You will learn
- Order decimals with same places.
- Order decimals with different places.
- Use a number line.
- Explain the order.
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
- Write the decimals with the same number of places.
- Compare place by place from the left.
- Ascending is least to greatest.
- Use a number line to check.
Words to know
Arrange.
Least to greatest.
Greatest to least.
Equal in value.
1. Discover: race times
Three pupils run 0.5, 0.45 and 0.7 km. Who ran farthest, and who least?
2. Understand: ordering decimals
Write all with the same number of places, then order.
- 0.5, 0.45, 0.7 → 0.50, 0.45, 0.70. Ascending: 0.45, 0.5, 0.7.
- 2.3, 2.03, 2.30: 2.03 < 2.3 = 2.30.
- Descending: 0.7, 0.5, 0.45.
Idea 1: Order
0.3, 0.03, 0.33: write 0.30, 0.03, 0.33. Least first: 0.03, 0.3, 0.33.
Idea 2: Next
1.2, 1.02, 1.22: write 1.20, 1.02, 1.22. Least first: 1.02, 1.2, 1.22.
Idea 3: Greatest and least
Greatest of 4.5, 4.05, 4.55 is 4.55. Least of 0.9, 0.09, 0.19 is 0.09. Descending 0.6, 0.65, 0.56: 0.65, 0.6, 0.56.
Why equal places? It makes the comparison fair.
3. Worked examples
Example 1 (I show you): Order
0.3, 0.03, 0.33 (least first)
- 0.30, 0.03, 0.33.
Answer: 0.03, 0.3, 0.33
Example 2 (We do it together): Greatest
4.5, 4.05, 4.55
- 4.50, 4.05, 4.55.
Answer: 4.55
Example 3 (You try): Descending
0.6, 0.65, 0.56
Show the steps and answer
- 0.60, 0.65, 0.56.
Answer: 0.65, 0.6, 0.56
Did you know?
Ascending starts with A for Up.
Why this matters
Ordering decimals helps us rank times, prices and distances.
4. Explore: order
You need paper.
- Write each decimal with two places.
- Compare.
- Order least to greatest.
- Check on a number line.
Think about it: what did you notice?
0.45, 0.5, 0.7.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I write them as ___, ___, ___.
- The least is ___.
- In ascending order: ___.
- In descending order: ___.
Guided practice
Question 1. Least of 0.5, 0.45, 0.7?
0.45.
Question 2. Greatest?
0.7.
Question 3. Order 2.3, 2.03, 2.5.
2.03, 2.3, 2.5.
Independent practice
Level 1: Start
- Order 0.3, 0.03, 0.33
- Order 1.2, 1.02, 1.22
- Greatest of 4.5, 4.05, 4.55
- Least of 0.9, 0.09, 0.19
- Descending: 0.6, 0.65, 0.56
Level 2: Grow
- Greatest of 0.7, 0.07, 0.17
- Order 0.4, 0.04, 0.44 least first
- Descending 1.5, 1.05, 1.55
Level 3: Stretch
- Order 5.6, 5.06, 5.66, 5.16 least first
- Write a decimal between 2.3 and 2.4
- Ben says 0.3 is the least of 0.3, 0.03 and 0.33 because it has the fewest digits. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Three ropes are 1.2, 1.02 and 1.22 m. Which is longest?
Show a sample answer
1.22 m.
Another one. Three runners finish in 11.5, 11.05 and 11.55 seconds. Who is fastest?
Show a sample answer
11.05 is the least time, so that runner is fastest.
7. Common mistakes
Fix: Line up places first.
Fix: Equalise the places and compare.
Fix: Compare place by place.
8. Lesson summary and revision card
- I can order decimals with the same places.
- I can order decimals with different places.
- I can use a number line.
- I can explain the order.
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
- Same places first.
- Compare tenths then hundredths.
- Check with a number line.
11. Next lesson
Next lesson: Fractions and 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.
- Order 0.3, 0.03, 0.33 from least. [3 marks]
- Order 1.2, 1.02, 1.22 from least. [3 marks]
- Find the greatest of 4.5, 4.05, 4.55. [1 mark]
- Find the least of 0.9, 0.09, 0.19. [1 mark]
- Ana says 0.6 is greater than 0.65. Is she right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 0.30, 0.03, 0.33 [1]; compare [1]; 0.03, 0.3, 0.33 [1]
- 1.20, 1.02, 1.22 [1]; compare [1]; 1.02, 1.2, 1.22 [1]
- 4.55 [1]
- 0.09 [1]
- No [1]. 0.6 = 0.60 [1]. 0.65 > 0.60 [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
- Order 0.3, 0.03, 0.33
- Order 1.2, 1.02, 1.22
- Greatest of 4.5, 4.05, 4.55
- Least of 0.9, 0.09, 0.19
- Descending 0.6, 0.65, 0.56
- Ascending of 0.5, 0.45, 0.7:
- Order 2.3, 2.03, 2.5 least first:
- Order 0.3, 0.03, 0.33 least first:
- Greatest of 4.5, 4.05, 4.55:
- Least of 0.9, 0.09, 0.19:
Homework
Order the lengths of five objects in metres.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Order 0.3, 0.03, 0.33 | 0.03, 0.3, 0.33 | 2 |
| Order 1.2, 1.02, 1.22 | 1.02, 1.2, 1.22 | 2 |
| Greatest of 4.5, 4.05, 4.55 | 4.55 | 2 |
| Least of 0.9, 0.09, 0.19 | 0.09 | 2 |
| Descending 0.6, 0.65, 0.56 | 0.65, 0.6, 0.56 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.03, 0.3, 0.33; 2 1.02, 1.2, 1.22; 3 4.55; 4 0.09; 5 0.65, 0.6, 0.56.
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 0.45, 0.5, 0.7; 7 2.03, 2.3, 2.5; 8 0.03, 0.3, 0.33; 9 4.55; 10 0.09.
Independent practice answers. Level 1: 1 0.03, 0.3, 0.33; 2 1.02, 1.2, 1.22; 3 4.55; 4 0.09; 5 0.65, 0.6, 0.56. Level 2: 1 0.7; 2 0.04, 0.4, 0.44; 3 1.55, 1.5, 1.05. Level 3: 1 5.06, 5.16, 5.6, 5.66; 2 for example 2.35; 3 0.03 is least (3 hundredths). Digits do not decide the size..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Order decimals with same 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 |
| O2 Order decimals with different 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 Use 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 |
| O4 Explain the order | 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: Ordering by the number of digits. Line up places first.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Order using a number line.
- 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 orders decimals from least to greatest and back. You do not need to be good at mathematics to help.
- Order prices on a menu.
- Ask: do they have the same places?
- Use number lines.
- 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: order decimals with same places; order decimals with different places; use a number line; explain the order.
Prerequisite knowledge. Lesson 5.
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. Did I match the places? Which is least? Which is greatest?
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. Ordering by the number of digits. Line up places first.
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. Order using a number line. 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 4 » Number & Operations—Fractions; Grade 4 » 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 4.NF.C.7 and 5.NBT.A.3d; Cambridge Primary Mathematics Stage 5 (ordering decimals). These sources informed the lesson.