{"id":206,"date":"2017-08-22T16:29:20","date_gmt":"2017-08-22T16:29:20","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/elementary-education\/?page_id=206"},"modified":"2019-02-28T05:36:51","modified_gmt":"2019-02-28T05:36:51","slug":"numbers","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/elementary-education\/numbers\/","title":{"rendered":"Numbers"},"content":{"rendered":"
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Workshop Index<\/a>\u00a0Next Lesson \u27a1<\/a><\/div>\n

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Numbers<\/h1>\n

Objective<\/h4>\n

The following lessons will examine whole numbers, rational and irrational numbers, integers, and their attendant operations. We\u2019ll also review prime factorizations, divisibility rules, and other basic topics pertaining to numbers.<\/p>\n

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Numbers, Numbers Everywhere<\/h3>\n

For some of you, it\u2019s been a long time since you\u2019ve darkened the doorway of a math classroom. And even for those of you who have a math background, it\u2019s helpful to review some of these key concepts from the ground up. So, let\u2019s start at mathematics\u2019 atomic level: numbers. Mathematicians have created a dizzying array of numbers\u2014imaginary, surreal, and transcendental, to name just a few. Fortunately for us, we only need to learn the basics. The diagram below shows the sets of numbers that we\u2019ll review here.<\/p>\n

\"Types<\/center>The above diagram shows the relationships among the following types of numbers: real numbers<\/abbr>, rational numbers<\/abbr>, irrational numbers<\/abbr>, whole numbers<\/abbr>, and integers<\/abbr>. For example, every type of number in the diagram is a real number. Moving in, all integers and whole numbers are rational numbers and, subsequently, all whole numbers are integers. And, as you move out from the center of the diagram, the same rule holds true. Every whole number is an integer, and every integer is a rational number.<\/p>\n

Many numbers fit into several sets of numbers. Think about putting the number into its most restrictive set in the diagram above, and then you\u2019ll be able to see how a number can exist in more than one set.<\/p>\n

For example, \u20137 is a real number, rational number, and integer, but it is not a whole number because it is negative.<\/p>\n

What categories does \u221a18 fit into? You should be thinking irrational number and real number.<\/p>\n

How about \u221a9? Since the square root of 9 is 3, it fits into the categories of real number, rational number, integer, and whole number.<\/p>\n

Try this one on your own:<\/p>\n

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Question<\/h4>\n

Choose the correct statement below:<\/p>\n

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  1. No rational numbers are integers.<\/li>\n
  2. All rational numbers are real numbers.<\/li>\n
  3. No irrational numbers are real numbers. All integers are whole numbers.<\/li>\n
  4. All integers are whole numbers.<\/li>\n<\/ol>\n

    Reveal Answer<\/a><\/p>\n

    The correct answer is B. The category of rational numbers is a subset of real numbers, as shown on the diagram. You can correct statements A and D by changing the first words to \u201csome.\u201d Correct C by making the first word \u201call.\u201d<\/p>\n<\/section>\n

    You may be thinking the whole thing doesn’t make sense at this point. Let’s take these numbers and lay them out in a traditional way.<\/p>\n

    What Can You Do With a Number Line?<\/h3>\n

    You can do more than you might have thought you could, especially if you haven\u2019t thought about it in a few years. Today, students of all ages use number lines for a wide variety of mathematical tasks, including:<\/p>\n