Mathematics

Intermediate

50 mins

Teacher/Student led

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Learning Outcomes

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+65 XP

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Adding and Subtracting Fractions with Different Denominators

Learn to add and subtract fractions with different denominators by re-expressing them over a common denominator, then simplify your answer.

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Work It in Your Copy
5 Class Challenge
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Imagine this: I ate 1/3 of the pizza and my friend ate 1/4 of the pizza. How much of the pizza did we eat between us? Look at the two fractions: is there any easy way to add a third and a quarter together? Have a good look at the bottom numbers before anyone answers.

Teacher Notes

Take two or three hands-up answers, not open call-outs. The point you are fishing for is that the pieces are different sizes (thirds are bigger than quarters), so you cannot just add the tops. Do not resolve it yet, that is what the lesson builds to.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

The strips show three fraction sums, two added and one taken away. Look at the top two strips in each: the pieces are different sizes, then re-written so they match. The bottom strip shows what they make.

Teacher Notes

1/3 + 1/4: pieces must be the same size before we count them. Multiply the bottoms, 3 × 4 = 12, so twelfths. 1/3 becomes 4/12, 1/4 becomes 3/12, giving 7/12. Name the common denominator here.

1/2 - 1/3: re-write over sixths, 1/2 becomes 3/6 and 1/3 becomes 2/6. Ask how many sixths are left when 2/6 is taken from 3/6, take a guess before looking. Third strip is static, so cover it or ask first, then reveal 1/6.

2/5 + 3/10: the key one, give it room. We don't always multiply the bottoms. Ask why tenths is already enough, 5 fits into 10. Only 2/5 changes, becoming 4/10, and 3/10 stays, making 7/10. The later reflection depends on pupils noticing this.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Today we work through these together on the twelfths strips, re-expressing each pair over a common denominator before we combine: first 1/3 + 1/4 over twelfths, then 3/4 - 1/3 over twelfths, then the trickier 5/6 + 1/4 over twelfths, and last 1/6 + 5/12, where sixths already fit into twelfths so only one fraction changes. Say each re-expressed fraction aloud before we shade it.

Re-express, then combine

Teacher Notes

This round is for talking it through together - pupils take turns at the board and the class agrees or corrects out loud.

The strips are set to twelfths, so build 1/3 + 1/4, 3/4 - 1/3, 5/6 + 1/4 and 1/6 + 5/12 on them. On 1/6 + 5/12, twelfths already fit sixths, so only 1/6 changes, becoming 2/12, while 5/12 stays: 2/12 + 5/12 = 7/12. Ask why multiplying the two bottoms is not needed here. For each pair, ask what denominator do BOTH strips fit into? before anyone shades. On 3/4 - 1/3 the class must re-write to 9/12 - 4/12 = 5/12. On 5/6 + 1/4 the answer crosses one whole (10/12 + 3/12 = 13/12), so revoice that 13/12 is one whole and one twelfth - a good bridge to next steps.

+15 XP

4 - Work It in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, re-write each pair of fractions over a common denominator first, then add or subtract. Underline the simplified final answer on each one.

1/3 + 1/4
1/2 - 1/3
3/4 - 1/3
2/5 + 3/10

Teacher Notes

Walk the room glancing for the common-denominator step written before the answer - this is whole-class copybook practice, not marking. Watch for pupils who add the tops without re-expressing first.

+10 XP

5 - Class Challenge ~8 mins

Today we work through these unlike-fraction problems together on the board, each one a step harder: 1/2 + 1/4, then 1/3 + 1/6, then 3/4 - 1/3, then 2/3 + 1/4, and finally 5/6 - 1/2. Re-express each pair over a common denominator, work out the answer, then build it on the strips to match the target and check.

Combine the unlike fractions

Teacher Notes

These are the practice questions - pupils take turns at the board, build each answer to match the target strip, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

Look-fors as they climb: on 1/3 + 1/6 the class should spot that thirds already fit into sixths (2/6 + 1/6 = 3/6, which simplifies to 1/2). On 2/3 + 1/4 the answer 11/12 is close to one whole - ask how far off a whole it is. On 5/6 - 1/2 the strip shows the sixths result 2/6, so revoice that 2/6 simplifies to 1/3.

+15 XP

Pupil practice

Module 3 · Fractions, Decimals and Percentages Number

Lesson 36 · Adding and Subtracting Fractions with Different Denominators

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Adding and Subtracting Fractions with Different Denominators

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

3 - Try It Together ~11 mins

Re-express, then combine

4 - Work It in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Combine the unlike fractions

Unlock the full learning experience

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