You will learn
- Use compensation.
- Make friendly numbers.
- Break numbers apart.
- Choose a strategy.
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
- Make a friendly number such as 300 or 1,000.
- Then fix the difference.
- Break numbers apart or find number bonds.
- Choose a strategy that suits the numbers.
Words to know
In your head.
Adjust to make a friendly number, then fix.
Two numbers that make a total.
A plan for solving.
1. Discover: quick sums
How can you do 398 + 247 in your head without writing a column?
2. Understand: mental strategies
Choose a friendly number, then fix.
- 398 + 247 = 400 + 247 − 2 = 647 − 2 = 645.
- 1,000 − 367: 367 + 33 = 400, +600 = 1,000. Answer 633.
- 25 + 48 + 75: 25 + 75 = 100, then 100 + 48 = 148.
- 46 + 38 = 46 + 40 − 2 = 84.
Idea 1: Compensate
299 + 156: think 300 + 156 = 456, then take 1 away: 455.
Idea 2: Number bonds
35 + 67 + 65: 35 + 65 = 100, then add 67: 167. 1,000 − 450 = 550.
Idea 3: Break apart
46 + 38: 46 + 40 = 86, then take 2 away: 84. 500 − 198: 500 − 200 = 300, add 2: 302.
Why fix it? We changed the number, so we change the answer back.
3. Worked examples
Example 1 (I show you): Add near 300
299 + 156
- 300 + 156 = 456, then −1.
Answer: 455
Example 2 (We do it together): Bond
35 + 67 + 65
- 35 + 65 = 100.
Answer: 167
Example 3 (You try): Subtract near 200
500 − 198
Show the steps and answer
- 500 − 200 = 300, then +2.
Answer: 302
Did you know?
Many market sellers use compensation every day.
Why this matters
Mental maths is faster than reaching for a calculator.
4. Explore: mind sums
You need nothing but your mind.
- Do 398 + 247 as 400 + 247 − 2.
- Do 1,000 − 367 by counting up.
- Do 25 + 48 + 75 by pairing.
- Explain one strategy.
Think about it: what did you notice?
645, 633, 148.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I change ___ to ___.
- Then I get ___.
- I fix it by ___.
- The answer is ___.
Guided practice
Question 1. 398 + 247?
645.
Question 2. 1,000 − 367?
633.
Question 3. 25 + 48 + 75?
148.
Independent practice
Level 1: Start
- 299 + 156
- 1,000 − 450
- 35 + 67 + 65
- 46 + 38
- 500 − 198
Level 2: Grow
- 199 + 325
- 1,000 − 620
- 48 + 27 + 52
Level 3: Stretch
- 396 + 407
- 3,000 − 1,995
- Ben says 500 − 198 = 300 because he took away 200. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A trader sells 298 mangoes and then 315. How many in all?
Show a sample answer
613.
Another one. A driver travels 199 km then 256 km. Use compensation to find the total.
Show a sample answer
200 + 256 = 456, then −1 = 455 km.
7. Common mistakes
Fix: If you add 2 extra, take 2 away.
Fix: Add or subtract the difference back.
Fix: If you added extra, take it away. If you took extra, add it back.
8. Lesson summary and revision card
- I can use compensation.
- I can make friendly numbers.
- I can break numbers apart.
- I can choose a good strategy.
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
- Make a friendly number.
- Adjust afterwards.
- Pair numbers that make 100.
11. Next lesson
Next lesson: Multistep 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.
- Find 299 + 156 using 300. [2 marks]
- Find 1,000 − 450. [1 mark]
- Find 35 + 67 + 65 using a number bond. [2 marks]
- Find 500 − 198. [2 marks]
- Ana says 46 + 38 = 74. Is she right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 300 + 156 = 456 [1]; 455 [1]
- 550 [1]
- 35 + 65 = 100 [1]; 167 [1]
- 500 − 200 = 300 [1]; 302 [1]
- No [1]. 46 + 40 = 86 [1]; 86 − 2 = 84 [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
- 299 + 156
- 1,000 − 450
- 35 + 67 + 65
- 46 + 38
- 500 − 198
- 398 + 247 =
- 1,000 − 450 =
- 35 + 67 + 65 =
- 46 + 38 =
- 500 − 198 =
Homework
Do five mental sums while walking and check on paper.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 299 + 156 | 455 | 2 |
| 1,000 − 450 | 550 | 2 |
| 35 + 67 + 65 | 167 | 2 |
| 46 + 38 | 84 | 2 |
| 500 − 198 | 302 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 455; 2 550; 3 167; 4 84; 5 302.
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): 6 645; 7 550; 8 167; 9 84; 10 302.
Independent practice answers. Level 1: 1 455; 2 550; 3 167; 4 84; 5 302. Level 2: 1 524; 2 380; 3 127. Level 3: 1 803; 2 1,005; 3 He took away 2 too many, so add 2 back: 302..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use compensation | 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 Make friendly numbers | 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 Break numbers apart | 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 Choose a strategy | 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: Forgetting to undo the adjustment. If you add 2 extra, take 2 away.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise number bonds to 100.
- 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 adds and subtracts in their head with friendly numbers. You do not need to be good at mathematics to help.
- Do one mental sum at meals.
- Ask: what friendly number could you use?
- Praise the strategy, not only the answer.
- 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 compensation; make friendly numbers; break numbers apart; choose a strategy.
Prerequisite knowledge. Lessons 1 to 3.
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 nothing but your mind. 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. Which friendly number helps? How do I fix the answer?
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. Forgetting to undo the adjustment. If you add 2 extra, take 2 away.
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 number bonds to 100. 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 4 » Operations & Algebraic Thinking; Grade 4 » 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 4.NBT.B.4 and 3.NBT.A.2 (fluency strategies); Cambridge Primary Mathematics Stage 4 (mental methods). These sources informed the lesson.