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Grade 4 Math Mastery | Inquiry AI Socratic Portal

Tackle Grade 4 multi-digit operations, factors, fractions, and angles through CCSS-aligned Socratic missions.

πŸ“– View Study Handbook

Curriculum Overview

Grade 4 deepens arithmetic and introduces number theory. Students learn the standard multi-digit multiplication and long-division algorithms via the area model and place-value sharing, find factor pairs and classify numbers as prime or composite, work with like-denominator fractions and mixed numbers, translate decimals to/from fractions, and measure and compose angles with a protractor.

Multi-DigitLong DivisionFactorsPrimesMixed NumbersDecimalsAnglesSymmetry

Addfractions

Adding Fractions (Same Denominator)

30 Missions

Angles

Measuring Angles (Protractor)

30 Missions

Anglesum

Angle Addition & Unknown Angles

30 Missions

Comparefractions

Compare Fractions (Unlike Denominators)

30 Missions

Decimals

Decimal Fractions (10ths & 100ths)

30 Missions

Factors

Factors & Multiples

30 Missions

Geometry

Lines & Symmetry

30 Missions

Longdivision

Long Division & Remainders

30 Missions

Multidigitmult

Multi-Digit Multiplication

30 Missions

Multiplyfractions

Multiply Fraction by Whole

30 Missions

Primes

Prime vs Composite Numbers

30 Missions

Unitconversion

Unit Conversion (Within System)

30 Missions

Learning Standards Alignment

  • βœ“ CCSS.MATH.CONTENT.4.NBT.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.
  • βœ“ CCSS.MATH.CONTENT.4.NBT.B.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.
  • βœ“ CCSS.MATH.CONTENT.4.OA.B.4: Find all factor pairs for a whole number 1-100; determine whether prime or composite.
  • βœ“ CCSS.MATH.CONTENT.4.NF.A.2: Compare two fractions with different numerators and different denominators.
  • βœ“ CCSS.MATH.CONTENT.4.NF.B.3: Add and subtract fractions with like denominators, including mixed numbers.
  • βœ“ CCSS.MATH.CONTENT.4.NF.B.4: Multiply a fraction by a whole number.
  • βœ“ CCSS.MATH.CONTENT.4.NF.C.6: Use decimal notation for fractions with denominators 10 or 100.
  • βœ“ CCSS.MATH.CONTENT.4.MD.C.6: Measure angles in whole-number degrees using a protractor.
  • βœ“ CCSS.MATH.CONTENT.4.MD.C.7: Recognize angle measure as additive; solve for unknown angles.
  • βœ“ CCSS.MATH.CONTENT.4.G.A.1: Draw and identify lines, angles, parallel and perpendicular lines.
  • βœ“ CCSS.MATH.CONTENT.4.MD.A.1: Convert measurements within a single system.

Missions are designed to meet and exceed CCSS requirements for 4th Grade.

Common Questions

Everything you need to know about the Socratic experience.

Why so much algorithm work in Grade 4?

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.

How do you make factors and primes feel concrete?

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 1Γ—N strips.

Is Inquiry AI Common Core aligned?

Yes. Every mission, handbook page, and topic hub is mapped to a specific CCSS code (visible in the page header). The curriculum follows the CCSS coherence map: Grade 1 number sense β†’ Grade 3 multiplicative thinking β†’ Grade 6 ratio reasoning, with each grade building strictly on the prior year's foundations.

What is inquiry-based learning, and how does Inquiry AI apply it?

Inquiry-based learning starts with a question, not a formula β€” students explore, hypothesize, and verify before being told the rule. In Inquiry AI, every mission opens with a "Discovery" step (manipulate the model), then "Abstraction" (write the equation), then "Reflect" (apply to a new case). The procedure is never given upfront; learners derive it from their own observations.

How is Guided Discovery Learning different from "just letting kids figure it out"?

Pure discovery is inefficient β€” 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.

What does it mean for a math platform to be "Socratic"?

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 β†’ reframe β†’ analogy β†’ only then a worked example, in that order.

What is the Concrete-Pictorial-Abstract (C-P-A) approach?

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 β€” 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.

Why does Inquiry AI let kids "struggle" before showing the answer?

Research on "productive struggle" shows that 20–60 seconds of focused effort BEFORE help dramatically improves long-term retention β€” the brain encodes the strategy more deeply. Inquiry AI's hint timing is calibrated to this window: short enough to prevent frustration, long enough to lock in the learning. Parents can adjust the threshold in settings if a learner needs faster scaffolding.