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Unit A0: Arithmetic Readiness and Repair

Adaptive support layer with complete instruction for students who need numerical repair. What must be dependable about numbers before symbols can carry meaning?

Prologue - Making quantity dependable

The 10-lesson path

The learner stabilizes numerical meaning: signed quantities, multiplicative structure, fractions, rates, units, powers, and roots. Diagnostic routing allows a student to enter only the pages needed and then return to the main Algebra spine.

Governing question

What must be dependable about numbers before symbols can carry meaning?

Adaptive support layer with complete instruction for students who need numerical repair.

Mastery design

Know when to continue

A ten-domain diagnostic routes each missed strand to one repair lesson followed by a short return check.

Unit outcomes
  1. Interpret signed numbers as position, direction, and change.
  2. Compute with whole numbers, fractions, decimals, and percentages while estimating plausibility.
  3. Use factors, multiples, ratios, rates, and units structurally.
  4. Interpret powers and roots and use scientific notation.
  5. Recognize when arithmetic output is unreasonable or dimensionally impossible.
Core sequence

Lessons

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

  1. 01Number lines and signed quantitiesInterpret sign as position, direction, and change; compare signed numbers and rewrite subtraction as addition of an opposite.
  2. 02Whole-number operations and estimationUse place value, the four operations, rounding, and order of magnitude to judge whether exact output is plausible.
  3. 03Factors, primes, GCF, and LCMDecompose whole numbers multiplicatively and distinguish common-factor questions from common-multiple questions.
  4. 04Fractions as numbersInterpret a fraction as aa number, quotient, ratio, and operator and locate it on a number line.
  5. 05Multiplying and dividing fractionsInterpret fraction multiplication as scaling and division as measuring how many groups fit.
  6. 06Adding, subtracting, and complex fractionsUse common-sized parts to combine fractions and simplify expressions containing fractions within fractions.
  7. 07Fractions, decimals, and percentsTranslate among equivalent representations and choose the form most useful for a question.
  8. 08Ratios, rates, proportions, and percent changeDistinguish ratios from rates, build equivalent comparisons, and interpret percent increase or decrease.
  9. 09Units and dimensional reasoningTreat units as multiplicative factors that constrain valid operations and conversions.
  10. 10Powers, roots, and scientific notationInterpret repeated multiplication, inverse power questions, and orders of magnitude.

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 taskCompare several phone, grocery, or subscription plans using estimation, rates, percentages, units, and exact calculations.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.