Inquiry AI

Full 1st Grade Math
Knowledge Points & Study Guide

The full 1st 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 1st Grade skill map

Grade 1 math should move children from counting one object at a time to seeing numbers as parts, tens, and relationships. The goal is not faster tapping; it is number sense that can explain addition, subtraction, place value, measurement, and shapes.

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1.OA.A.1 addition 1.OA.A.1 subtraction 1.NBT.B.2 placevalue 1.NBT.B.2 teennumbers 1.G.A.2 shapes
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Summer Plan · Free Printable PDF

Prevent the 1st Grade math summer slide in 15 minutes a day

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

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1st Grade Knowledge Points

12 Topics · Common Core Aligned
  1. ➕
    01

    Addition

    1.OA.A.1

    Understanding addition as putting together and adding to, within 20, with a focus on the "make 10" strategy.

    Add Plus Sum Total Together Make 10
    Read Guide Practice Printable PDF
  2. ⚖️
    02

    Comparing Numbers (Greater Than, Less Than)

    1.NBT.B.3

    Comparing two-digit numbers using the symbols >, <, and =.

    Greater Than Less Than Equal To Balance
    Read Guide Practice Printable PDF
  3. 🍕
    03

    Fractions (Halves & Quarters)

    1.G.A.3

    Partition circles and rectangles into two and four equal shares — halves and quarters as the first fraction concept.

    Half Quarter Fourth Equal Share Whole Partition
    Read Guide Practice Printable PDF
  4. 📐
    04

    Indirect Length Comparison

    1.MD.A.1

    Compare the lengths of two objects indirectly by using a third object — the transitivity of length.

    Indirect Comparison Third Object Transitivity Reference Longer Shorter
    Read Guide Practice Printable PDF
  5. 🔄
    05

    Inverse Operations & Fact Families

    1.OA.B.4

    Understand subtraction as an unknown-addend problem — addition and subtraction are two views of the same fact.

    Fact Family Inverse Unknown Addend Missing Number Undo
    Read Guide Practice Printable PDF
  6. 📏
    06

    Measurement & Length

    1.MD.A.1

    Ordering and comparing objects by length, using the "same starting line" rule.

    Longer Shorter Order Compare Endpoint
    Read Guide Practice Printable PDF
  7. 🔟
    07

    Place Value (Tens and Ones)

    1.NBT.B.2

    Understanding that two-digit numbers are built from tens and ones — the power of grouping by 10.

    Tens Ones Digit Value Bundle Base-10
    Read Guide Practice Printable PDF
  8. 🔺
    08

    Shape Attributes (Defining vs Non-defining)

    1.G.A.1

    Distinguish defining attributes (sides, vertices, closed) from non-defining attributes (color, size, orientation).

    Defining Attribute Non-defining Attribute Side Vertex Orientation
    Read Guide Practice Printable PDF
  9. 🔷
    09

    Shapes (Recognize & Compose)

    1.G.A.2

    Recognizing 2D shapes by defining attributes, and composing larger shapes from smaller ones.

    Triangle Square Rectangle Circle Hexagon Side Vertex Compose
    Read Guide Practice Printable PDF
  10. ➖
    10

    Subtraction

    1.OA.A.1

    Understanding subtraction as taking from, taking apart, and comparing — within 20.

    Subtract Minus Difference Left Over Take Away
    Read Guide Practice Printable PDF
  11. 1️⃣
    11

    Teen Numbers (11-19)

    1.NBT.B.2

    Compose and decompose teen numbers (11–19) as 1 ten and a number of ones.

    Teen Eleven Compose Decompose Ten and Ones
    Read Guide Practice Printable PDF
  12. 🔟
    12

    Adding Multiples of 10

    1.NBT.C.4

    Add multiples of 10 within 100 — when you add tens, the ones digit never changes.

    Tens Bundle Multiple of 10 Ten More Skip Count
    Read Guide Practice Printable PDF

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

FAQ

1st Grade Math Handbook — FAQ

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

01 Is Grade 1 too early for Socratic learning?

Never! At this age, children are naturally inquisitive. We use visual objects and story-based scenarios to make logical inquiry feel like play.

02 How does this help with first-grade word problems?

By teaching children to visualize the 'scenario' (like birds on a tree) before they see the numbers, we eliminate the confusion that often comes with word problems.

03 Is there a free printable PDF of the 1st Grade math handbook?

Yes — every 1st 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 1st Grade handbook cover?

The 1st Grade handbook lists 12 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 1st 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 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 → reframe → analogy → only then a worked example, in that order.

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

Inquiry-based learning starts with a question, not a formula — 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.