Here is a quick one to puzzle over. Aoife eats 1/4 of a pizza and Conor eats 1/3 of the same pizza. Someone says they ate 2/7 of it together. Is that right?
Have a think: can the bottom numbers just be added together like that?
Take three hands-up answers, not open call-outs. Don't confirm or correct yet — let the doubt sit. The 2/7 claim is the misconception this whole lesson dismantles, so resist explaining; just gather a couple of gut reactions and move on.
The fraction strips show three calculations. Watch how each fraction is renamed so the parts are the same size before we add or subtract. Notice what size both strips have to become each time.
Common denominator is the make-or-break move: name it aloud every time before adding or subtracting.
1/4 + 1/3: strips are different sizes, so we can't add as they are. Point back to why 2/7 was wrong. Twelfths is the smallest size fitting both quarters and thirds: quarter becomes 3/12, third becomes 4/12, together 7/12.
5/6 - 1/2: only the half needs renaming, since 6 already works for both. Renamed to 3/6, then 5/6 - 3/6 = 2/6. Stress the tidy-up: 2/6 is correct but 1/3 is tidier.
3/4 - 2/3: both become twelfths, 9/12 and 8/12, difference 1/12. Ask: does this need simplifying? No, 1/12 is already simplest.
Today we work through three problems together on the board, one at a time: first 2/5 + 3/10, then 1/2 + 1/4, then 7/8 minus 3/4. For each one we clear the strips, lay both fractions on them as they start, rename them to the same size, then combine and check before moving to the next.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud. The strips start blank. Clear the shading after each problem and re-shade for the next pair, so the same four strips carry all three in turn.
Listen for pupils who try to add the bottom numbers — send them straight back to the strips so the size mismatch is visible.
In your maths copy, rewrite each sum or difference with a common denominator, then write the answer and simplify it. Circle the simplest form.
Work these four:
Walk the room glancing at the renaming line and the circled answer — this is whole-class copybook practice, not marking. Watch for pupils who skip straight to the answer without showing the common-denominator step.
Today's challenge: for each pair, one pupil works at the board while the rest of the class watches and agrees the renaming aloud first. The pupil shades the answer in the common-denominator strips, then the class confirms before they press Check, which checks the final shaded answer.
These are the practice questions — pupils take turns at the board and the class confirms each answer before moving on. Keep the board work brisk rather than over-explaining.
What is the quickest way to find a common denominator for two fractions? When does only one fraction need renaming, and when do both?
Listen for pupils noticing that when one denominator divides into the other (like 6 and 3, or 8 and 4) only the smaller-bottomed fraction needs renaming. Revoice a strong answer: 'so if one bottom number fits into the other, that bigger one is already the common denominator.' Head off the lingering 'just add the bottoms' idea one last time if it surfaces.
Next we add and subtract mixed numbers — whole numbers and fractions together, like 2½ + 1¾ — and meet the trick of renaming across a whole.
Tie the day's work back to the opening pizza: Aoife and Conor ate 7/12 of it together, not 2/7. The renaming habit is the bridge into mixed numbers next lesson.
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