Mathematics Common Core Standards: The Real Number System

High school students need to have an understanding of the real number system to satisfy Common Core Standards. The real number system contains all numbers that can be represented on a number line, including rational and irrational numbers:

  • Rational numbers are whole numbers and fractions. You'll encounter rational numbers in various decimal forms. Even though a repeating decimal (such 0.33333333...) may not look rational, it can still be written as the fraction 1/3. Terminating decimals, such as 0.25, are also rational and can be written as a fraction (in this case, 1/4). Students encounter rational numbers starting in kindergarten.

  • Irrational numbers can't be written as a fraction or a ratio. You'll frequently see irrational numbers in decimal forms that can't be written as fractions. For example, pi (3.14159…) is an irrational number that is non-repeating but also can't be expressed as a fraction. Students begin working with irrational numbers in Grade 8.

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In high school, students begin to extend the properties of exponents to rational exponents. By graduation, students are expected to:

  • Understand and explain how the properties of integer (whole number) exponents extend to all rational exponents, including fractional exponents, such as 1251/3

  • Express radicals in terms of rational exponents. For example:

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and

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By graduation, high-school students must also be able to explain the properties of irrational numbers and why

  • Adding two rational numbers results in a rational number.

  • Multiplying two rational numbers results in a rational number.

  • Adding two irrational numbers results in an irrational number.

  • Multiplying a nonzero rational number with an irrational number results in an irrational number; for example, if π is irrational, explain why 2π is irrational.

One of the best ways to learn anything is to try to teach it. When your child is working with rational and irrational numbers, ask her to define each term and explain the difference.

After making sure that your child has an accurate understanding of these concepts, write out five or six numbers and let her identify which ones are rational and which ones are irrational. Be sure to include examples of the various types of decimals.

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