Master core mathematical concepts through our interactive Socratic curriculum.
Search Intent Match
This hub is for students who need free multiplyfractions practice that shows the reasoning, not just the answer. It groups 30 browser-based missions around finding a fraction of a fraction or scaling by a fractional factor, aligned with 4.NF.B.4.
The companion guide explains it as: Multiply a fraction by a whole number, e.g., understand 3 × (1/4) as 3 copies of 1/4.
Practice Goals
Common Mistakes
Use Cases
Use after students understand unit fractions and area models.
Ask whether the factor is less than 1 and what that means for size.
Complete one mission, then say what changed, what stayed the same, and why the final answer makes sense.
Indexable Practice
Everything you need to know about the Socratic experience.
There are 30 missions in this topic — 10 Seedling (entry-level), 10 Explorer (core), and 10 Challenger (stretch). Each mission has 3 Socratic steps with adaptive hints.
This topic is aligned with CCSS 4.NF.B.4. Open the topic guide for the standard's full text and a step-by-step breakdown of the cognitive sub-skills.
Start with Seedling missions to anchor the visual model, then move to Explorer for the core abstraction, and tackle Challenger only when Explorer is flawless. Difficulty badges on each card show this progression.
Grade 4 is when arithmetic becomes *strategic*. We teach the area model first so the standard algorithm feels like a shortcut, not a magic trick.
We use the rectangle test: every rectangle a child can build with N tiles is a factor pair. Primes are the numbers that only fit in 1×N strips.
Socratic teaching answers a question with a better question. Instead of "the answer is 12", the system asks "if you had 3 groups of 4, how could you skip-count?" The goal is to externalize the learner's reasoning so they hear themselves think. Every Inquiry AI hint follows this pattern: nudge → reframe → analogy → only then a worked example, in that order.
Pure discovery is inefficient — kids hit a wall and quit. Guided Discovery scaffolds the path: a careful sequence of questions, models, and adaptive hints leads the learner toward the insight without revealing it. Inquiry AI's hint system fires automatically after ~15s of hesitation or on the first mistake, escalating from a Socratic nudge to a worked example only when needed. Mistakes are diagnosed via "misconception keys" so the hint matches the actual wrong-thinking pattern.
