You will learn
- Compare place by place.
- Recognise equivalent decimals.
- Use >, < and =.
- Order decimals.
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
- Compare decimals place by place from the left.
- Adding zeros at the end does not change the value.
- Use >, < and =.
- Order by comparing tenths, hundredths, thousandths.
Words to know
Say which is greater.
e.g. 0.45 = 0.450.
Arrange.
Value by position.
1. Discover: which is bigger?
Is 0.305 bigger or smaller than 0.35? Is 0.45 equal to 0.450?
2. Understand: comparing decimals
- 0.45 = 0.450 (add a zero at the end).
- 0.305 vs 0.35 = 0.350: tenths equal (3); hundredths 0 < 5, so 0.305 < 0.35.
- Order 0.3, 0.033, 0.303: 0.033 < 0.3 < 0.303.
Idea 1: Compare
0.6 and 0.58: 0.60 and 0.58, so 0.6 > 0.58. 1.09 and 1.9: tenths 0 < 9, so <.
Idea 2: Equivalent
0.7 = 0.70, so =.
Idea 3: Order
0.52, 0.5, 0.502 become 0.520, 0.500, 0.502, so ascending is 0.5, 0.502, 0.52. Greatest of 4.5, 4.05, 4.505 is 4.505.
Why add zeros? Equal places make comparing easy.
3. Worked examples
Example 1 (I show you): Compare
0.6 __ 0.58
- 0.60 and 0.58.
Answer: >
Example 2 (We do it together): Compare
0.7 __ 0.70
- Same value.
Answer: =
Example 3 (You try): Order
0.52, 0.5, 0.502
Show the steps and answer
- 0.520, 0.500, 0.502.
Answer: 0.5, 0.502, 0.52
Did you know?
A decimal with more digits is not always greater.
Why this matters
Comparing decimals matters for prices, times and measurements.
4. Explore: order
You need paper.
- Write all with 3 places.
- Compare from the left.
- Order.
- Check.
Think about it: what did you notice?
0.033, 0.300, 0.303.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I write both with ___ decimal places.
- The first place that differs is ___.
- So ___ is greater.
- In ascending order: ___.
Guided practice
Question 1. 0.45 ? 0.450
=
Question 2. 0.305 ? 0.35
<
Question 3. Least of 0.3, 0.033, 0.303?
0.033.
Independent practice
Level 1: Start
- 0.6 ? 0.58
- 1.09 ? 1.9
- 0.7 ? 0.70
- Order 0.52, 0.5, 0.502
- Greatest of 4.5, 4.05, 4.505
Level 2: Grow
- 0.45 __ 0.405
- 3.2 __ 3.20
- 0.09 __ 0.1
Level 3: Stretch
- Order 1.01, 1.1, 1.001 from least
- 6.7 __ 6.07
- Ben says 0.3 < 0.25 because 3 < 25. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Ada’s time is 12.35 s and Bayo’s is 12.305 s. Who is faster (smaller)?
Show a sample answer
Bayo.
Another one. Ana jumps 1.45 m and Ben jumps 1.5 m. Who jumps farther?
Show a sample answer
1.50 > 1.45, so Ben.
7. Common mistakes
Fix: Compare place by place.
Fix: Compare place by place.
Fix: Line up the places.
8. Lesson summary and revision card
- I can compare place by place.
- I can recognise equivalent decimals.
- I can use >, < and =.
- I can order decimals.
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
- Add zeros to line up.
- Compare left to right.
- More digits is not bigger.
11. Next lesson
Next lesson: Rounding decimals. 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.
- Compare 0.6 and 0.58. [3 marks]
- Compare 1.09 and 1.9. [2 marks]
- Compare 0.7 and 0.70. [2 marks]
- Order 0.52, 0.5, 0.502 from least. [3 marks]
- Ali says 4.05 > 4.5 because 05 > 5. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 0.60 and 0.58 [1]; 60 hundredths > 58 [1]; > [1]
- Tenths 0 < 9 [1]; < [1]
- Add a zero: 0.70 [1]; = [1]
- 0.520, 0.500, 0.502 [1]; ascending [1]; 0.5, 0.502, 0.52 [1]
- No [1]. Tenths 0 < 5 [1]. 4.05 < 4.5 [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 0.6 ? 0.58
- 1.09 ? 1.9
- 0.7 ? 0.70
- Order 0.52, 0.5, 0.502
- Greatest of 4.5, 4.05, 4.505
- 0.45 __ 0.450
- 0.305 __ 0.35
- 0.6 __ 0.58
- 1.09 __ 1.9
- Least of 0.3, 0.033, 0.303:
Homework
Order the masses of five objects in kilograms.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 0.6 ? 0.58 | > | 2 |
| 1.09 ? 1.9 | < | 2 |
| 0.7 ? 0.70 | = | 2 |
| Order 0.52, 0.5, 0.502 | 0.5, 0.502, 0.52 | 2 |
| Greatest of 4.5, 4.05, 4.505 | 4.505 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 >; 2 <; 3 =; 4 0.5, 0.502, 0.52; 5 4.505.
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 =; 7 <; 8 >; 9 <; 10 0.033.
Independent practice answers. Level 1: 1 >; 2 <; 3 =; 4 0.5, 0.502, 0.52; 5 4.505. Level 2: 1 >; 2 =; 3 <. Level 3: 1 1.001, 1.01, 1.1; 2 >; 3 0.30 > 0.25. Compare tenths: 3 > 2..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Compare place by place | 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 Recognise equivalent decimals | 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 Use >, < and = | 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 Order decimals | 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: Thinking more digits is bigger. Compare place by place.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Compare hundredths.
- 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 compares and orders decimals. You do not need to be good at mathematics to help.
- Compare prices and race times.
- Ask: what happens if we add zeros?
- Use a number line.
- 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: compare place by place; recognise equivalent decimals; use >, < and =; order decimals.
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. Which place differs first? Are the places lined up?
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 more digits is bigger. Compare place by place.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-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. Compare hundredths. 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 5.NBT.A.3b; Cambridge Primary Mathematics Stage 5 (comparing decimals). These sources informed the lesson; no official alignment is claimed.