You will learn
- Convert mixed numbers.
- Add mixed numbers.
- Subtract mixed numbers with regrouping.
- Simplify results.
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.
- Convert to improper fractions when helpful.
- Add wholes and fractions separately.
- Regroup 1 whole when subtracting.
Words to know
Whole and fraction.
Numerator ≥ denominator.
Trade 1 whole for fractions.
Change form.
1. Discover: cups of flour
A recipe needs 2 1/2 cups of flour and another needs 1 1/3 cups. How much in all?
2. Understand: mixed numbers
- 3 2/5 = 17/5.
- 2 1/2 + 1 1/3 = 2 3/6 + 1 2/6 = 3 5/6.
- 4 1/4 − 1 3/4 = 17/4 − 7/4 = 10/4 = 2 1/2.
Idea 1: Add
2 1/4 + 1 1/2 = 2 1/4 + 1 2/4 = 3 3/4. 1 2/3 + 2 3/4 = 1 8/12 + 2 9/12 = 3 17/12 = 4 5/12.
Idea 2: Subtract
3 1/3 − 1 1/6 = 3 2/6 − 1 1/6 = 2 1/6.
Idea 3: Regroup
5 − 2 3/4: 5 = 4 4/4, so 4 4/4 − 2 3/4 = 2 1/4. 4 1/2 − 2 2/3 = 4 3/6 − 2 4/6 = 3 9/6 − 2 4/6 = 1 5/6.
Why regroup? We trade one whole for fractions so we can subtract.
3. Worked examples
Example 1 (I show you): Add
2 1/4 + 1 1/2
- Make quarters.
Answer: 3 3/4
Example 2 (We do it together): Regroup
5 − 2 3/4
- 5 = 4 4/4.
Answer: 2 1/4
Example 3 (You try): Regroup
4 1/2 − 2 2/3
Show the steps and answer
- 4 3/6 = 3 9/6.
Answer: 1 5/6
Did you know?
Mixed numbers can be changed into improper fractions and back.
Why this matters
Mixed numbers appear in recipes, lengths and carpentry.
4. Explore: mixed
You need paper.
- Write 2 1/2 and 1 1/3.
- Common denominator.
- Add wholes and fractions.
- Simplify.
Think about it: what did you notice?
3 5/6.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I make the denominators ___.
- I add the wholes ___ and the fractions ___.
- I regroup 1 whole as ___.
- The answer is ___.
Guided practice
Question 1. 3 2/5 as a fraction?
17/5.
Question 2. 2 1/2 + 1 1/3?
3 5/6.
Question 3. 4 1/4 − 1 3/4?
2 1/2.
Independent practice
Level 1: Start
- 2 1/4 + 1 1/2
- 3 1/3 − 1 1/6
- 5 − 2 3/4
- 1 2/3 + 2 3/4
- 4 1/2 − 2 2/3
Level 2: Grow
- 1 2/5 as an improper fraction
- 11/3 as a mixed number
- 1 1/2 + 1 1/3
Level 3: Stretch
- 3 3/4 + 2 5/6
- 7 − 3 2/5
- Ben says 3 1/4 − 1 1/2 = 2 1/4. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Two recipes use 2 1/2 and 1 1/3 cups of flour. Total?
Show a sample answer
3 5/6 cups.
Another one. A ribbon is 4 1/2 m long. Ana cuts off 1 3/4 m. How much is left?
Show a sample answer
4 2/4 − 1 3/4 = 2 3/4 m
7. Common mistakes
Fix: Regroup a whole.
Fix: Regroup when the top fraction is smaller.
Fix: Write 17/12 as 1 5/12.
8. Lesson summary and revision card
- I can convert mixed numbers.
- I can add mixed numbers.
- I can subtract with regrouping.
- I can simplify results.
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
- Convert or split.
- Regroup to subtract.
- Simplify.
11. Next lesson
Next lesson: Multiplying fractions by whole numbers. 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.
- Find 2 1/4 + 1 1/2. [3 marks]
- Find 3 1/3 − 1 1/6. [3 marks]
- Find 5 − 2 3/4. [3 marks]
- Find 1 2/3 + 2 3/4. [3 marks]
- Ali says 4 1/2 − 2 2/3 = 2 1/6. Is he right? Explain. [3 marks]
Total: 15 marks.
Marking guide and model answers
- 1/4 + 2/4 [1]; 3 wholes [1]; 3 3/4 [1]
- 3 2/6 − 1 1/6 [1]; 2 wholes and 1/6 [1]; 2 1/6 [1]
- Regroup 5 as 4 4/4 [1]; 4 4/4 − 2 3/4 [1]; 2 1/4 [1]
- 1 8/12 + 2 9/12 [1]; 3 17/12 [1]; 4 5/12 [1]
- No [1]. 4 3/6 = 3 9/6, so 3 9/6 − 2 4/6 [1]. The answer is 1 5/6 [1].
Score guide: 13 to 15 = secure. 9 to 12 = nearly there, revise the parts you missed. Under 9 = work through the lesson again with a grown-up.
Printable worksheet
- 3 2/5 as a fraction
- 2 1/4 + 1 1/2
- 5 − 2 3/4
- 3 1/3 − 1 1/6
- 1 2/3 + 2 3/4
- 3 2/5 as a fraction
- 2 1/2 + 1 1/3 =
- 4 1/4 − 1 3/4 =
- 2 1/4 + 1 1/2 =
- 5 − 2 3/4 =
Homework
Make a recipe with three mixed-number amounts and total them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3 2/5 as a fraction | 17/5 | 2 |
| 2 1/4 + 1 1/2 | 3 3/4 | 2 |
| 5 − 2 3/4 | 2 1/4 | 2 |
| 3 1/3 − 1 1/6 | 2 1/6 | 2 |
| 1 2/3 + 2 3/4 | 4 5/12 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 17/5; 2 3 3/4; 3 2 1/4; 4 2 1/6; 5 4 5/12.
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 17/5; 7 3 5/6; 8 2 1/2; 9 3 3/4; 10 2 1/4.
Independent practice answers. Level 1: 1 3 3/4; 2 2 1/6; 3 2 1/4; 4 4 5/12; 5 1 5/6. Level 2: 1 7/5; 2 3 2/3; 3 2 5/6. Level 3: 1 6 7/12; 2 3 3/5; 3 1/4 is smaller than 1/2, so regroup: 2 5/4 − 1 2/4 = 1 3/4..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Convert 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 Add 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 |
| O3 Subtract mixed numbers with regrouping | 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 Simplify results | 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: Subtracting the smaller fraction from the larger. Regroup a whole.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Review mixed numbers.
- 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 adds and subtracts mixed numbers. You do not need to be good at mathematics to help.
- Measure ingredients in mixed numbers.
- Ask: do we need to regroup?
- Use a number line for jumps.
- 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: convert mixed numbers; add mixed numbers; subtract mixed numbers with regrouping; simplify results.
Prerequisite knowledge. Lessons 3 and 4.
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 denominators the same? Do I need to regroup?
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. Subtracting the smaller fraction from the larger. Regroup a whole.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 15-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. Review mixed numbers. 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 5 » Number & Operations—Fractions; Grade 5 » 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 5.NF.A.1; Cambridge Primary Mathematics Stage 5 and 6 (mixed numbers). These sources informed the lesson.