Resources
Return to the source, clarify a term, or use the questions in a lesson.
Learning companions
Online book
Six chapters and the master download.
Workbooks
Printable activities and answer guides.
Parents and teachers
A session plan and physical-tool activities.
Quizzes
Topic-based questions with explanations.
Squares and roots
Calculation, diagrams and limits.
The master document
The integrated review edition contains the mathematics, original frame diagrams and limitations behind these pages.
Download the master documentLearn to Learn
Your learning can begin with a question: what, why, how, where or when? Make a prediction, explore the representation, connect ideas, then explain and check.
This website adapts Amalan’s handwritten Tamil article and extends the approach with reflection and application. It does not promise examination marks or learning speed.
Give learners time to reason. Use a cue before a complete explanation when helpful. Ask what changed, what remained the same and how the answer could be checked.
Glossary
| Term | Meaning |
|---|---|
| Active bead | A bead moved into the counting area and included in the reading. |
| Base | The grouping factor between adjacent places. |
| Digit | A symbol used in one position of a numeral. |
| Place value | The value of one unit at a position, such as ten or one tenth. |
| Magnitude | The size of a number without its sign. |
| Regrouping | Exchanging equal values between places. |
| Carry | One unit recorded in the next larger place after reaching the base. |
| Complement | For a decimal digit a from 1 to 9, the ten’s complement is 10 − a. |
| Quotient | The result of division, or whole group count in division with a remainder. |
| Remainder | The quantity left after whole groups have been accounted for. |
| Precision | The smallest place or level of detail retained. |
Original page 24’s prototype photograph remains in Meet the Frame; the notation from page 25 is adapted below.
Symbols, abbreviations and powers
Adapted from original page 25. Whole and fractional place names are written in full to avoid ambiguous abbreviations.
| Symbol | Meaning |
|---|---|
| = | Equal to |
| > | Greater than |
| < | Less than |
| · or . | Decimal-point marker in base ten (not multiplication in this frame) |
| 10⁰ | 1; the exponent is zero, not a degree sign |
| 10¹, 10², 10³ | 10, 100, 1000 |
| 10⁻¹ | 1/10 = 0.1 (one tenth) |
| 10⁻² | 1/(10 × 10) = 0.01 (one hundredth) |
| 10⁻³ | 1/(10 × 10 × 10) = 0.001 (one thousandth) |
| 10⁻⁴, 10⁻⁵, 10⁻⁶ | One ten-thousandth, one hundred-thousandth, one millionth |
Here T = tens, H = hundreds and M = millions when abbreviations are needed. Full labels distinguish thousands from thousandths. Negative powers require a denominator containing the whole product.
Scope and limitations
The frame has finite range and precision. Bead-size differences are cues, not a proportional scale. The photograph shows a positive prototype, not verification of the complete signed mechanism.
The four sign/place regions are not a coordinate plane. Educational effectiveness, accessibility and long-term durability require independent evaluation.
Using these resources
The pages are free to read. A formal reuse licence has not yet been selected; free access should not be treated as an unrestricted licence.
Short demonstration
Watch nine units become one ten: play or step through the regrouping.