L8 · Ordering clinic: mixed comparisons

Learning goal

“I can order long mixed lists of fractions, decimals and whole numbers quickly and accurately - choosing the fastest strategy per item, and catching the standard traps: padding, repeating decimals, and conversions in disguise.”

Strategy — a chosen plan of attack: benchmarks for rough sorting, conversion for exact order. Picking the strategy is part of the skill.

Trap pair — two numbers designed to fool a shortcut: 0.8 and 5/6 look alike but are not equal.

Disguised number — a value written in an unexpected form, like 6/5 hiding the decimal 1.2.

Worked example

Order from least to greatest: 0.4, 5/8, 1.1, 0.95, 3/5. Step 1 (zones): Benchmarks 1/2 and 1 split the list. Below 1/2: 0.4. Between 1/2 and 1: 5/8, 0.95, 3/5. Above 1: 1.1. Step 2 (convert inside the busy zone): 5/8 = 0.625; 3/5 = 0.6. Zone order: 0.6 (3/5) < 0.625 (5/8) < 0.95. Step 3 (assemble): 0.4 < 3/5 < 5/8 < 0.95 < 1.1. Say it plainly: never convert all five numbers. Zones first - most numbers place themselves - then spend your conversion work only where numbers are crowded.

Check yourself — explain it

Why not just convert everything to decimals immediately?

Paired problem — example still visible

Order from least to greatest: 0.3, 2/5, 0.55, 4/5 -> 0.3 < 2/5 < 0.55 < 4/5

Faded completion — last step is yours

"Order: 1.4, 7/5, 1.35. First convert: 7/5 = 1.4 exactly - a tie, two forms of one number. So the order is 1.35 < ___ = ___" -> 1.4; 7/5 (ties are real answers: equal numbers share a rank)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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