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For Basic 5 pupils, one of the most straightforward and efficient methods to teach square roots, especially for perfect squares, is the [b]Prime Factorization method[/b]. This method is concrete and builds on their prior knowledge of multiplication and division. Here’s a simple way to teach it:

Prime Factorization Method for Square Roots:
Factorization: Begin by having the students factor the number into its prime factors. For example, if finding the square root of 36, the factorization would be 2 x 2 x 3 x 3.
Pair the Factors: Teach the students to pair the prime factors into identical pairs. In the case of 36, the pairs would be (2 x 2) and (3 x 3).
Multiply One from Each Pair: Have the students take one number from each pair and multiply them together. For 36, that would be 2 x 3 = 6.
Result is the Square Root: The result from the multiplication step gives the square root of the original number. So, √36 = 6.

DOWNSIDE TO THIS METHOD; While it is easy to grasp for introduction sake, it is less efficient when working with larger numbers.

If you want you pupils to be able to find square roots of any number regardless of how large very quickly, use [b] Long Division Method [/b]. unlike the usual long division method, this one has its own approach with very short steps that any child can memorize and use mentally.

LONG DIVISION METHOD FOR SQUARE ROOTS:

STEP 1. Set Up: Group the digits of the number into pairs from right to left. If there is an odd number of digits, the leftmost group may have only one digit.
STEP 2. Find the Largest Square: Find the largest square smaller than the first leftmost group, and write its square root as the first digit of the result.
STEP 3. Subtract & Bring Down: Subtract the square of the first digit of the result from the first group, and bring down the next group next to the remainder.
STEP 4. Double & Divide: Double the number already found as the square root (ignore any decimal for now). STEP 5. Guess the largest possible digit to put next to it so that when this new number is multiplied by the guessed digit, the product is less than or equal to the subtracted remainder with the next group brought down.
STEP 6. Repeat: Continue this process of subtracting, bringing down the next pair of digits, doubling, and guessing until all pairs of digits have been brought down.

How to Use It:

• Demonstration: Start by demonstrating the method with smaller numbers to help students understand the procedure without getting overwhelmed.
• Guided Practice: Work through several examples together as a class, slowly increasing the difficulty of the numbers.
• Worksheets and Drills: Provide plenty of practice problems to help students get accustomed to the steps and logic of the method.

Advantages:

• Applicable to Any Number: Unlike prime factorization, the long division method can be used for non-perfect squares and does not get overly cumbersome with very large numbers.
• Develops Number Sense: This method helps students develop a deeper understanding of how numbers work together, enhancing their overall number sense.
• Teaching the long division method for square roots can be a bit challenging at first, but with practice, students can become quite proficient. It’s a powerful tool for their mathematical toolkit, especially as they advance in their math education.