You will learn
- Say that a tenth is one of ten equal parts.
- Write tenths as fractions and decimals.
- Read a decimal point.
- Place tenths 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
- A tenth is one of ten equal parts.
- Write tenths as a fraction and as a decimal.
- The decimal point separates ones from tenths.
- 10 tenths make 1 whole.
Words to know
One of ten equal parts.
A number with a decimal point.
Separates ones from tenths.
Part of a whole.
1. Discover: a ruler
A ruler is split into 10 equal parts. If you shade 3 parts, what fraction and what decimal is shaded?
2. Understand: tenths
One whole split into 10 equal parts gives tenths.
- 1 tenth = 1/10 = 0.1.
- 3 tenths = 3/10 = 0.3.
- 10 tenths = 1 whole = 1.0.
- 1.7 means 1 whole and 7 tenths.
The digit after the decimal point is the tenths place.
Idea 1: Tenths
9/10 = 0.9. 1 tenth = 0.1. 3/10 = 0.3.
Idea 2: Decimal to fraction
0.4 = 4/10. 0.7 = 7/10.
Idea 3: Reading
2.5 is 2 ones and 5 tenths. 10 tenths = 1 whole.
Why a decimal point? It tells us where the whole numbers stop and parts begin.
3. Worked examples
Example 1 (I show you): To decimal
9/10
- 9 tenths.
Answer: 0.9
Example 2 (We do it together): To fraction
0.4
- 4 tenths.
Answer: 4/10
Example 3 (You try): Reading
2.5
Show the steps and answer
- 2 ones and 5 tenths.
Answer: 2 and 5 tenths
Did you know?
Money uses the same idea: 10 dimes make a dollar.
Why this matters
Decimals let us measure things more exactly than whole numbers.
4. Explore: shade it
You need a 10-part strip.
- Shade 3 parts.
- Write the fraction.
- Write the decimal.
- Shade 7 parts and repeat.
Think about it: what did you notice?
3/10 = 0.3.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The digit after the decimal point is ___.
- ___ tenths is ___.
- As a fraction it is ___.
- 10 tenths make ___.
Guided practice
Question 1. 3/10 as a decimal?
0.3.
Question 2. 0.7 as a fraction?
7/10.
Question 3. 1.7 means?
1 and 7 tenths.
Independent practice
Level 1: Start
- 9/10 as a decimal
- 0.4 as a fraction
- 1 tenth as a decimal
- 2.5 means 2 and ___ tenths
- 10 tenths equal ___
Level 2: Grow
- 5/10 as a decimal
- 0.8 as a fraction
- 3.2 means 3 and ___ tenths
Level 3: Stretch
- 0.5 as a fraction in simplest form
- Between which two whole numbers is 0.6?
- Ben writes 3/10 as 3.10. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A rope is 0.6 m long. What fraction of a metre?
Show a sample answer
6/10.
Another one. A ribbon is 7/10 m long. Write its length as a decimal and say what the 7 means.
Show a sample answer
0.7 m. The 7 means 7 tenths.
7. Common mistakes
Fix: Tenths are right after the point.
Fix: Tenths use one place after the point: 0.3.
Fix: Tenths are small parts; tens are big groups.
8. Lesson summary and revision card
- I can say a tenth is one of ten equal parts.
- I can write tenths as fractions and decimals.
- I can read a decimal point.
- I can place tenths 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
- Tenths: first place after the point.
- 0.1 = 1/10.
- 10 tenths = 1.
11. Next lesson
Next lesson: Understanding hundredths. 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.
- Write 9/10 as a decimal. [1 mark]
- Write 0.4 as a fraction. [1 mark]
- What does 2.5 mean? [2 marks]
- How many tenths make 1 whole? [2 marks]
- Ali says 0.1 is the same as 1/100. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 0.9 [1]
- 4/10 [1]
- 2 ones [1]; 5 tenths [1]
- 1 whole is split into 10 equal parts [1]; 10 tenths [1]
- No [1]. 0.1 = 1/10 [1]. 1/100 is 0.01 [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
- 9/10 as a decimal
- 0.4 as a fraction
- 1 tenth as a decimal
- 2.5 means 2 and ___ tenths
- 10 tenths equal
- 3/10 as a decimal is
- 0.7 as a fraction is
- 1.7 means
- 9/10 as a decimal is
- 10 tenths equal
Homework
Measure five objects in tenths of a metre.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 9/10 as a decimal | 0.9 | 2 |
| 0.4 as a fraction | 4/10 | 2 |
| 1 tenth as a decimal | 0.1 | 2 |
| 2.5 means 2 and ___ tenths | 5 | 2 |
| 10 tenths equal | 1 whole | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.9; 2 4/10; 3 0.1; 4 5; 5 1 whole.
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 0.3; 7 7/10; 8 1 and 7 tenths; 9 0.9; 10 1 whole.
Independent practice answers. Level 1: 1 0.9; 2 4/10; 3 0.1; 4 5; 5 1. Level 2: 1 0.5; 2 8/10; 3 2. Level 3: 1 1/2; 2 0 and 1; 3 3/10 = 0.3. The 3 is in the tenths place..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say that a tenth is one of ten equal parts | 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 Write tenths as fractions and 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 Read a decimal point | 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 tenths 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: Writing 3/10 as 0.03. Tenths are right after the point.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Shade tenths on a strip.
- 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 learns tenths as fractions and decimals. You do not need to be good at mathematics to help.
- Use money: 10 dimes make a dollar.
- Ask: how many tenths?
- Look at rulers marked in millimetres and centimetres.
- 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: say that a tenth is one of ten equal parts; write tenths as fractions and decimals; read a decimal point; place tenths on a number line.
Prerequisite knowledge. Fractions.
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 a 10-part strip. 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. How many parts in the whole? Which digit is the tenths?
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. Writing 3/10 as 0.03. Tenths are right after the point.
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. Shade tenths on a strip. 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.6 (decimal notation for tenths); Cambridge Primary Mathematics Stage 4 (tenths). These sources informed the lesson.