You will learn
- Round to the nearest whole.
- Round to decimal places.
- Estimate sums and products.
- Check 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
- Look at the next digit to round.
- Five or more rounds up; four or less stays.
- Round numbers make estimating easy.
- Check answers are reasonable.
Words to know
Change to a nearby simple number.
Approximate answer.
Digit after the point.
Makes sense.
1. Discover: about how much?
3.746 kg of rice is about how many kilograms?
2. Understand: rounding decimals
- 3.746 to the nearest whole: 4; to 1 decimal place: 3.7; to 2 decimal places: 3.75.
- Look at the next digit: 5 or more, round up.
- 2.95 to 1 d.p. is 3.0.
- Estimate 4.9 × 6.1 ≈ 5 × 6 = 30.
Idea 1: Round
8.05 to the nearest whole: tenths digit 0, so 8. 2.95 to 1 d.p.: hundredths digit 5, round up to 3.0.
Idea 2: Decimal places
6.349 to 2 d.p.: third digit 9, round up to 6.35. 3.746 to 1 d.p. is 3.7.
Idea 3: Estimate
4.9 × 6.1 ≈ 5 × 6 = 30. 19.6 + 0.8 ≈ 20 + 1 = 21.
Why estimate? It shows if an exact answer is sensible.
3. Worked examples
Example 1 (I show you): Round
8.05 to the nearest whole
- Tenths digit is 0.
Answer: 8
Example 2 (We do it together): Round
6.349 to 2 d.p.
- Third digit is 9, round up.
Answer: 6.35
Example 3 (You try): Estimate
4.9 × 6.1
Show the steps and answer
- 5 × 6.
Answer: 30
Did you know?
Rounding 2.95 to 1 d.p. gives 3.0, and the zero shows the place.
Why this matters
Rounding and estimating make quick, sensible decisions about quantities and money.
4. Explore: round
You need paper.
- Find the place.
- Look at the next digit.
- Round up or stay.
- Check.
Think about it: what did you notice?
3.7.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The digit after the rounding place is ___.
- So I round ___.
- The estimate is ___.
- It is reasonable because ___.
Guided practice
Question 1. 3.746 to 1 d.p.?
3.7.
Question 2. 3.746 to 2 d.p.?
3.75.
Question 3. 4.9 × 6.1 ≈ ?
30.
Independent practice
Level 1: Start
- Round 8.05 to the nearest whole
- Round 2.95 to 1 d.p.
- Round 6.349 to 2 d.p.
- Estimate 4.9 × 6.1
- Estimate 19.6 + 0.8
Level 2: Grow
- Round 3.7 to the nearest whole
- Round 0.84 to 1 d.p.
- Estimate 9.8 + 2.1
Level 3: Stretch
- Round 12.495 to 2 d.p.
- Estimate 7.9 × 2.1
- Ben says 19.6 + 0.8 is about 19 + 1 = 20. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Rice weighs 3.746 kg. Round to the nearest tenth of a kilogram.
Show a sample answer
3.7 kg.
Another one. Three items cost 4.95, 5.10 and 9.85. Estimate the total.
Show a sample answer
About 20
7. Common mistakes
Fix: The next digit is 5, so round up.
Fix: 5 or more rounds up.
Fix: Keep zeros to show the place.
8. Lesson summary and revision card
- I can round to the nearest whole.
- I can round to decimal places.
- I can estimate sums and products.
- I can check 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
- Look at the next digit.
- 5 or more rounds up.
- Estimate to check.
11. Next lesson
Next lesson: Decimal 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.
- Round 8.05 to the nearest whole number. [2 marks]
- Round 2.95 to 1 decimal place. [2 marks]
- Round 6.349 to 2 decimal places. [2 marks]
- Estimate 4.9 × 6.1. [2 marks]
- Ali says 19.6 + 0.8 is about 20. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Tenths digit is 0, so round down [1]; 8 [1]
- Hundredths digit is 5, so round up [1]; 3.0 [1]
- Third decimal digit is 9, so round up [1]; 6.35 [1]
- Round to 5 × 6 [1]; 30 [1]
- No [1]. 19.6 rounds to 20 and 0.8 rounds to 1 [1]. 20 + 1 = 21 [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
- 8.05 to nearest whole
- 2.95 to 1 d.p.
- 6.349 to 2 d.p.
- 4.9 × 6.1 estimate
- 19.6 + 0.8 estimate
- 8.05 to the nearest whole
- 2.95 to 1 d.p.
- 6.349 to 2 d.p.
- Estimate 4.9 × 6.1
- Estimate 19.6 + 0.8
Homework
Round 5.678 to 0, 1 and 2 d.p.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 8.05 to nearest whole | 8 | 2 |
| 2.95 to 1 d.p. | 3.0 | 2 |
| 6.349 to 2 d.p. | 6.35 | 2 |
| 4.9 × 6.1 estimate | 30 | 2 |
| 19.6 + 0.8 estimate | 21 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 8; 2 3.0; 3 6.35; 4 30; 5 21.
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 8; 7 3.0; 8 6.35; 9 30; 10 21.
Independent practice answers. Level 1: 1 8; 2 3.0; 3 6.35; 4 30; 5 21. Level 2: 1 4; 2 0.8; 3 12. Level 3: 1 12.50; 2 16; 3 19.6 rounds to 20: 20 + 1 = 21..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Round to the nearest whole | 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 Round to decimal places | 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 sums and 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 |
| O4 Check 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: Rounding 2.95 to 2.9. The next digit is 5, so round up.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Rounding to 10.
- 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 rounds decimals and estimates. You do not need to be good at mathematics to help.
- Estimate shopping totals.
- Ask: what is the next digit?
- Round before calculating.
- 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 to the nearest whole; round to decimal places; estimate sums and products; check reasonableness.
Prerequisite knowledge. Lesson 1.
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 is the next digit? Is my estimate sensible?
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 2.95 to 2.9. The next digit is 5, so round up.
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. Rounding to 10. 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 6 » Ratios & Proportional Relationships; Grade 6 » The Number System. 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.A.4; Cambridge Primary Mathematics Stage 6 (rounding and estimation). These sources informed the lesson.