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BetterGrades Algebra · Unit A1 · Unit Hub

Unit A1: Quantities, Variables, and Mathematical Objects

Establish what algebra describes before asking students to manipulate it. How can symbols name quantities and relationships without erasing their meaning?

Act I - Giving general names to quantities

The 8-lesson path

Concrete quantities become tables, graphs, verbal rules, expressions, equations, and inequalities. Students learn what kind of object each notation represents and how substitution preserves structure.

Governing question

How can symbols name quantities and relationships without erasing their meaning?

Establish what algebra describes before asking students to manipulate it.

Mastery design

Know when to continue

Students classify mathematical objects, translate representations, and evaluate formulas with signed inputs and units.

Unit outcomes
  1. Identify changing, fixed, unknown, and parameter quantities.
  2. Translate among verbal, numerical, graphical, and symbolic representations.
  3. Distinguish expressions, equations, and inequalities.
  4. Parse terms, factors, coefficients, and grouping structure.
  5. Substitute and evaluate while preserving units and parentheses.
Core sequence

Lessons

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

  1. 01Variables and changing quantitiesDistinguish unknowns, changing quantities, parameters, constants, and labels.
  2. 02Expressions, equations, and inequalitiesClassify symbolic objects by whether they name a value or make a true-or-false claim.
  3. 03Terms, factors, coefficients, and structureRead nested sums and products without flattening them incorrectly.
  4. 04Substitution and evaluationReplace variables or subexpressions with equal-valued expressions while preserving grouping.
  5. 05Grouping and order of operationsInterpret grouping symbols as explicit structure and precedence as a shared reading convention.
  6. 06Properties of real-number operationsUse commutative, associative, identity, inverse, and distributive properties to justify rewrites.
  7. 07Equivalent expressions and like termsRecognize rewrites that preserve value for every allowed input and combine only structurally alike terms.
  8. 08Formulas, units, and mathematical communicationRead formulas as reusable relationships and communicate transformations unambiguously.

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.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.