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🔢 Math Fundamentals

Build real number sense — count, compare, group, and recognize patterns. From counting toys on the rug to spotting why even and odd numbers behave the way they do.

20 lessonsAges 3–10Four age versions per lessonPattern RecognitionLogicSequencingProblem Solving

Complete lesson syllabus

Every lesson below contains age-banded facts and quiz questions. Some lessons also include a make-or-explain artifact prompt. Titles are shown in their current course order.

  1. Counting Things You Can See
    Pattern Recognition · Logic · Math.number.count 10
    Example: When you count past 20, you're using a pattern: every group of ten gets a name (twenty, thirty, forty…) and the ones repeat the small-number pattern (twenty-one, twenty-two…). Learning the pattern lets you count to 100 without memorizing 100 separate words.
  2. The Number Line
    Logic · Sequencing · Math.number.compare
    Example: The number line keeps going past 100, past 1,000, past a million — there's no end. We just don't draw all of it.
  3. Counting in Groups
    Pattern Recognition · Sequencing · Math.patterns.basic
    Example: Skip-counting and multiplication are the same idea in different clothes. Counting by 3s — 3, 6, 9, 12, 15 — gives you the answers to 1×3, 2×3, 3×3, 4×3, 5×3.
  4. Tens and Ones
    Pattern Recognition · Logic · Math.number.place Value
  5. Even and Odd
    Pattern Recognition · Logic · Math.patterns.basic
  6. Adding Stories
    Logic · Problem Solving · Math.ops.add Sub Small
  7. Taking-Away Stories
    Logic · Problem Solving · Math.ops.add Sub Small
  8. Equal Groups & Arrays
    Pattern Recognition · Logic · Math.ops.multiplication
  9. Fair Share
    Logic · Problem Solving · Math.ops.division
  10. Fact Families
    Pattern Recognition · Logic · Math.ops.add Sub Small
  11. Halves and Quarters
    Pattern Recognition · Logic · Math.fractions.halves Quarters
  12. Comparing Fractions
    Pattern Recognition · Logic · Math.fractions.equivalent
  13. Decimals as Money
    Counting Money · Logic · Math.fractions.decimals
  14. Percent Off
    Counting Money · Wants Vs Needs · Logic
  15. Ratios in the Kitchen
    Experimentation · Sequencing · Math.ops.ratio
  16. Equations as Balance
    Logic · Problem Solving · Math.patterns.function
  17. Word Problem Detective
    Logic · Problem Solving · Math.ops.add Sub 100
  18. Estimation Power
    Logic · Experimentation · Math.number.compare
  19. Pattern → Rule
    Pattern Recognition · Logic · Math.patterns.basic
  20. Why Math Works
    Logic · Critical Thinking · Math.patterns.function

Open a representative lesson

See age-by-age facts, a sample quiz prompt, sourcing where available, and the artifact prompt from Counting Things You Can See.

View the Counting Things You Can See sample lesson →

How age adaptation works

The lesson record contains separate fact sets and quiz questions for Pre-K, kindergarten, early elementary, and upper elementary. This is not the same paragraph with a smaller font: vocabulary, detail, and question demands can change by age band. Parents can still choose a different level if their child needs it.

Assessment and records

Course quizzes provide immediate practice feedback. Completion and progress can feed parent-managed records, but a quiz score is not a teacher-issued grade, independent diagnosis, or accredited course credit.

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