You will learn
- Round factors.
- Estimate a product.
- Check if an exact product is reasonable.
- Use compatible numbers.
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
- Round each factor to a friendly number.
- Multiply the rounded numbers.
- Use compatible numbers when easier.
- Check that an exact product is reasonable.
Words to know
A close answer.
Make a friendly number.
Numbers easy to compute.
Makes sense.
1. Discover: quick check
48 trays hold 21 oranges each. Is the total about 100, 1,000 or 10,000?
2. Understand: estimating products
Round each factor to its greatest place, then multiply.
- 48 × 21 ≈ 50 × 20 = 1,000 (exact 1,008).
- 312 × 6 ≈ 300 × 6 = 1,800 (exact 1,872).
- 79 × 32 ≈ 80 × 30 = 2,400 (exact 2,528).
- 604 × 5 ≈ 600 × 5 = 3,000 (exact 3,020).
Idea 1: Round both
29 × 41 is about 30 × 40 = 1,200.
Idea 2: Round one
604 × 5 is about 600 × 5 = 3,000. 312 × 6 is about 300 × 6 = 1,800.
Idea 3: Reasonable
72 × 19 is about 70 × 20 = 1,400.
Why estimate? If the exact answer is far from the estimate, we check again.
3. Worked examples
Example 1 (I show you): Both
29 × 41
- 30 × 40.
Answer: about 1,200
Example 2 (We do it together): One factor
604 × 5
- 600 × 5.
Answer: about 3,000
Example 3 (You try): Two factors
72 × 19
Show the steps and answer
- 70 × 20.
Answer: about 1,400
Did you know?
Compatible numbers are numbers that are easy to multiply, like 25 × 4.
Why this matters
Estimating products helps us budget and check calculations.
4. Explore: estimate it
You need paper.
- Round 48 and 21.
- Multiply the rounded numbers.
- Do the exact product.
- Compare.
Think about it: what did you notice?
About 1,000.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I round ___ to ___.
- I round ___ to ___.
- The estimate is ___.
- The exact answer should be near ___.
Guided practice
Question 1. 48 × 21 is about?
1,000.
Question 2. 312 × 6 is about?
1,800.
Question 3. 79 × 32 is about?
2,400.
Independent practice
Level 1: Start
- 29 × 41
- 604 × 5
- 72 × 19
- 312 × 6
- 95 × 11
Level 2: Grow
- 51 × 19
- 398 × 5
- 82 × 31
Level 3: Stretch
- 297 × 32
- 49 × 51
- Ben says 72 × 19 is about 14 because 7 × 2 = 14. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
48 trays hold 21 oranges. About how many oranges?
Show a sample answer
About 1,000.
Another one. A shop packs 62 packets with 38 sweets in each. Estimate the number of sweets.
Show a sample answer
60 × 40 = 2,400 sweets.
7. Common mistakes
Fix: Round both.
Fix: Keep the place value: 70 × 20 = 1,400.
Fix: The exact answer is close to the estimate.
8. Lesson summary and revision card
- I can round factors.
- I can estimate a product.
- I can check if a product is reasonable.
- I can use compatible numbers.
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 both factors.
- Multiply the rounded numbers.
- Compare with exact.
11. Next lesson
Next lesson: Multiplication 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.
- Estimate 29 × 41. [2 marks]
- Estimate 604 × 5. [2 marks]
- Estimate 72 × 19. [2 marks]
- Estimate 312 × 6. [2 marks]
- Ana finds 95 × 11 = 1,045. Use an estimate to decide if it is reasonable. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 30 × 40 [1]; 1,200 [1]
- 600 × 5 [1]; 3,000 [1]
- 70 × 20 [1]; 1,400 [1]
- 300 × 6 [1]; 1,800 [1]
- 100 × 10 = 1,000 [1]; 1,045 is close [1]; yes, reasonable [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
- 29 × 41 ≈
- 604 × 5 ≈
- 72 × 19 ≈
- 312 × 6 ≈
- 95 × 11 ≈
- 48 × 21 is about
- 312 × 6 is about
- 79 × 32 is about
- 604 × 5 is about
- 29 × 41 is about
Homework
Estimate five products from a shopping list.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 29 × 41 ≈ | 1,200 | 2 |
| 604 × 5 ≈ | 3,000 | 2 |
| 72 × 19 ≈ | 1,400 | 2 |
| 312 × 6 ≈ | 1,800 | 2 |
| 95 × 11 ≈ | 1,000 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1,200; 2 3,000; 3 1,400; 4 1,800; 5 1,000.
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 1,000; 7 1,800; 8 2,400; 9 3,000; 10 1,200.
Independent practice answers. Level 1: 1 1,200; 2 3,000; 3 1,400; 4 1,800; 5 1,000. Level 2: 1 1,000; 2 2,000; 3 2,400. Level 3: 1 9,000; 2 2,500; 3 Round to 70 × 20 = 1,400, keeping the tens and zeros..
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 a product | 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 if an exact product is reasonable | 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 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 |
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: Rounding only one factor. Round both.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise rounding to the nearest 10 and 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 estimates products by rounding the factors. You do not need to be good at mathematics to help.
- Estimate the cost of bulk items.
- Ask: is the exact answer near the estimate?
- Round to the biggest place.
- 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 a product; check if an exact product is reasonable; use compatible numbers.
Prerequisite knowledge. Lessons 3 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. What do I round to? Is my answer near 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. Rounding only one factor. Round both.
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. Practise rounding to the nearest 10 and 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
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.NBT.B.5 and 4.OA.A.3; Cambridge Primary Mathematics Stage 4 (estimating products). These sources informed the lesson; no official alignment is claimed.