Here are two fractions: 3/4 and 5/6. Which one is bigger?
This one is trickier than comparing 3/4 and 1/4. When the bottom numbers are different, your gut can point the wrong way. What could we do to settle it for certain?
Take three hands-up answers, not open call-outs, and don't confirm yet — leave the question genuinely open. Listen for whether pupils reach for a rule or just a hunch; you'll return to this exact pair in the model.
Each pair shows two strips of the same length, cut into different numbers of pieces. Watch how we decide which fraction is bigger — sometimes by matching the pieces, sometimes with a quicker check. See if you can predict the winner before it appears.
3/4 vs 5/6 — the opening pair. Stress both strips start the same length. Common denominator twelfths: 3/4 becomes 9/12, 5/6 becomes 10/12, so 10 beats 9 and 5/6 is bigger. Name it: common-denominator strategy.
E2/3 vs 3/5 — same idea. Ask them to predict the shared bottom number before you reveal: fifteenths. 2/3 becomes 10/15, 3/5 becomes 9/15, so 2/3 is bigger. Point out the shaded amount never changed, only the pieces.
2/7 vs 5/9 — the key one, pause here. Ask 'do we even need a common denominator?' 2/7 fills under half, 5/9 over half, so 5/9 wins with no calculation. Benchmark-to-a-half: works when the two land on different sides of halfway.
4/9 vs 4/11 — longest beat, the one pupils invert. Same top number, so ask which pieces are bigger, ninths or elevenths. Predict first, then reveal: ninths are bigger, so 4/9 wins. Say the rule twice — a bigger bottom makes smaller slices, so with matching tops the smaller bottom wins. Common-numerator strategy.
The board has two twelfths strips, an eighths strip and a fifths strip, all blank to start. We build each of these pairs together, one at a time: 1/2 versus 1/4, then 3/8 versus 1/2, then 3/4 versus 3/5, then 3/4 versus 2/3. Each pair asks a bit more of us than the last. Before we shade each one, predict which strategy fits best: common denominator, benchmark to a half, or common numerator (same top number). When a fraction has no strip of its own, build it on a twelfths strip: six twelfths is one half, three twelfths is one quarter, nine twelfths is three quarters and eight twelfths is two thirds.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
Four strips stay on screen all through: two twelfths, one eighths, one fifths. Clear the shading between pairs, then hand the mouse to a pupil to shade the next one. Order builds deliberately: 1/2 vs 1/4 is an easy common-numerator warm-up; 3/8 vs 1/2 invites the benchmark; 3/4 vs 3/5 is a common-numerator call, same top number; 3/4 vs 2/3 needs twelfths. For each pair, ask a pupil to name the strategy before shading, then a second pupil to shade and read the comparison line. Revoice a strong answer: so once the bottoms match, we just count the shaded slices.
In your maths copy, work each comparison and put the correct sign between the two fractions. For each pair, choose the smartest strategy — sometimes you re-write over a common bottom number, and sometimes you spot a quicker route.
Write these three pairs, one under the other:
The first two pairs are easiest over a common bottom number. The last pair, 4/9 and 4/11, has the same top number, so you do not need to convert — just compare the slice sizes. Circle the bigger fraction in each pair.
Walk the room glancing for whether pupils pick a strategy that fits each pair — this is whole-class copybook practice, not marking. On 4/9 vs 4/11, praise pupils who use the common-numerator shortcut rather than grinding out twelfths.
Today we work through these comparisons: 5/6 versus 7/8, then 3/10 versus 2/5, then the stretch 7/12 versus 5/8. Each one is a step trickier than the last. Predict the bigger fraction before we shade and check.
These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
5/6 vs 7/8 needs twenty-fourths; 3/10 vs 2/5 rewards spotting that fifths become tenths; 7/12 vs 5/8 is the key one, common ground twenty-fourths. Before grinding out a common denominator, prompt: would a benchmark to a half decide it faster? Three pairs across eight minutes gives each one a full predict-shade-confirm cycle.
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