shreeman-iyer/llm_multiplication_training

Triple-Tier Multiplication Curriculum (Area Model)

A structured curriculum for teaching multiplication to small language models. This dataset moves from rote memorization to logical decomposition.

Curriculum Structure

1. Tier 1: Basic Tables (1-100) - Sequential and shuffled pairs for results up to 1000 to establish "Instant Recall" weights.
2. Tier 2: Sign Logic - Explicitly teaches the rules of arithmetic signs: $(+) \times (+)$, $(-) \times (+)$, and $(-) \times (-)$.
3. Tier 3: Distributive Property (Large) - Uses the "Area Model" to split 4-digit by 2-digit problems into manageable partial products.

Why this works

By splitting a problem like $450 \times 12$ into $(450 \times 10) + (450 \times 2)$, the model avoids "Dimensionality Collapse" and learns a scalable algorithm for any number size.