Teaching Explanation

To square a number like 97, we look at how far it is from its "base" (100). 97 is 3 less than 100.

1. Left Part: Subtract that difference from the number: 97 - 3 = 94.
2. Right Part: Square the difference: 3² = 09. (We use two digits because the base 100 has two zeros).

Combine them to get 9409. If the number is above the base, like 103, we add the difference instead.

Method Condition

Best for numbers within 10 units of 10 or 100 (e.g., 9, 12, 97, 104).

Standard Fallback

Multiply the number by itself using Lesson 08 crosswise or standard multiplication.

Misconception & Correction

• Misconception: Always subtracting the difference, even if the number is above the base.

Correction: If the number is above the base, add the surplus. If it is below*, subtract the deficiency.