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Full 4th Grade Math
Knowledge Points & Study Guide

The full 4th Grade Common Core knowledge-point list. Free printable practice, downloadable PDF checklist, and Socratic missions — covering every CCSS standard for this grade.

Download PDF Checklist Free Printable Practice

Tip: every topic guide below is printer-friendly — open a guide and choose "Print → Save as PDF" to generate a free worksheet.

Handbook Learning Route

Use this handbook to cover the full 4th Grade skill map

Grade 4 should turn procedures into explainable strategies. Students extend multi-digit multiplication and long division, analyze factors and primes, compare fractions, connect fractions to decimals, and measure angles, symmetry, and unit conversions.

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4th grade math games online free long division games 4th grade multi digit multiplication games 4th grade fraction games decimal games for 4th grade angle measurement games

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4.NBT.B.5 multidigitmult 4.NBT.B.6 longdivision 4.NF.A.2 comparefractions 4.NF.C.6 decimals 4.MD.C.6 angles
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Summer Plan · Free Printable PDF

Prevent the 4th Grade math summer slide in 15 minutes a day

3-week plan, free printable worksheets, no tutors required.

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4th Grade Knowledge Points

13 Topics · Common Core Aligned
  1. ➕
    01

    Adding Fractions (Same Denominator)

    4.NF.B.3

    Add and subtract fractions with like denominators, including mixed numbers, by joining and separating parts referring to the same whole.

    Like Denominator Mixed Number Improper Fraction Whole
    Read Guide Practice Printable PDF
  2. 📐
    02

    Measuring Angles (Protractor)

    4.MD.C.6

    Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

    Degree Protractor Vertex Ray Right Angle
    Read Guide Practice Printable PDF
  3. ➕
    03

    Angle Addition & Unknown Angles

    4.MD.C.7

    Recognize angle measure as additive. Solve addition and subtraction problems to find unknown angles.

    Decomposed Angle Unknown Angle Adjacent Angles Sum
    Read Guide Practice Printable PDF
  4. ⚖️
    04

    Compare Fractions (Unlike Denominators)

    4.NF.A.2

    Compare two fractions with different numerators and different denominators by creating common denominators or by comparing to a benchmark fraction.

    Common Denominator Benchmark Cross-Multiply Equivalent
    Read Guide Practice Printable PDF
  5. 🔢
    05

    Decimal Fractions (10ths & 100ths)

    4.NF.C.6

    Use decimal notation for fractions with denominators 10 or 100.

    Tenths Hundredths Decimal Point Place Value
    Read Guide Practice Printable PDF
  6. 🧩
    06

    Factors & Multiples

    4.OA.B.4

    Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors.

    Factor Multiple Factor Pair Divisor
    Read Guide Practice Printable PDF
  7. 📏
    07

    Geometry: Lines & Symmetry

    4.G.A.1

    Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

    Parallel Perpendicular Symmetry Right Angle Line of Symmetry
    Read Guide Practice Printable PDF
  8. ➗
    08

    Long Division & Remainders

    4.NBT.B.6

    Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value.

    Dividend Divisor Quotient Remainder Place Value
    Read Guide Practice Printable PDF
  9. ✖️
    09

    Multi-Digit Multiplication

    4.NBT.B.5

    Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using strategies based on place value.

    Partial Product Area Model Standard Algorithm Place Value
    Read Guide Practice Printable PDF
  10. ✖️
    10

    Multiply Fraction by Whole

    4.NF.B.4

    Multiply a fraction by a whole number, e.g., understand 3 × (1/4) as 3 copies of 1/4.

    Unit Fraction Whole Number Repeated Addition Numerator
    Read Guide Practice Printable PDF
  11. 🔢
    11

    Prime vs Composite Numbers

    4.OA.B.4

    Determine whether a given whole number in the range 1-100 is prime or composite.

    Prime Composite Factor Divisor 1 is special
    Read Guide Practice Printable PDF
  12. 🪞
    12

    Lines of Symmetry

    4.G.A.3

    Recognize a line of symmetry for a two-dimensional figure as a line such that the figure folded along it has matching halves; identify line-symmetric figures and draw their lines of symmetry.

    line of symmetry reflect mirror congruent axis
    Read Guide Practice Printable PDF
  13. 📏
    13

    Unit Conversion (Within System)

    4.MD.A.1

    Know relative sizes of measurement units within one system; convert from a larger unit to a smaller unit.

    Unit Conversion Factor Bigger Unit Smaller Unit
    Read Guide Practice Printable PDF

All guides are free · No login required · Printable on any device

FAQ

4th Grade Math Handbook — FAQ

Free printable practice, PDF downloads, and how to use this handbook at home or in the classroom.

01 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.

02 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 1×N strips.

03 Is there a free printable PDF of the 4th Grade math handbook?

Yes — every 4th Grade topic guide on this page is printable. Use your browser's "Print → Save as PDF" on any topic guide to generate a free printable practice worksheet you can use at home or in the classroom. A consolidated downloadable PDF checklist is linked at the top of this handbook.

04 What knowledge points does the 4th Grade handbook cover?

The 4th Grade handbook lists 13 CCSS-aligned topics. Each topic has a knowledge-point summary, the matching CCSS code, key vocabulary, and a free interactive practice mission you can play in the browser.

05 Can I use the 4th Grade handbook for homeschool or after-school practice?

Yes. The handbook is free, ad-free, and works on any device. Print the topic guides as worksheets, or have your student practice the interactive missions — both paths cover the same Common Core knowledge points.

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

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.

07 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 → Grade 3 multiplicative thinking → Grade 6 ratio reasoning, with each grade building strictly on the prior year's foundations.