You will learn
- Round numbers before calculating.
- Estimate sums and differences.
- Decide whether an answer is sensible.
- Say that an estimate is not exact.
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 before you calculate.
- An estimate is close, not exact.
- Use estimates to check answers.
- Decide if an answer is sensible.
Words to know
A close answer.
Change to a nearby simple number.
Makes sense.
About.
1. Discover: a quick check
A trader adds 4,862 + 2,135 and gets 8,997. Can you tell quickly that this is wrong, without adding exactly?
2. Understand: estimating answers
To estimate, round each number first and then calculate.
4,862 + 2,135: round to the nearest hundred, 4,900 + 2,100 = 7,000. The trader’s 8,997 is far from 7,000, so it is not sensible.
6,789 − 2,314 ≈ 6,800 − 2,300 = 4,500. 5,980 + 3,020, rounded to the nearest thousand, is 6,000 + 3,000 = 9,000.
An estimate is close but not exact.
Idea 1: Round first
4,862 rounds to 4,900 and 2,135 rounds to 2,100. So 4,862 + 2,135 is about 7,000.
Idea 2: Subtract
6,789 − 2,314: 6,800 − 2,300 = 4,500.
Idea 3: Sensible?
If a learner gets 8,756 for 4,862 + 2,135 and the estimate is 7,000, the answer is not sensible.
Why estimate? It catches big mistakes quickly.
3. Worked examples
Example 1 (I show you): Round
Round 4,862 to the nearest hundred.
- Tens digit 6 rounds up.
Answer: 4,900
Example 2 (We do it together): Estimate
Estimate 4,862 + 2,135.
- 4,900 + 2,100.
Answer: about 7,000
Example 3 (You try): Thousand
Estimate 5,980 + 3,020 to the nearest thousand.
Show the steps and answer
- 6,000 + 3,000.
Answer: about 9,000
Did you know?
The word approximately means about.
Why this matters
Estimating helps us check change, bills and measurements fast.
4. Explore: round and add
You need paper and a pencil.
- Round 4,862 and 2,135 to the nearest hundred.
- Add the rounded numbers.
- Find the exact answer.
- Compare estimate and exact.
Think about it: what did you notice?
Estimate 7,000; exact 6,997.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I round ___ to ___.
- My estimate is ___.
- The exact answer is ___.
- The answer is sensible because ___.
Guided practice
Question 1. Round 4,862 to the nearest hundred.
4,900.
Question 2. Estimate 4,862 + 2,135.
4,900 + 2,100 = 7,000.
Question 3. Estimate 6,789 − 2,314.
6,800 − 2,300 = 4,500.
Independent practice
Level 1: Start
- Round 4,862 to the nearest hundred
- Estimate 4,862 + 2,135
- Estimate 6,789 − 2,314
- Estimate 5,980 + 3,020 (nearest thousand)
- Is an estimate exact?
Level 2: Grow
- Round 5,672 to the nearest hundred
- Estimate 3,278 + 4,615 to the nearest hundred
- Estimate 7,845 − 2,310 to the nearest hundred
Level 3: Stretch
- Estimate 9,120 − 4,870 to the nearest hundred
- Estimate 2,490 + 3,520 to the nearest thousand
- Ben says an estimate must be exactly right. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A learner says 4,862 + 2,135 = 8,756. Is that sensible?
Show a sample answer
No. The estimate is 7,000.
Another one. A learner says 3,278 + 4,615 = 9,500. Use an estimate to decide if it is sensible.
Show a sample answer
3,300 + 4,600 = 7,900, so 9,500 is not sensible
7. Common mistakes
Fix: An estimate is close, not exact.
Fix: An estimate is only close.
Fix: Read the question: nearest ten, hundred or thousand.
8. Lesson summary and revision card
- I can round before calculating.
- I can estimate sums and differences.
- I can judge if an answer is sensible.
- I can say an estimate is not exact.
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.
- Estimate shows if an answer is sensible.
- Not exact.
11. Next lesson
Next lesson: Checking calculations. 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 4,862 to the nearest hundred. [1 mark]
- Estimate 4,862 + 2,135 to the nearest hundred. [2 marks]
- Estimate 6,789 − 2,314 to the nearest hundred. [2 marks]
- Is an estimate exact? [1 mark]
- A learner gets 8,756 for 4,862 + 2,135. Is this sensible? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 4,900 [1]
- 4,900 + 2,100 [1] = 7,000 [1]
- 6,800 − 2,300 [1] = 4,500 [1]
- No, it is close [1]
- No [1]. The estimate is 7,000 [1]. 8,756 is too far away [1].
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Round 4,862 to nearest hundred
- Estimate 4,862 + 2,135
- Estimate 6,789 − 2,314
- Estimate 5,980 + 3,020 (nearest thousand)
- Is an estimate exact? (yes/no)
- Round 4,862 to the nearest hundred
- Estimate 4,862 + 2,135
- Estimate 6,789 − 2,314
- Estimate 5,980 + 3,020 to the nearest thousand
- An estimate is close but not ___.
Homework
Estimate three sums using prices. Then find the exact sums.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Round 4,862 to nearest hundred | 4,900 | 2 |
| Estimate 4,862 + 2,135 | 7,000 | 2 |
| Estimate 6,789 − 2,314 | 4,500 | 2 |
| Estimate 5,980 + 3,020 (nearest thousand) | 9,000 | 2 |
| Is an estimate exact? (yes/no) | no | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4,900; 2 7,000; 3 4,500; 4 9,000; 5 no.
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 4,900; 7 7,000; 8 4,500; 9 9,000; 10 exact.
Independent practice answers. Level 1: 1 4,900; 2 7,000; 3 4,500; 4 9,000; 5 No, an estimate is close but not exact. Level 2: 1 5,700; 2 7,900; 3 5,500. Level 3: 1 4,200; 2 6,000; 3 An estimate is close, not exact..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Round numbers before calculating | 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 sums and differences | 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 Decide whether an answer is sensible | 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 Say that an estimate is not exact | 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 estimate must equal the exact answer. An estimate is close, not exact.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Round to the nearest ten 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 rounds numbers to make quick estimates and checks that answers make sense. You do not need to be good at mathematics to help.
- Estimate bills in shops before the cashier tells you.
- Ask: is the answer sensible?
- Round to the nearest ten or hundred.
- 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 numbers before calculating; estimate sums and differences; decide whether an answer is sensible; say that an estimate is not exact.
Prerequisite knowledge. Lessons 2, 4; rounding in Unit 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 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 do I round to? What is my estimate? Is the answer close to it?
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 estimate must equal the exact answer. An estimate is close, not exact.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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 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 3 » Operations & Algebraic Thinking; Grade 3 » 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 3.OA.D.8 and 3.NBT.A.1 (estimate and round); Cambridge Primary Mathematics Stage 3 (estimation). These sources informed the lesson.