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BetterGrades Algebra · Unit A2 · Unit Hub

Unit A2: Expressions, Equality, and Linear Equations

Build the central equivalence engine of elementary algebra. How can an equation change form without changing its solutions?

Act II - Preserving truth while changing form

The 10-lesson path

Students first test solutions, then use inverse operations and simplification to construct equivalent equations. The unit ends with strategy selection and one-variable modeling.

Governing question

How can an equation change form without changing its solutions?

Build the central equivalence engine of elementary algebra.

Mastery design

Know when to continue

Mixed equations without method labels; students must show an equivalence-preserving chain and verify the result.

Unit outcomes
  1. Define a solution and solution set.
  2. Construct equivalent linear equations using legal operations.
  3. Solve equations containing parentheses, fractions, decimals, and variables on both sides.
  4. Recognize identities and contradictions.
  5. Build and check one-variable models.
Core sequence

Lessons

Move in order when this material is new; use prerequisites and repair links when entering mid-unit.

  1. 01Solutions, solution sets, and checkingDetermine whether candidate values make an equation true and distinguish a proposed answer from a verified solution.
  2. 02Addition and subtraction equationsUse additive inverses to isolate a variable while preserving equality.
  3. 03Multiplication and division equationsUse reciprocals and equal scaling to isolate aa variable, with explicit zero restrictions.
  4. 04Simplifying before solvingCombine like terms and distribute before isolating the variable.
  5. 05Multistep linear equationsUndo layered operations in an order determined by structure.
  6. 06Equations with fractions and decimalsSolve equations with rational coefficients directly or by clearing denominators strategically.
  7. 07Variables on both sidesCollect variable terms and constants strategically and interpret the resulting coefficient.
  8. 08One solution, no solution, or infinitely manyRecognize identities and contradictions produced by simplification.
  9. 09Translating one-variable modelsDefine a variable and build a linear equation from a verbal or diagrammatic relationship.
  10. 10Linear equation strategy studioClassify structure, choose a first move, and defend the solution route.

Practice around the path

Review, mixed practice, mastery, and investigation

Every route contains a fixed set of concrete questions, with detailed solutions available after an attempt.

ReviewCumulative reviewRevisit this unit with prior-unit retrieval.PracticeMixed practiceClassify the structure before choosing a method.MasteryMastery checkUse the supplied grading and cumulative-share contract.InvestigationPerformance taskReconstruct an original quantity after a sequence of fees, discounts, or changes.Response guideMastery response guideAttempt-gated rubric support; no invented canonical answers.

Source & rights

Original storyboard, rights-separated references.

Public page content comes from the BetterGrades Algebra editorial storyboard supplied by the owner. Reference books named in provenance remain separate and are not copied into the application.