You will learn
- Compare two decimals.
- Order decimals.
- Use equal-length decimals.
- Place decimals on a number line.
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
- Compare digits from the left.
- Add zeros to make equal lengths.
- Equivalent decimals have the same value.
- Order decimals from least to greatest.
Words to know
Say which is larger.
Arrange by size.
Same value, e.g. 0.5 and 0.50.
A symbol 0–9.
1. Discover: fastest runner
Two runners take 0.45 s and 0.5 s to react. Who reacts faster?
2. Understand: comparing decimals
- Write 0.5 as 0.50 and compare 0.45 with 0.50: 0.5 is larger.
- Order 0.3, 0.29, 0.305: as thousandths 0.300, 0.290, 0.305.
- So 0.29 < 0.3 < 0.305.
- More digits does not mean larger.
Idea 1: Equal length
0.6 and 0.58: write 0.60 and 0.58. 0.6 is larger. 0.07 and 0.1: 0.07 and 0.10, so 0.1 is larger.
Idea 2: Order
0.3, 0.29, 0.305 as 0.300, 0.290, 0.305. Ascending: 0.29, 0.3, 0.305.
Idea 3: Equivalent
0.50 = 0.5. 1.09 is smaller than 1.1 (1.10).
Why add zeros? They do not change the value but make comparing easy.
3. Worked examples
Example 1 (I show you): Compare
0.6 and 0.58
- 0.60 and 0.58.
Answer: 0.6
Example 2 (We do it together): Order
0.3, 0.29, 0.305
- 0.300, 0.290, 0.305.
Answer: 0.29, 0.3, 0.305
Example 3 (You try): Smaller
1.09 or 1.1
Show the steps and answer
- 1.09 and 1.10.
Answer: 1.09
Did you know?
A longer decimal is not always larger.
Why this matters
Comparing decimals helps with money, times and measurements.
4. Explore: order
You need paper.
- Pad with zeros.
- Compare digit by digit.
- Order.
- Check.
Think about it: what did you notice?
0.29 < 0.3 < 0.305.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I write them with the same number of places: ___.
- Compare the ___ digit first.
- So ___ is larger.
- In order: ___.
Guided practice
Question 1. Larger: 0.45 or 0.5?
0.5.
Question 2. 0.3 as thousandths?
0.300.
Question 3. Smallest of 0.3, 0.29, 0.305?
0.29.
Independent practice
Level 1: Start
- Larger: 0.6 or 0.58
- Larger: 0.07 or 0.1
- Order 0.3, 0.29, 0.305
- Is 0.50 equal to 0.5?
- Smaller: 1.09 or 1.1
Level 2: Grow
- Larger: 0.4 or 0.35
- Smaller: 0.09 or 0.1
- Is 0.70 equal to 0.7?
Level 3: Stretch
- Order 2.5, 2.05, 2.45 ascending
- Smaller: 3.099 or 3.1
- Ben says 0.125 is larger than 0.5 because 125 is bigger than 5. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Reaction times 0.45 s and 0.5 s. Who is faster?
Show a sample answer
The 0.45 s runner (less time).
Another one. Two runners take 11.8 s and 11.75 s. Who is faster and why?
Show a sample answer
11.75 s; it is less than 11.80 s
7. Common mistakes
Fix: Pad to equal places.
Fix: Add zeros to compare.
Fix: Compare from the left.
8. Lesson summary and revision card
- I can compare two decimals.
- I can order decimals.
- I can use equal-length decimals.
- I can place decimals on a number line.
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
- Pad with zeros.
- Compare place by place.
- Longer is not larger.
11. Next lesson
Next lesson: Decimal addition. 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.
- Which is larger, 0.6 or 0.58? Explain. [2 marks]
- Which is larger, 0.07 or 0.1? Explain. [2 marks]
- Order 0.3, 0.29 and 0.305 from least. [3 marks]
- Is 0.50 equal to 0.5? Explain. [2 marks]
- Ali says 1.09 is larger than 1.1 because 9 is bigger than 1. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 0.60 and 0.58 [1]; 0.6 is larger [1]
- 0.07 and 0.10 [1]; 0.1 is larger [1]
- Write as 0.300, 0.290, 0.305 [1]; compare the thousandths [1]; 0.29, 0.3, 0.305 [1]
- A zero at the end adds no value [1]; yes, equal [1]
- No [1]. 1.1 = 1.10 [1]. 1.10 is larger than 1.09 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Larger: 0.6 or 0.58
- Larger: 0.07 or 0.1
- Order 0.3, 0.29, 0.305
- 0.50 = 0.5? (yes/no)
- Smaller: 1.09 or 1.1
- Larger: 0.6 or 0.58
- Larger: 0.07 or 0.1
- Ascending 0.3, 0.29, 0.305
- 0.50 and 0.5 are:
- Smaller: 1.09 or 1.1
Homework
Order 0.8, 0.08, 0.808 and 0.88.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Larger: 0.6 or 0.58 | 0.6 | 2 |
| Larger: 0.07 or 0.1 | 0.1 | 2 |
| Order 0.3, 0.29, 0.305 | 0.29, 0.3, 0.305 | 2 |
| 0.50 = 0.5? (yes/no) | yes | 2 |
| Smaller: 1.09 or 1.1 | 1.09 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.6; 2 0.1; 3 0.29, 0.3, 0.305; 4 yes; 5 1.09.
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 0.6; 7 0.1; 8 0.29, 0.3, 0.305; 9 equal; 10 1.09.
Independent practice answers. Level 1: 1 0.6; 2 0.1; 3 0.29, 0.3, 0.305; 4 yes, equal; 5 1.09. Level 2: 1 0.4; 2 0.09; 3 yes. Level 3: 1 2.05, 2.45, 2.5; 2 3.099; 3 Compare 0.125 and 0.500: 0.5 is larger..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Compare two 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 |
| O2 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 |
| O3 Use equal-length 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 |
| O4 Place decimals on a number line | 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 0.45 > 0.5 because 45 > 5. Pad to equal places.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Tenths comparison.
- 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 in a shop.
- Ask: can we add zeros?
- Draw a number line from 0 to 1.
- 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 two decimals; order decimals; use equal-length decimals; place decimals on a number line.
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. Do the lengths match? Which digit differs first?
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 0.45 > 0.5 because 45 > 5. Pad to equal places.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Tenths comparison. 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.3b; Cambridge Primary Mathematics Stage 6 (comparing decimals). These sources informed the lesson.