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Focused preparation · Year 9 numeracy

Keep the equation balanced.

Solve linear equations with brackets or an unknown on both sides. Follow worked examples, then try twenty questions with gradually less help.

This is one algebra foundation. It is not an official NAPLAN paper, complete numeracy programme, tailored test or score estimate.

Choose this learning goalBrowse Year 9 mathematics

The lesson and practice open from a saved Year 9 equations goal with current learning access.

See both sides change together

MoveLeft=Right
Start5x − 7=2x + 11
Subtract 2x on both sides3x − 7=11
Add 7 on both sides3x=18
Divide both sides by 3x=6
The same operation reaches both sides. Check x = 6 in the original: each side equals 23.

How you learn it

  1. Diagnose. Four short checks point to earlier ideas to revisit.
  2. I do. Follow two worked examples and their substitution checks.
  3. We do. Solve five guided equations with three prompts each.
  4. You do. Try five with two prompts, then ten independently.
  5. Revisit. Return after 3, 7 and 14 days to test the method again.

Learner and full teaching explanations use the same tasks. Four A4 student and tutor print editions use the same answers and equality diagrams.

Your route in the learning tree

The target skill and its 29 authored prerequisites form one saved route. Earlier lessons remain available for review.

View all 30 lessons in the route
  1. Earlier foundationCounts forwards and backwards to 20Kindergarten
  2. Earlier foundationReads and writes numerals to 10Kindergarten
  3. Earlier foundationCompares two groups to say which has more or fewerKindergarten
  4. Earlier foundationCounts to 100 by ones and tensYears 1–2
  5. Earlier foundationCombines and separates small groups to model adding and taking awayKindergarten
  6. Earlier foundationSkip counts by 2s, 5s and 10sYears 1–2
  7. Earlier foundationRepresents two-digit numbers as tens and onesYears 1–2
  8. Earlier foundationPlaces numbers up to 100 on a number lineYears 1–2
  9. Earlier foundationReads, writes and orders numbers to 1000Years 1–2
  10. Earlier foundationRecalls addition facts to 20Years 1–2
  11. Earlier foundationRecalls the related subtraction facts to 20Years 1–2
  12. Earlier foundationAdds two-digit numbers with and without regroupingYears 1–2
  13. Earlier foundationRecalls multiplication facts for 2s, 5s and 10sYears 3–4
  14. Earlier foundationSubtracts two-digit numbers with and without regroupingYears 1–2
  15. Earlier foundationRecalls multiplication facts to 10 × 10Years 3–4
  16. Earlier foundationModels division as equal sharing and groupingYears 3–4
  17. Earlier foundationUses fact families to link multiplication and divisionYears 3–4
  18. Earlier foundationMultiplies two- and three-digit numbers by a one-digit numberYears 3–4
  19. Earlier foundationOrders, adds and subtracts positive and negative integersYears 7–8
  20. Earlier foundationDescribes number patterns and writes the ruleYears 7–8
  21. Earlier foundationDivides two- and three-digit numbers by a one-digit number, with remaindersYears 3–4
  22. Earlier foundationApplies the order of operations to whole-number calculationsYears 7–8
  23. Earlier foundationMultiplies and divides integers, including with the order of operationsYears 7–8
  24. Earlier foundationUses algebraic notation with pronumeralsYears 7–8
  25. Earlier foundationSimplifies algebraic expressions by collecting like termsYears 7–8
  26. Earlier foundationSolves one-step linear equationsYears 7–8
  27. Earlier foundationExpands expressions with brackets using the distributive lawYears 7–8
  28. Earlier foundationSolves two-step linear equations, including with bracketsYears 7–8
  29. Earlier foundationExpands and simplifies algebraic expressions using the distributive lawYears 9–10
  30. Target conceptSolves linear equations of up to 3 steps, including pronumerals on both sides and grouping symbolsYears 9–10

What this covers

ACARA’s Year 9 numeracy proficiency descriptions include solving linear equations algebraically. This foundation develops the mapped NSW Stage 5 Core equations skill; it does not stand in for the other numeracy strands.

The 2026 Year 9 Numeracy assessment has 48 items across three tailored testlets and a 65-minute limit. It begins with a short non-calculator section before calculator-allowed work.

Algebra has a 10–20% target range across the full test. These twenty untimed practice questions do not copy that design.

Sources: 2026 assessment framework, NAPLAN proficiency descriptions, what is in the tests and NSW Stage 5 Mathematics (checked 5 October 2026). TutorForAll is not endorsed by the assessment provider.