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Module I: Numbers and Operations



Rationale: People use numbers to quantify, describe, and label things in the world around them. It is important to know the many uses of numbers and various ways of representing them. Number sense is a matter of necessity, not only in one's occupation but also in the conduct of daily life, such as shopping, cooking, planning a budget, or analyzing information reported in the media. When computing, an educated person needs to know which operations (e.g., addition, multiplication), which procedures (e.g., mental techniques, algorithms), or which technological aids (e.g., calculator, spreadsheet) are appropriate.

From: Wisconsin Model Academic Standards for Mathematics http://dpi.state.wi.us/standards/matintro.html


Three related content areas are numeration, the real number system and number theory. According to the PRAXIS II Study Guide, these content areas account for 50% of the mathematics component of the Middle School Content Examination and includes the following topics.

  1. Number Sense (20%): Examinees should understand the meaning of number and number concepts as they relate to problem solving, using cardinal and ordinal numbers, place value, ordering of fractions, decimals, and whole numbers.
  2. Number Systems (20%): Examinees should be able to solve real-world situational problems using the real number system and work with both standard and alternative algorithms.
  3. Number Theory (10%): Examinees should be able to solve problems that demonstrate an understanding of prime and composite numbers, divisibility rules, least common multiple, greatest common divisor, and set theory.

To review these mathematical concepts, visit the five submodules listed below:


Subsets of the Real Number System

The real number system includes both rational and irrational numbers. To learn more about the Real Number System, select the appropriate tutorial.

Operations with Numbers

Aligned with the standard algorithms for addition, subtraction, multiplication and division, this module examines some of the alternative ways for working with rational numbers.

Fractions, Decimals, and Percents

Decimals are a way to represent rational numbers (fractions) and are a natural extension of our place-value system.

Percents, Ratios, Rates, and Proportions

Ratios are one number expressed in relation to another by dividing the one number by the other. Proportions are special kinds of ratios where the denominator is the total while the numerator is a sub part of the total. Rates are a special form of a ratio which represents the probability of a certain event.

Number Theory

Consider the following true statement: 4 divides 12. In mathematics, this is equivalent to the following statements: 4 is a divisor of 12; 4 is a factor of 12; 12 isdivisible by 4; 12 is a multiple of 4.


You may view the full text for Module I and print resources pertaining to these topics.