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P4 Maths | Adding and Subtracting Fractions Lesson-Prep Guide (for tutors) | 45 minutes from same denominators to common denominators
Students add the numerators and then add the denominators too. The single hurdle in fraction addition is that the unit must match: the denominator is the unit, so different denominators must be converted before anything can be counted.
Objectives — Students can: (1) add and subtract fractions with the same denominator by working on the numerators only; (2) convert unlike denominators using the lowest common multiple and then calculate; (3) handle mixed numbers by treating the whole-number and fraction parts separately and reducing the answer; (4) explain in one sentence why denominators are never added.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Meaning of a fraction | What does 3/4 mean? | A whole split into 4 parts, 3 of them taken |
| Equivalent fractions | How many quarters equal one half? | Two, that is 2/4 |
| Lowest common multiple | LCM of 4 and 6 | 12 |
| Simplifying | Reduce 6/8 | 3/4 |
02 Lesson flow (45 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-8 min | Opening: one cake | Cut a cake into 4, take 1 piece then 2 more, ask how many quarters in total | Answer 3/4 and say the denominator stays 4 |
| 8-18 min | Same denominators | Show 1/4 + 2/4 = 3/4, numerators add, denominator unchanged | Six questions, all correct before moving on |
| 18-27 min | Why convert at all | Use a half cake and a third cake to show the units differ | Say that both must be cut to the same size |
| 27-35 min | Common denominators and the LCM | Show 1/2 + 1/3 with denominator 6: 3/6 + 2/6 = 5/6 | Five questions, writing the conversion step |
| 35-43 min | Mixed numbers and word problems | Add whole numbers and fractions separately, then reduce | Four questions, two of them word problems |
| 43-45 min | Exit check | Three quick oral questions | Independent answers |
03 Teaching script (read it out)
Scene 1: The denominator is a unit, not a quantity
Students see 1/2 + 1/3 and write 2/5 because they treat denominators as amounts to add. Start with objects: half a cake and a third of a cake are different sizes, so adding them cannot be described in pieces without cutting them the same way.
Only when both are cut into sixths is there a shared unit to count. The denominator records how many pieces a whole was cut into, so unify it first, then add.
Only when both are cut into sixths is there a shared unit to count. The denominator records how many pieces a whole was cut into, so unify it first, then add.
Students do: explain in one sentence why denominators cannot simply be added.
Scene 2: Converting means the LCM, not any product
Students remember to multiply denominators, so 1/4 + 1/6 becomes twenty-fourths, the numbers grow and the simplification goes wrong. The right move is the lowest common multiple, 12.
List multiples side by side: 4, 8, 12 and 6, 12, and take the first match. Multiplying is only convenient when the two denominators share no factor.
List multiples side by side: 4, 8, 12 and 6, 12, and take the first match. Multiplying is only convenient when the two denominators share no factor.
Students do: write two lines of multiples and circle the LCM before calculating.
Scene 3: Reduce, and recognise an improper fraction
P4 marking looks at the final form: 6/8 must be written 3/4, and 7/4 may be written as 1 3/4. Students often calculate correctly and still lose marks on form.
Build a closing habit: after every answer ask whether numerator and denominator share a factor, then whether the numerator exceeds the denominator. Three seconds each, cheaper than losing a mark.
Build a closing habit: after every answer ask whether numerator and denominator share a factor, then whether the numerator exceeds the denominator. Three seconds each, cheaper than losing a mark.
Students do: write “in simplest form” under every answer.
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Same denominator | 1/4 + 2/4 | Add numerators, keep the denominator | 3/4 |
| Unlike denominators, addition | 1/2 + 1/3 | Common denominator 6: 3/6 + 2/6 | 5/6 |
| Unlike denominators, subtraction | 3/4 – 1/6 | Common denominator 12: 9/12 – 2/12 | 7/12 (already reduced) |
| Mixed numbers in context | 1 1/2 cups plus 3/4 cup | Add whole parts and fraction parts separately, then reduce | 2 1/4 cups |
Sanity check (teach this): Sanity checks: the answer cannot exceed the sum of the addends; a same-denominator answer keeps its denominator; a conversion must use the lowest common multiple rather than an arbitrary product; the final answer must be reduced; whole numbers and numerators are never mixed together; word-problem answers carry units; subtraction never gives a negative result.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| Six same-denominator items | Three additions, three subtractions, denominators 4 to 12 | Check the denominators were not added |
| Five unlike-denominator items | Two with coprime denominators, three sharing a factor | Check the LCM was used |
| Four mixed items | Two mixed numbers, two word problems | Check reduction and units |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Adding the denominators | 1/2 + 1/3 answered as 2/5 | The denominator says how many pieces a whole was cut into, it is not an amount. Cut both to the same size before counting. |
| Changing only the denominator | 1/2 rewritten as 1/6 | If the denominator is multiplied by 3, the numerator must be too, otherwise the fraction shrinks. |
| Forgetting to reduce | Answer left as 6/8 | Both 6 and 8 divide by 2, so the simplest form is 3/4. Reduce means dividing top and bottom together. |
| Adding whole numbers into numerators | 1 1/2 + 3/4 answered as 1 4/6 | Keep whole numbers and fractions apart: 1 1/2 is 6/4, and 6/4 + 3/4 = 9/4 = 2 1/4. |
07 Homework (paper, section and question numbers)
- Primary maths chapter index — All chapters for this subject
- Lesson-prep guides index — Similar chapters in other subjects
- Redo this chapter — Redo five unlike-denominator items with two lines of multiples each
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| Same denominators | Add numerators, keep the denominator | Adding denominators means going back to the second stage |
| Why convert | The denominator is a unit and units must match | Answering “because we were told to” means going back to the third stage |
| 1/2 + 1/3 | 5/6 | Answering 2/5 means going back to the third stage |
| Final step | Reduce to simplest form | Not knowing means going back to the fifth stage |
09 Tutor FAQ
What if the times tables are not secure?
Restrict practice to denominators 2, 3, 4 and 6 and require written multiples; run a separate five-minute tables warm-up instead of stretching one question.
Must the LCM be used every time?
Yes. Any common denominator gives the same value but larger numbers and more reduction errors; only accept the product when the denominators are coprime.
Should mixed numbers become improper first?
For addition and subtraction, keeping whole numbers and fractions apart is faster; multiplication and division require improper fractions. P4 only needs the additive case.
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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.