Curriculum · Foundations
Foundations
Arithmetic fluency, proportional reasoning, and estimation — rebuilt as thinking tools rather than procedures. The bedrock of every contest.
Number Fluency
Arithmetic as Structure
Computation reorganized around structure: regrouping, factoring, distributivity.
- Compute by restructuring, not grinding
- Exploit the distributive law
- Recognize friendly numbers
Mental Math & Clever Computation
Contest-speed computation: difference of squares, pairing, telescoping sums.
- Square and multiply mentally
- Pair terms in long sums
- Choose the fastest route
prerequisite: arithmetic-fluency
Estimation & Number Sense
Bounding, approximation, and the art of knowing roughly — before knowing exactly.
- Bound quantities above and below
- Estimate products, quotients, and roots
- Use estimates to eliminate answer choices
prerequisite: arithmetic-fluency
Proportional Reasoning
Fractions, Deeply
Fractions as division, as ratio, as operator — and the arithmetic that follows.
- Interpret fractions three ways
- Compare fractions without common denominators
- Handle complex fractions
Ratios & Proportional Reasoning
The ratio toolbox: scaling, sharing, mixing, and the part-to-whole shift that unlocks contest problems.
- Translate between ratios and fractions of a whole
- Scale ratios through shared quantities
- Solve mixture and rate problems by ratio
prerequisite: fractions-core
Percents, Rates & Averages
Percent change, successive discounts, weighted averages, and rate problems.
- Compose percent changes multiplicatively
- Set up rate equations
- Use weighted averages
prerequisite: ratios-proportional-reasoning