Summary Place value

A positional notation or place-value notation system is a numeral system in which each digit is related to the next by a constant multiplier, (a common ratio) called the base or radix of that numeral system. The value of each digit position is the value of its digit multiplied by a power of the base; the power is determined by the digit's position. The total value of a positional number is the total of the values of all positions.

Various bases are commonly used. For example, the decimal system uses ten unique symbols, whereas the sexagesimal system usually uses a decimal-like system for each position and separates each position from the next by punctuation. Modern computers use binary, octal, and hexadecimal numbers, the last using decimal numerals (0–9) plus the letters A–F to provide the sixteen possible symbols in each position.

example :

There are basically two ways of illustrating division with concrete objects. The first method has to do with dividing objects between a certain number of persons. For example, the problem 12 ÷ 3 would be, “If you have 12 bananas and 3 people, how many bananas does each one get?”

The second method has to do with grouping. The problem 12 ÷ 3 would be: “If you have 12 people, how many groups of 3 people can you make?” These two interpretations of division are important to understand so that your child can solve problems of everyday life.

The book at hand provides plenty of practice and stresses understanding of concepts. I don't wish the student to memorize procedures without understanding the “why” (rote memorization).

For example, when studying the remainder, the student first finds the remainder with the help of pictures - which is equivalent to using manipulatives. Then he explores the pattern found in dividing sequential numbers by the same number, such as 25 ÷ 3, 26 ÷ 3, 27 ÷ 3, 28 ÷ 3, etc. After that, it is explained that you can find the remainder by looking at a certain difference, and finally the typical school-book method is presented.