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Mathematics: Mathematics

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Math - Student Resources in Context



Mathematics (often abbreviated Math), in the very broadest sense, is the systematic study of relationships in the physical world and relationships between symbols that need not pertain to the real world. In relation to the world, mathematics is the language of science. It operates within the laws and constraints of science as it examines physical phenomena. Mathematicians, those who delve into and study mathematics, formulate new conjectures from the deduction of existing axioms and definitions. Unlike science, however, mathematics has no constraints. So, in relation to symbols, mathematics can be considered a pure mental activity that is capable of generating...View More

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Biography in Context

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Lesson Plan

An Introduction to Fractions

Subject(s): Mathematics
Grade Level(s): 3-5, 6-8


Students will be introduced to fractions, including equivalent fractions, nominators, and denominators.


Copy and distribute the printable Resources section below. Have students read the essay for background information and consult any or all of the encyclopedia articles that follow it to learn more about the topic.


Essay: Numbers such as 1, 2, 3, 5, 10, 120, and 4,000 are called whole numbers, or integers. When you multiply one integer by another, the answer is always an integer: 5 × 6 = 30; 7 × 9 = 63. However, it is not always possible to obtain an integer as an answer when you divide one integer by another. If 8 apples are to be divided into 3 equal shares, the result is 8/3, which is a fraction. This fraction can be reduced to a whole number and a remaining fraction—that is, 8/3 equals 22/3. Therefore, if you were to divide 8 apples equally among 3 people, each person would receive 2 whole apples plus 2/3 apple.


Create a display showing the fractions of men and women in different occupations—for example, teachers in your school, police officers in your community, legislators in your state, senators and representatives in the U.S. Congress.

For Discussion

What are the numerator and denominator of a fraction? Can zero be a denominator? Why or why not?

How does one add fractions when all the denominators are the same? How does one add fractions when the denominators are different?

Give some examples of how fractions are used in everyday life.


Go further by completing one or more of the following assignments:

  • Compare prime and composite numbers. Give examples of each.
  • Compare mixed numbers and improper fractions. Give examples.
  • Define and give examples of equivalent fractions. In each group of equivalent fractions, indicate the simplest form.


Use drawings of pizzas to demonstrate the fractions 1/ 3, 1/4, 3/4, and 7/8.

Suggested Terms for Searching:




Fractions and Decimals

Numbers and Number Systems

Suggested Resources:


Great resource for Science Projects!

Science Online

Mathematics Links

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Fun Math Books

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