About this worksheet

This free Year 8 ordering rational and irrational numbers worksheet is written for the Western Australian curriculum and mapped to SCSA content description WA8MNAUN2. It targets one skill so students can practise until it sticks: by the end, students can say “I can locate, order and compare rational and irrational numbers on a number line using , ≤ and ≥.”

What’s inside

• Key idea box – a short explanation with worked examples to read before starting.
• A · Fluency (16 questions) – quick practice to build accuracy.
• B · Core (10 questions) – worded problems set in everyday Australian contexts.
• C · Reasoning (4 questions) – explain, justify and spot the error.
• D · Challenge (4 questions) – harder multi-step and problem-solving questions for students ready to stretch.
• Separate marking key – every answer with working, plus mark allocations and marking criteria for reasoning questions.

Skills covered

• Placing fractions, negatives and square roots on a number line
• Ordering mixed rational and irrational numbers
• Using <, >, ≤ and ≥ to compare and list integer solutions

How to use this worksheet

Start with the Key idea box, then complete Section A (use a calculator only where a question says so). Most students should attempt Sections B and C; Section D suits students aiming for the top of the class or preparing for accelerated or extension maths. The worksheet is marked out of 58, and the score box on the last page helps students see which section needs more practice.

Common mistakes to watch for

• Thinking −4.5 is larger than −4 because 4.5 > 4
• Estimating square roots badly, e.g. √20 ≈ 10
• Confusing ≤ with <
• Comparing fractions and decimals without converting

Where this fits in the WA Year 8 sequence

Ordering Rational and Irrational Numbers sits in the Understanding number sub-strand of Number and algebra. It is one of a set of short, single-skill EduLift worksheets that split each Year 8 content description into sub-skills. Use the previous and next links to work through the sequence in order.

Common errors we see in tutoring

• Thinking −4.5 is larger than −4 because 4.5 > 4
• Estimating square roots badly, e.g. √20 ≈ 10
• Confusing ≤ with <
• Comparing fractions and decimals without converting