Thinking Summary · 1
MasteredVisual Logic: 0 of 1 parts shaded.
[Discovery] Shade 2/7 on a fraction bar — this is one copy.
1
Active StepWelcome to "Asteroid Quarter Stack", a 4th Grade Multiplyfractions mission at the Explorer (core) level, staged in our space exploration scenario. The mission opens with a hands-on prompt: "Shade 2/7 on a fraction bar — this is one copy." You'll work with the numbers 2, 7, 9 and arrive at a final answer of 7 across 3 guided steps.
Behind the space exploration story, this lesson is really about multiplyfractions aligned to CCSS 4.NF.B.4. Multiply a fraction by a whole number, e. The key strategy this mission asks you to internalise: Top: 9 × 2, bottom: 7.
A general pattern to watch for in 4th Grade multiplyfractions — illustrated with example numbers below, which may differ from this lesson's: Forgetting to simplify or convert to a mixed number. If the result is improper (numerator > denominator), convert: 8/5 = 1 3/5. If you get stuck on "Asteroid Quarter Stack", the adaptive Socratic hints below escalate from a gentle nudge to a worked-out strategy — the same way a one-on-one tutor would coach you through it.
Grade 4 · Multiplyfractions
Mission Progress
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Thinking Summary · 1
MasteredVisual Logic: 0 of 1 parts shaded.
[Discovery] Shade 2/7 on a fraction bar — this is one copy.
1
Active StepEverything you need to know about the Socratic experience.
Shade 2/7 on a fraction bar — this is one copy. Hint: Bar in 7 parts, shade 2.
Is 18/7 greater than, less than, or equal to 1? If you get stuck, the adaptive hint is: Numerator > denominator ⇒ improper ⇒ > 1.
Explorer missions hit the core abstraction at typical numeric ranges — this is where conceptual mastery is built. Within 4th Grade Multiplyfractions, expect numbers in the corresponding range.
Multiplying both numerator AND denominator (3 × 1/4 = 3/12). Only the numerator multiplies. The denominator names the slice size — it does not change.
Multiplydividefractions (Grade 5 extends this to fraction × fraction.). Open /grade-4/multiplydividefractions to start that topic's missions.
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.
C-P-A is the Singapore Math sequence proven to deepen number sense: first manipulate physical objects (Concrete), then draw pictures of them (Pictorial), and only then write equations (Abstract). Inquiry AI structures every mission as exactly these three steps — a manipulative, a picture/grid model, and finally the equation. Skipping straight to symbols is the #1 cause of math anxiety; the platform refuses to do it.