You will learn
- Read and write mixed numbers.
- Show on a number line.
- Convert a mixed number to a fraction.
- Compare with whole numbers.
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 mixed number has a whole part and a fraction part.
- Improper fractions have a numerator at least as big as the denominator.
- Convert by dividing or multiplying.
- Compare using the whole part first.
Words to know
A whole number and a fraction.
Numerator at least the denominator.
Complete units.
A line with numbers.
1. Discover: pizzas
You have 1 whole pizza and 3/4 of another. How would you write that?
2. Understand: mixed numbers
- 1 whole and 3/4 is 1 3/4.
- 2 1/2 = 2 + 1/2 = 5/2 (2 × 2 + 1 = 5 halves).
- 7/4 = 4/4 + 3/4 = 1 3/4.
- On a number line, 1 3/4 is between 1 and 2.
Idea 1: To mixed
9/4: 9 ÷ 4 = 2 r1, so 2 1/4. 11/5: 11 ÷ 5 = 2 r1, so 2 1/5.
Idea 2: To fraction
3 1/3: 3 × 3 + 1 = 10, so 10/3. 1 1/2: 1 × 2 + 1 = 3, so 3/2.
Idea 3: Compare
2 1/2 and 2 1/4: wholes are equal, and 1/2 > 1/4, so 2 1/2 is greater.
Why multiply then add? We turn each whole into parts, then add the extra parts.
3. Worked examples
Example 1 (I show you): To mixed
9/4
- 9 ÷ 4 = 2 r1.
Answer: 2 1/4
Example 2 (We do it together): To fraction
3 1/3
- 3 × 3 + 1.
Answer: 10/3
Example 3 (You try): Compare
2 1/2 or 2 1/4
Show the steps and answer
- Same whole, compare fractions.
Answer: 2 1/2
Did you know?
The remainder is the numerator of the fraction part.
Why this matters
Mixed numbers are how we measure things in everyday life.
4. Explore: mixed
You need paper.
- Draw 1 whole and 3/4.
- Count quarters.
- Write 7/4.
- Write 1 3/4.
Think about it: what did you notice?
7/4 = 1 3/4.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ ÷ ___ = ___ remainder ___.
- So the mixed number is ___.
- ___ × ___ + ___ = ___.
- So the fraction is ___.
Guided practice
Question 1. 7/4 as a mixed number?
1 3/4.
Question 2. 2 1/2 as a fraction?
5/2.
Question 3. Is 1 3/4 more than 1?
Yes.
Independent practice
Level 1: Start
- 9/4 as a mixed number
- 3 1/3 as a fraction
- 1 1/2 as a fraction
- 11/5 as a mixed number
- Which is greater: 2 1/2 or 2 1/4?
Level 2: Grow
- 7/2 as a mixed number
- 2 2/5 as a fraction
- Which is greater: 1 3/4 or 1 2/3?
Level 3: Stretch
- 29/6 as a mixed number
- 6 3/4 as a fraction
- Ben says 2 1/3 = 3/3. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Ada has 2 whole cakes and half of another. Write it as a mixed number.
Show a sample answer
2 1/2.
Another one. A recipe needs 2 1/2 cups of flour. How many half cups is that?
Show a sample answer
2 1/2 = 5/2, so 5 half cups.
7. Common mistakes
Fix: Divide to find the whole part.
Fix: 3 × 3 + 1, not 3 × 3.
Fix: The quotient is the whole part; the remainder is the numerator.
8. Lesson summary and revision card
- I can read and write mixed numbers.
- I can show them on a number line.
- I can convert a mixed number to a fraction.
- I can compare with whole numbers.
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
- Mixed = whole + fraction.
- Convert both ways.
- Number line helps.
11. Next lesson
Next lesson: Fractions greater than one. 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 9/4 as a mixed number. [2 marks]
- Write 3 1/3 as an improper fraction. [2 marks]
- Write 1 1/2 as an improper fraction. [2 marks]
- Write 11/5 as a mixed number. [2 marks]
- Ana says 2 1/4 is greater than 2 1/2. Is she right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 9 ÷ 4 = 2 r1 [1]; 2 1/4 [1]
- 3 × 3 + 1 = 10 [1]; 10/3 [1]
- 1 × 2 + 1 = 3 [1]; 3/2 [1]
- 11 ÷ 5 = 2 r1 [1]; 2 1/5 [1]
- No [1]. 1/4 is less than 1/2 [1]. 2 1/2 is greater [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
- 9/4 as a mixed number
- 3 1/3 as a fraction
- 1 1/2 as a fraction
- 11/5 as a mixed number
- Greater: 2 1/2 or 2 1/4
- 7/4 as a mixed number
- 2 1/2 as an improper fraction
- 9/4 is
- 3 1/3 as a fraction
- Greater: 2 1/2 or 2 1/4?
Homework
Write five mixed numbers and convert them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 9/4 as a mixed number | 2 1/4 | 2 |
| 3 1/3 as a fraction | 10/3 | 2 |
| 1 1/2 as a fraction | 3/2 | 2 |
| 11/5 as a mixed number | 2 1/5 | 2 |
| Greater: 2 1/2 or 2 1/4 | 2 1/2 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2 1/4; 2 10/3; 3 3/2; 4 2 1/5; 5 2 1/2.
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 1 3/4; 7 5/2; 8 2 1/4; 9 10/3; 10 2 1/2.
Independent practice answers. Level 1: 1 2 1/4; 2 10/3; 3 3/2; 4 2 1/5; 5 2 1/2. Level 2: 1 3 1/2; 2 12/5; 3 1 3/4. Level 3: 1 4 5/6; 2 27/4; 3 2 = 6/3, so 2 1/3 = 7/3..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read and write mixed numbers | 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 Show 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 |
| O3 Convert a mixed number to a fraction | 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 Compare with whole numbers | 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 7/4 as 7 4. Divide to find the whole part.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Draw wholes and parts.
- 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 reads, writes and converts mixed numbers. You do not need to be good at mathematics to help.
- Cut pizzas into slices and count whole and part pizzas.
- Ask: how many wholes? what is left?
- Show on 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: read and write mixed numbers; show on a number line; convert a mixed number to a fraction; compare with whole numbers.
Prerequisite knowledge. Lessons 1 and 6.
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. How many wholes? What fraction is left?
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 7/4 as 7 4. Divide to find the whole part.
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. Draw wholes and parts. 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.B.3 (mixed numbers); Cambridge Primary Mathematics Stage 5 (improper fractions and mixed numbers). These sources informed the lesson.