About this worksheet

This free Year 7 number laws with variables worksheet is written for the Western Australian curriculum and mapped to SCSA content description WA7MNAA5. It targets one skill so students can practise until it sticks: by the end, students can say “I can use the commutative and associative laws with variables to rewrite and simplify expressions, and test whether statements are true.”

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

• Applying commutative and associative laws to variables
• Simplifying products and like terms
• Testing whether statements are always true

How to use this worksheet

Start with the Key idea box, then complete Section A without a calculator. 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 57, and the score box on the last page helps students see which section needs more practice.

Common mistakes to watch for

• Assuming subtraction or division is commutative
• Combining unlike terms (3a + 2b = 5ab)
• Dropping a variable when simplifying
• Testing only one value

Where this fits in the WA Year 7 sequence

Number Laws with Variables sits in the Algebraic techniques sub-strand of Number and algebra. It is one of a set of short, single-skill EduLift worksheets that split each Year 7 content description into sub-skills. Use the previous and next links to work through the sequence in order.

Common errors we see in tutoring

• Assuming subtraction or division is commutative
• Combining unlike terms (3a + 2b = 5ab)
• Dropping a variable when simplifying
• Testing only one value