PA / Foundation
Prealgebra
Number Meadow
Build a foundation in number structure, algebra, geometry and mathematical reasoning.
Preparation: Whole-number arithmetic and a willingness to explain your thinking.
Current coverage: 15 topic levels, from signed numbers to a problem-solving toolkit.
LEVEL 1 · DIFFICULTY 1/5 within this course
Arithmetic & Number Structure
Use signed numbers, operation structure and reciprocals to explain calculations.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 147 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 2 · DIFFICULTY 1/5 within this course
Powers & Exponent Structure
Reason about repeated multiplication, exponent laws and reciprocal powers.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 149 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 3 · DIFFICULTY 1/5 within this course
Number Theory Foundations
Use divisibility and prime structure to solve factor and multiple problems.
Explore 6 knowledge islands
Choose an island to read its lesson.
- MINI QUEST 3.1Divisibility & RemaindersRead the lesson
- MINI QUEST 3.2Prime & Composite NumbersRead the lesson
- MINI QUEST 3.3Prime FactorizationRead the lesson
- MINI QUEST 3.4Greatest Common DivisorRead the lesson
- MINI QUEST 3.5Least Common MultipleRead the lesson
- MINI QUEST 3.6Factor–Multiple Problem SolvingRead the lesson
6 stages · 48 library problems · 298 checked variations · 2 × 12 assessment questions
Read the lessons →LEVEL 4 · DIFFICULTY 2/5 within this course
Fractions & Equal Shares
Compare, combine and reinterpret quantities measured in equal parts.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 130 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 5 · DIFFICULTY 2/5 within this course
Expressions, Equations & Inequalities
Represent unknown quantities and justify each transformation.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 150 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 6 · DIFFICULTY 2/5 within this course
Decimals & Precision
Connect place value, fractions, rounding and repeating patterns.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 150 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 7 · DIFFICULTY 3/5 within this course
Ratios, Units & Rates
Compare related quantities and coordinate changes across units.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 150 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 8 · DIFFICULTY 3/5 within this course
Percents & Changing Baselines
Find parts, recover wholes and reason about successive changes.
Explore 3 knowledge islands
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3 stages · 24 library problems · 149 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 9 · DIFFICULTY 3/5 within this course
Counting & Probability
Describe a sample space and count possibilities without omission or duplication.
Explore 3 knowledge islands
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3 stages · 24 library problems · 148 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 10 · DIFFICULTY 4/5 within this course
Square Roots & Exact Values
Estimate roots, simplify radical structure and keep exact quantities.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 148 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 11 · DIFFICULTY 4/5 within this course
Angles & Geometric Relationships
Use stated geometric relationships to justify angle calculations.
Explore 3 knowledge islands
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3 stages · 24 library problems · 150 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 12 · DIFFICULTY 4/5 within this course
Perimeter, Area & Circles
Choose appropriate measurements and decompose composite regions.
Explore 3 knowledge islands
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3 stages · 24 library problems · 150 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 13 · DIFFICULTY 4/5 within this course
Right Triangles & Quadrilaterals
Connect side lengths, angle structure and shape properties.
Explore 3 knowledge islands
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3 stages · 24 library problems · 138 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 14 · DIFFICULTY 5/5 within this course
Data & Statistical Reasoning
Summarize actual observations, read displays and examine what summaries omit.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 149 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 15 · DIFFICULTY 5/5 within this course
Problem-Solving Workshop
Choose, explain and check strategies across unfamiliar contexts.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 150 checked variations · 2 × 6 assessment questions
Read the lessons →Progress earned through practice
Earn two independent practice stars and one application star, then complete the library skill check for that stage. The check covers the stage’s library prompts, so changing numbers alone is not enough. Hints help you learn; your existing stars and earned rewards stay yours. Clear every stage to clear a level.
Every stage includes an explanation, two worked examples and eight library practice problems, plus checked variations with changing numbers and applications. Each level also has a separate unit test and a later review form. Parents see actual attempts, hint use and results.
These are independently authored core-skills courses, with the current scope listed for each course. They do not reproduce complete textbook contents. Difficulty describes the teaching sequence within each course; course preparation matters when comparing subjects. This site is not affiliated with or endorsed by AoPS. Results reflect these exercises and are not standardized scores. Content release math-courses-2026.09.27-university-guides-v2.