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The Hero Academy · Mathematics

The Architect's Blueprint

Concrete quantities develop into numerical fluency, geometry, algebra, data analysis, and mathematical modeling. Explanations and worked methods accompany answers.

Proposed K–12 pathway · initial section available
Read & downloadView the learning sequence
The Architect's Blueprint illustrated curriculum cover

Available section · MATH-K-01

Counting and quantities

No numeral writing or independent reading is required. The learner may point, move objects, or answer orally.

  1. MATH-K-01-L01

    One object, one count

    Count a small group without skipping or counting an object twice.

    Companion activity: MATH-K-01-W01
  2. MATH-K-01-L02

    The last number tells how many

    Recognize that rearranging an unchanged group does not change its quantity.

    Companion activity: MATH-K-01-W02
  3. MATH-K-01-L03

    Numerals record quantities

    Match the numerals 0–5 to small quantities.

    Companion activity: MATH-K-01-W03

A proposed path from K through 12

The learning sequence

Levels organize increasing complexity. They are not age deadlines. Detailed standards coverage, prerequisites, and topic research remain in development beyond the starter section.

Kindergarten entry

Adult-supported observation, communication, and access adaptations; no independent reading required

  1. MATH-K-01Counting and quantitiesIntroductory section available; further strand coverage in development
  2. MATH-K-02Comparing, joining, and separatingPlanned · research and writing pending
  3. MATH-K-03Shapes and spatial relationshipsPlanned · research and writing pending
  4. MATH-K-04Measurement, sorting, and teen numbersPlanned · research and writing pending

Proposed demonstrations

  • Count and represent quantities through 20, and continue the oral sequence to 100 by ones and tens
  • Model joining and separating groups within 10, explaining a chosen strategy
  • Classify and compose familiar shapes and compare measurable attributes

These are proposed targets, not a complete assessment or verified standards checklist.

Level 1

Demonstrated prerequisite skills from level K; placement is skill-based

  1. MATH-1-01Numbers and operations to 20Planned · research and writing pending
  2. MATH-1-02Counting to 120; place value and operations within 100Planned · research and writing pending
  3. MATH-1-03Length, time, and dataPlanned · research and writing pending
  4. MATH-1-04Shapes and equal sharesPlanned · research and writing pending

Proposed demonstrations

  • Count, read, and represent numbers through 120 and explain tens and ones
  • Solve addition and subtraction situations within 20 and explain place-value strategies within 100
  • Measure lengths with repeated equal units, interpret simple data, and partition shapes into equal shares

These are proposed targets, not a complete assessment or verified standards checklist.

Level 2

Demonstrated prerequisite skills from level 1; placement is skill-based

  1. MATH-2-01Place value to 1000Planned · research and writing pending
  2. MATH-2-02Addition and subtraction strategiesPlanned · research and writing pending
  3. MATH-2-03Measurement, money, and dataPlanned · research and writing pending
  4. MATH-2-04Arrays, shapes, and equal sharesPlanned · research and writing pending

Proposed demonstrations

  • Represent and compare numbers through 1000 using hundreds, tens, and ones
  • Explain and carry out addition and subtraction strategies with place-value models
  • Solve length and money situations, interpret data, and represent arrays and equal shares

These are proposed targets, not a complete assessment or verified standards checklist.

Level 3

Demonstrated prerequisite skills from level 2; placement is skill-based

  1. MATH-3-01Multiplication and divisionPlanned · research and writing pending
  2. MATH-3-02Fractions on a number linePlanned · research and writing pending
  3. MATH-3-03Area, perimeter, and measurementPlanned · research and writing pending
  4. MATH-3-04Data and problem solvingPlanned · research and writing pending

Proposed demonstrations

  • Use equal groups and arrays to solve multiplication and division situations
  • Place and compare simple fractions on number lines with a specified whole
  • Solve area, perimeter, measurement, and data problems with labeled units

These are proposed targets, not a complete assessment or verified standards checklist.

Level 4

Demonstrated prerequisite skills from level 3; placement is skill-based

  1. MATH-4-01Multi-digit operationsPlanned · research and writing pending
  2. MATH-4-02Equivalent fractions and operationsPlanned · research and writing pending
  3. MATH-4-03Decimals and measurement conversionsPlanned · research and writing pending
  4. MATH-4-04Geometry and dataPlanned · research and writing pending

Proposed demonstrations

  • Explain multi-digit multiplication and division using place value and models
  • Generate equivalent fractions and solve supported fraction-operation problems
  • Connect decimal notation to fractions and interpret measurement, angle, and data problems

These are proposed targets, not a complete assessment or verified standards checklist.

Level 5

Demonstrated prerequisite skills from level 4; placement is skill-based

  1. MATH-5-01Place value and decimal operationsPlanned · research and writing pending
  2. MATH-5-02Fraction addition, subtraction, multiplication, and introductory divisionPlanned · research and writing pending
  3. MATH-5-03Volume and measurementPlanned · research and writing pending
  4. MATH-5-04Coordinates, patterns, and dataPlanned · research and writing pending

Proposed demonstrations

  • Use place value to explain whole-number and decimal operations
  • Add and subtract unlike-denominator fractions, multiply fractions, and model introductory division cases
  • Calculate volumes of rectangular prisms and plot points to describe patterns

These are proposed targets, not a complete assessment or verified standards checklist.

Level 6

Demonstrated prerequisite skills from level 5; placement is skill-based

  1. MATH-6-01Ratios, rates, and percentPlanned · research and writing pending
  2. MATH-6-02Rational-number operations, fraction division, and expressionsPlanned · research and writing pending
  3. MATH-6-03Equations, inequalities, and geometryPlanned · research and writing pending
  4. MATH-6-04Statistical questions and distributionsPlanned · research and writing pending

Proposed demonstrations

  • Represent ratios, unit rates, and percentages and solve proportional-context problems
  • Interpret signed quantities, divide fractions, and solve simple equations or inequalities
  • Calculate geometric measures and describe a statistical distribution using context

These are proposed targets, not a complete assessment or verified standards checklist.

Level 7

Demonstrated prerequisite skills from level 6; placement is skill-based

  1. MATH-7-01Proportional relationshipsPlanned · research and writing pending
  2. MATH-7-02Signed-number operations and equationsPlanned · research and writing pending
  3. MATH-7-03Scale, circles, and three-dimensional geometryPlanned · research and writing pending
  4. MATH-7-04Probability and samplingPlanned · research and writing pending

Proposed demonstrations

  • Solve proportional problems and explain scale factors and percent changes
  • Compute with signed rational numbers and justify transformations of equations
  • Solve circle and solid-measurement problems and evaluate probability and sample-based claims

These are proposed targets, not a complete assessment or verified standards checklist.

Level 8

Demonstrated prerequisite skills from level 7; placement is skill-based

  1. MATH-8-01Linear equations and systemsPlanned · research and writing pending
  2. MATH-8-02Functions and transformationsPlanned · research and writing pending
  3. MATH-8-03Exponents, roots, and Pythagorean relationshipsPlanned · research and writing pending
  4. MATH-8-04Bivariate data and modelingPlanned · research and writing pending

Proposed demonstrations

  • Solve linear equations and systems and interpret their solutions in context
  • Compare functions and describe transformations using graphs, tables, and expressions
  • Apply exponent rules and Pythagorean relationships and interpret bivariate data

These are proposed targets, not a complete assessment or verified standards checklist.

Level 9

Demonstrated prerequisite skills from level 8; placement is skill-based

  1. MATH-9-01Algebra I foundations and linear modelsPlanned · research and writing pending
  2. MATH-9-02Systems and inequalitiesPlanned · research and writing pending
  3. MATH-9-03Polynomials, factoring, and quadraticsPlanned · research and writing pending
  4. MATH-9-04Exponential models and dataPlanned · research and writing pending

Proposed demonstrations

  • Build and interpret linear and exponential models with stated assumptions
  • Solve systems and inequalities and check candidate solutions in their original context
  • Factor suitable polynomials and connect quadratic expressions, graphs, and roots

These are proposed targets, not a complete assessment or verified standards checklist.

Level 10

Demonstrated prerequisite skills from level 9; placement is skill-based

  1. MATH-10-01Geometry, constructions, and proofPlanned · research and writing pending
  2. MATH-10-02Congruence and similarityPlanned · research and writing pending
  3. MATH-10-03Right-triangle trigonometry and circlesPlanned · research and writing pending
  4. MATH-10-04Coordinate geometry, area, and volumePlanned · research and writing pending

Proposed demonstrations

  • Construct and justify geometric arguments from stated definitions and premises
  • Use congruence and similarity to determine unknown measures
  • Apply right-triangle trigonometry and coordinate methods to circles, area, and volume

These are proposed targets, not a complete assessment or verified standards checklist.

Level 11

Demonstrated prerequisite skills from level 10; placement is skill-based

  1. MATH-11-01Algebra II polynomial and rational functionsPlanned · research and writing pending
  2. MATH-11-02Exponential and logarithmic functionsPlanned · research and writing pending
  3. MATH-11-03Trigonometric functions and identitiesPlanned · research and writing pending
  4. MATH-11-04Sequences, probability, and statisticsPlanned · research and writing pending

Proposed demonstrations

  • Analyze polynomial, rational, exponential, and logarithmic functions with domains stated
  • Model periodic behavior with trigonometric functions and explain selected identities
  • Represent sequences and assess probability and statistical claims with assumptions stated

These are proposed targets, not a complete assessment or verified standards checklist.

Level 12

Demonstrated prerequisite skills from level 11; placement is skill-based

  1. MATH-12-01Precalculus and mathematical modelingPlanned · research and writing pending
  2. MATH-12-02Statistical inference and financial mathematicsPlanned · research and writing pending
  3. MATH-12-03Calculus extension: limits and derivativesPlanned · research and writing pending
  4. MATH-12-04Calculus extension: integrals and capstonePlanned · research and writing pending

Proposed demonstrations

  • Compare mathematical models and justify choices using data and assumptions
  • Analyze financial scenarios and statistical inferences with uncertainty and limitations stated
  • For the optional calculus extension, interpret limits, derivatives, and integrals in connected problems

These are proposed targets, not a complete assessment or verified standards checklist.

Subject strands inside this book

  • Number Sense and Place Value
  • Arithmetic and Operations
  • Fractions, Decimals, and Percentages
  • Ratios, Rates, and Proportions
  • Measurement and Units
  • Patterns and Pre-Algebra
  • Algebra
  • Geometry
  • Trigonometry
  • Statistics and Probability
  • Precalculus and Calculus
  • Mathematical Reasoning and Problem Solving
  • Practical and Financial Mathematics

Evidence and scope

Selected introductory work toward K.CC.3–5 with quantities 0–5. Numeral recognition is practiced; independent numeral writing is not assessed. This section does not complete those standards.

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