Mathematics | Grade : 8
Domain - The Number System
Cluster - Know that there are numbers that are not rational, and approximate them by rational numbers.
[8.NS.A.2] - Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g.,π2). For example, by truncating the decimal expansion of √2 show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
- Decimal expansion
Writing a rational number as a decimal. - Expression
A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a). - Irrational number
A number that cannot be expressed as a quotient of two integers, e.g.,√2 . It can be shown that a number is irrational if and only if it cannot be written as a repeating or terminating decimal. - Number line diagram
A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity. - Rational number
A number expressible in the form a∕b or – a∕b for some fraction a∕b. The rational numbers include the integers.
[8.NS.A.1] -
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
[8.EE.A.2] -
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.