: Thinking an answer is right because it looks neat. Always check 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 learns to check answers using opposite operations and estimates. You do not need to be good at mathematics to help.
- Ask your child to check every sum using the opposite operation.
- Estimate shopping totals before you pay.
- Ask: does the answer make sense?
- 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 with subtraction; check subtraction with addition; estimate by rounding; spot a wrong answer.
Prerequisite knowledge. Lessons 1 to 7.
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 opposite operation? What is the estimate? Is it close?
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. Thinking an answer is right because it looks neat. Always check with the opposite operation.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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 2 » Operations & Algebraic Thinking; Grade 2 » 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 2.OA.B.2 and 2.NBT.B.5 (check and estimate); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.