You will learn
- Round factors.
- Estimate products.
- Estimate quotients with compatible numbers.
- Judge reasonableness.
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
- Round the numbers to friendly ones.
- Estimate the product or quotient.
- Use compatible numbers for division.
- Decide if the answer is reasonable.
Words to know
About.
Easy-to-compute numbers.
Make friendly.
Makes sense.
1. Discover: is it about?
Is 48 × 52 closer to 250, 2,500 or 25,000?
2. Understand: estimation
- 48 × 52 ≈ 50 × 50 = 2,500 (exact 2,496).
- 389 × 21 ≈ 400 × 20 = 8,000 (exact 8,169).
- 7,812 ÷ 9 ≈ 8,100 ÷ 9 = 900 (exact 868).
Idea 1: Products
61 × 39 ≈ 60 × 40 = 2,400. 298 × 11 ≈ 300 × 10 = 3,000.
Idea 2: Quotients
5,980 ÷ 6 ≈ 6,000 ÷ 6 = 1,000. 4,100 ÷ 8 ≈ 4,000 ÷ 8 = 500.
Idea 3: Compare
82 × 18 ≈ 80 × 20 = 1,600.
Why estimate? It catches big mistakes quickly.
3. Worked examples
Example 1 (I show you): Estimate
61 × 39
- 60 × 40.
Answer: 2,400
Example 2 (We do it together): Estimate
5,980 ÷ 6
- 6,000 ÷ 6.
Answer: 1,000
Example 3 (You try): Estimate
82 × 18
Show the steps and answer
- 80 × 20.
Answer: 1,600
Did you know?
Many estimates are fine: 300 × 10 or 298 × 10 both work.
Why this matters
Estimating is used when shopping, planning and checking answers.
4. Explore: estimate
You need paper.
- Round 48 and 52.
- Multiply.
- Find the exact product.
- Compare.
Think about it: what did you notice?
2,500 vs 2,496.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I round to ___ and ___.
- The estimate is ___.
- The exact answer should be near ___.
- It is reasonable because ___.
Guided practice
Question 1. Estimate 48 × 52.
2,500.
Question 2. Estimate 389 × 21.
8,000.
Question 3. Estimate 7,812 ÷ 9.
900.
Independent practice
Level 1: Start
- Estimate 61 × 39
- Estimate 298 × 11
- Estimate 5,980 ÷ 6
- Estimate 82 × 18
- Estimate 4,100 ÷ 8
Level 2: Grow
- Estimate 49 × 21
- Estimate 312 × 9
- Estimate 2,010 ÷ 4
Level 3: Stretch
- Estimate 19 × 98
- Estimate 7,900 ÷ 8
- Ana estimates 48 × 52 as 40 × 50 = 2,000. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A school buys 48 boxes of 52 pencils. About how many pencils?
Show a sample answer
About 2,500.
Another one. A cinema has 38 rows of 22 seats. Estimate the seats.
Show a sample answer
40 × 20 = 800 seats
7. Common mistakes
Fix: Estimates are about.
Fix: Round to the nearest friendly number.
Fix: Choose compatible numbers.
8. Lesson summary and revision card
- I can round factors.
- I can estimate products.
- I can estimate quotients with compatible numbers.
- I can judge reasonableness.
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
- Round first.
- Compatible numbers.
- Estimate to check.
11. Next lesson
Next lesson: Mental strategies. 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.
- Estimate 61 × 39. [2 marks]
- Estimate 298 × 11. [2 marks]
- Estimate 5,980 ÷ 6. [2 marks]
- Estimate 82 × 18. [2 marks]
- Ali says 4,100 ÷ 8 is about 5,000. Is that reasonable? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 60 × 40 [1]; 2,400 [1]
- 300 × 10 [1]; 3,000 [1]
- 6,000 ÷ 6 [1]; 1,000 [1]
- 80 × 20 [1]; 1,600 [1]
- No [1]. 4,000 ÷ 8 = 500 [1]. 5,000 is far too big [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
- Estimate 61 × 39
- Estimate 298 × 11
- Estimate 5,980 ÷ 6
- Estimate 82 × 18
- Estimate 4,100 ÷ 8
- 48 × 52 ≈
- 389 × 21 ≈
- 7,812 ÷ 9 ≈
- 61 × 39 ≈
- 5,980 ÷ 6 ≈
Homework
Estimate five products and check them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Estimate 61 × 39 | 2,400 | 2 |
| Estimate 298 × 11 | 3,000 | 2 |
| Estimate 5,980 ÷ 6 | 1,000 | 2 |
| Estimate 82 × 18 | 1,600 | 2 |
| Estimate 4,100 ÷ 8 | 500 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2,400; 2 3,000; 3 1,000; 4 1,600; 5 500.
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 2,500; 7 8,000; 8 900; 9 2,400; 10 1,000.
Independent practice answers. Level 1: 1 2,400; 2 3,000; 3 1,000; 4 1,600; 5 500. Level 2: 1 1,000; 2 2,700; 3 500. Level 3: 1 2,000; 2 1,000; 3 48 is far from 40. Use 50 × 50 = 2,500..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Round factors | 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 Estimate products | 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 quotients with compatible 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 |
| O4 Judge reasonableness | 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: Giving the estimate as exact. Estimates are about.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Round to the nearest ten.
- 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 estimates products and quotients. You do not need to be good at mathematics to help.
- Estimate your shopping total.
- Ask: what friendly numbers can we use?
- Check calculator answers with estimates.
- 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: round factors; estimate products; estimate quotients with compatible numbers; judge reasonableness.
Prerequisite knowledge. Lessons 1 and 2.
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. What friendly numbers can I use? Is my answer reasonable?
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. Giving the estimate as exact. Estimates are about.
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. Round to the nearest ten. 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 5 » Operations & Algebraic Thinking; Grade 5 » 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 5.NBT.B.5 and 5.NBT.B.6; Cambridge Primary Mathematics Stage 5 (estimation). These sources informed the lesson.