**Sample Math Lessons**

**1. Placement of the Decimal Point**

Everyone learns the rule for placing the decimal point, but few can explain the rule. The rule comes about from pattern recognition and the definition of fractions. We discovered that when we multiply numbers that are powers of ten, we add the number of zeros in the multiplier and multiplicand to find the number of zeros in the answer: 100 x 1000 = 100,000

2 + 3 5

We can write the numbers 1.23 and 1.356 as 123 / 100 and 1356 / 1000, respectively. It follows from the definition of a fraction that

1 / 100 x 1 / 1000 = 1 / (100 x 1000) = 1 / 100,000

Therefore, 1.23 x 1.356 = 123 x 1356 / (100 x 1000)

= 166788 / 100,000

= 1.66788

We can visualize the result of multiplying the denominators by using a manipulative rectangle. We see that 1/3 x 1/2 = 1 / (3 x 2) = 1/6.