You will learn
- Write improper fractions.
- Convert between forms.
- Place on a number line.
- Add to make a fraction greater than 1.
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
- An improper fraction is 1 or more.
- Convert by dividing or multiplying.
- Place them on a number line past 1.
- Adding fractions can give more than 1.
Words to know
Numerator ≥ denominator.
Whole and fraction.
Change form.
Parts in the whole.
1. Discover: many cakes
A baker has 11 quarter-cakes. How many whole cakes is that?
2. Understand: fractions over 1
- 11/4 = 2 3/4 (11 ÷ 4 = 2 remainder 3).
- 3 2/5 = (3 × 5 + 2)/5 = 17/5.
- 4/4 = 1, 8/4 = 2.
- 5/6 + 4/6 = 9/6 = 1 1/2.
Idea 1: To mixed
13/5: 13 ÷ 5 = 2 r3, so 2 3/5. 3/2: 3 ÷ 2 = 1 r1, so 1 1/2.
Idea 2: To improper
4 1/2: 4 × 2 + 1 = 9, so 9/2. 8/8 = 1 whole.
Idea 3: Adding
7/3 + 2/3 = 9/3 = 3. 5/6 + 4/6 = 9/6 = 1 3/6 = 1 1/2.
Why 8/8 = 1? All eight parts make the whole.
3. Worked examples
Example 1 (I show you): Mixed
13/5
- 13 ÷ 5 = 2 r3.
Answer: 2 3/5
Example 2 (We do it together): Improper
4 1/2
- 4 × 2 + 1.
Answer: 9/2
Example 3 (You try): Add
7/3 + 2/3
Show the steps and answer
- 9/3.
Answer: 3
Did you know?
Improper does not mean wrong. It is just a fraction of 1 or more.
Why this matters
Fractions greater than one appear when we measure more than one whole.
4. Explore: convert
You need paper.
- Write 11/4.
- Divide 11 by 4.
- Write 2 3/4.
- Convert back.
Think about it: what did you notice?
2 3/4 = 11/4.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The fraction is greater than 1 because ___.
- ___ ÷ ___ = ___ remainder ___.
- So it is ___.
- On the number line it lies between ___ and ___.
Guided practice
Question 1. 11/4 as a mixed number?
2 3/4.
Question 2. 3 2/5 as a fraction?
17/5.
Question 3. 5/6 + 4/6?
1 1/2.
Independent practice
Level 1: Start
- 13/5 as a mixed number
- 4 1/2 as a fraction
- 8/8 as a whole
- 3/2 as a mixed number
- 7/3 + 2/3
Level 2: Grow
- 9/2 as a mixed number
- 3 1/4 as a fraction
- 6/6 as a whole
Level 3: Stretch
- 47/10 as a mixed number
- 5 3/8 as a fraction
- Kofi says 7/3 + 2/3 = 9/6. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A baker has 11 quarter-cakes. How many whole cakes and quarters?
Show a sample answer
2 whole and 3 quarters.
Another one. Ana has 5 half-litre bottles of juice. How many litres is that?
Show a sample answer
5/2 = 2 1/2 litres
7. Common mistakes
Fix: Remainder over the denominator.
Fix: Keep the denominator.
Fix: Divide to find the wholes.
8. Lesson summary and revision card
- I can write improper fractions.
- I can convert between forms.
- I can place them on a number line.
- I can add to make a fraction greater than 1.
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
- Improper means at least one whole.
- Convert both ways.
- Sums can exceed 1.
11. Next lesson
Next lesson: Fraction word problems. 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 13/5 as a mixed number. [2 marks]
- Write 4 1/2 as an improper fraction. [2 marks]
- Write 8/8 as a whole number. [1 mark]
- Write 3/2 as a mixed number. [2 marks]
- Find 7/3 + 2/3. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 13 ÷ 5 = 2 r3 [1]; 2 3/5 [1]
- 4 × 2 + 1 = 9 [1]; 9/2 [1]
- 1 [1]
- 3 ÷ 2 = 1 r1 [1]; 1 1/2 [1]
- Add numerators: 9/3 [1]; 9 ÷ 3 [1]; 3 [1]
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 13/5 as a mixed number
- 4 1/2 as a fraction
- 8/8
- 3/2 as a mixed number
- 7/3 + 2/3
- 11/4 =
- 3 2/5 =
- 13/5 =
- 4 1/2 =
- 5/6 + 4/6 =
Homework
Write six fractions greater than 1 and convert them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 13/5 as a mixed number | 2 3/5 | 2 |
| 4 1/2 as a fraction | 9/2 | 2 |
| 8/8 | 1 | 2 |
| 3/2 as a mixed number | 1 1/2 | 2 |
| 7/3 + 2/3 | 3 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2 3/5; 2 9/2; 3 1; 4 1 1/2; 5 3.
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 2 3/4; 7 17/5; 8 2 3/5; 9 9/2; 10 1 1/2.
Independent practice answers. Level 1: 1 2 3/5; 2 9/2; 3 1; 4 1 1/2; 5 9/3 = 3. Level 2: 1 4 1/2; 2 13/4; 3 1. Level 3: 1 4 7/10; 2 43/8; 3 The denominator stays 3. 9/3 = 3..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write improper fractions | 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 Convert between forms | 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 Place 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 |
| O4 Add to make a fraction greater than 1 | 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: Forgetting the remainder as a fraction. Remainder over the denominator.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Count quarters.
- 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 works with fractions greater than one. You do not need to be good at mathematics to help.
- Count slices of pizza past one whole.
- Ask: how many wholes are in it?
- Use a number line past 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: write improper fractions; convert between forms; place on a number line; add to make a fraction greater than 1.
Prerequisite knowledge. Lesson 8.
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. Is the numerator bigger than the denominator? How many wholes?
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. Forgetting the remainder as a fraction. Remainder over the denominator.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. Count quarters. 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; Cambridge Primary Mathematics Stage 5 (improper fractions). These sources informed the lesson.