You will learn
- Compare whole parts first.
- Compare tenths then hundredths.
- Use >, < and =.
- Explain why 0.5 = 0.50.
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 the whole parts first.
- Then compare tenths, then hundredths.
- Add zeros to match the places.
- Use >, < and =.
Words to know
Say which is greater.
Value by position.
Same value, e.g. 0.5 and 0.50.
>
1. Discover: which is bigger?
Is 0.6 bigger or smaller than 0.58? Is 3.45 bigger than 3.5?
2. Understand: comparing decimals
Compare from the left: ones, then tenths, then hundredths.
- 0.6 = 0.60 and 0.58: 6 tenths > 5 tenths, so 0.6 > 0.58.
- 3.45 and 3.5 = 3.50: 4 tenths < 5 tenths, so 3.45 < 3.5.
- 0.5 = 0.50.
Idea 1: Equalise places
0.7 vs 0.65: write 0.70 vs 0.65. 70 hundredths > 65 hundredths, so 0.7 > 0.65.
Idea 2: Tenths first
2.34 vs 2.4: write 2.40. 2.34 < 2.40, so 2.34 < 2.4. 1.08 vs 1.8: 1.08 < 1.8.
Idea 3: Equal
5.5 = 5.50, so 5.5 = 5.50. 0.09 vs 0.1 = 0.10: 0.09 < 0.1.
Why add a zero? It does not change the value but lines up the places.
3. Worked examples
Example 1 (I show you): Compare
0.7 __ 0.65
- 0.70 vs 0.65.
Answer: >
Example 2 (We do it together): Compare
2.34 __ 2.4
- 2.34 vs 2.40.
Answer: <
Example 3 (You try): Equal
5.5 __ 5.50
Show the steps and answer
- Add a zero.
Answer: =
Did you know?
A zero at the end of a decimal does not change its value.
Why this matters
Comparing decimals helps us read prices, times and measures.
4. Explore: line up
You need paper.
- Write 0.6 as 0.60.
- Compare tenths.
- Compare 3.45 and 3.50.
- Write > or <.
Think about it: what did you notice?
0.6 > 0.58; 3.45 < 3.5.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I write both with ___ places.
- The whole parts are ___.
- The tenths are ___ and ___.
- So ___ is greater / less than ___.
Guided practice
Question 1. 0.6 ? 0.58
>
Question 2. 3.45 ? 3.5
<
Question 3. 0.5 ? 0.50
=
Independent practice
Level 1: Start
- 0.7 ? 0.65
- 2.34 ? 2.4
- 0.09 ? 0.1
- 5.5 ? 5.50
- 1.08 ? 1.8
Level 2: Grow
- 0.4 __ 0.35
- 6.7 __ 6.70
- 1.25 __ 1.3
Level 3: Stretch
- 3.04 __ 3.4
- 0.88 __ 0.9
- 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 runs 3.45 km and Bayo runs 3.5 km. Who ran farther?
Show a sample answer
Bayo.
Another one. Ife swam 1.45 km and Ola swam 1.5 km. Who swam farther? Explain.
Show a sample answer
1.5 = 1.50, which is more than 1.45, so Ola swam farther.
7. Common mistakes
Fix: Compare place by place.
Fix: Compare place by place.
Fix: Add zeros to equalise the places first.
8. Lesson summary and revision card
- I can compare whole parts first.
- I can compare tenths then hundredths.
- I can use >, < and =.
- I can explain why 0.5 = 0.50.
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
- Compare left to right.
- Add zeros to line up.
- Longer is not bigger.
11. Next lesson
Next lesson: Ordering 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 0.7 and 0.65 with >, < or =. Explain. [2 marks]
- Compare 2.34 and 2.4 with >, < or =. Explain. [2 marks]
- Compare 0.09 and 0.1 with >, < or =. Explain. [2 marks]
- Compare 5.5 and 5.50 with >, < or =. Explain. [2 marks]
- Kofi says 1.08 > 1.8 because 108 > 18. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 0.70 and 0.65 [1]; > [1]
- 2.40 [1]; < [1]
- 0.10 [1]; < [1]
- Same value [1]; = [1]
- No [1]. 1.8 = 1.80 [1]. 1.08 < 1.80 [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
- 0.7 ? 0.65
- 2.34 ? 2.4
- 0.09 ? 0.1
- 5.5 ? 5.50
- 1.08 ? 1.8
- 0.6 __ 0.58
- 3.45 __ 3.5
- 0.5 __ 0.50
- 0.09 __ 0.1
- 1.08 __ 1.8
Homework
Compare six pairs of decimals.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 0.7 ? 0.65 | > | 2 |
| 2.34 ? 2.4 | < | 2 |
| 0.09 ? 0.1 | < | 2 |
| 5.5 ? 5.50 | = | 2 |
| 1.08 ? 1.8 | < | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 >; 2 <; 3 <; 4 =; 5 <.
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 <.
Independent practice answers. Level 1: 1 >; 2 <; 3 <; 4 =; 5 <. Level 2: 1 >; 2 =; 3 <. Level 3: 1 <; 2 <; 3 0.3 = 0.30, and 0.30 > 0.25. Compare place by place, not as whole numbers..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Compare whole parts first | 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 Compare tenths then hundredths | 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 Explain why 0.5 = 0.50 | 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 longer decimals are bigger. Compare place by place.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use a hundred grid.
- 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 decimals with >, < and =. You do not need to be good at mathematics to help.
- Compare prices like 3.45 and 3.50.
- Ask: what happens if we add a zero?
- 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 whole parts first; compare tenths then hundredths; use >, < and =; explain why 0.5 = 0.50.
Prerequisite knowledge. Lesson 3.
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. Are the places equal? Which place decides?
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 longer decimals are bigger. Compare place by place.
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. Use a hundred grid. 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.NF.C.7 (compare decimals); Cambridge Primary Mathematics Stage 4 and 5 (comparing decimals). These sources informed the lesson; no official alignment is claimed.