Unit 6

(15 days)

Properties of Exponents
Applying Properties in Scientific Notation

Essential Questions

Are students able to recognize the properties of integer exponents to compare large and small numbers?
How do radicals and exponents influence one’s understanding of other content, such as geometry and science?

Questioning

How do you evaluate square roots and cube roots?
How can you develop and use the properties of integer exponents?
How can you use scientific notation to express very large and very small quantities?
To what extent does scientific notation apply to the real world?

Common Core Standards:

8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example,
8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the USA as 3 x 10⁸and the population of the world as 7 x 10⁹, and determine that the world population is more than 20 times larger.
8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. *

*Students will have a calculator available for PARCC assessments

Unit Vocabulary (new vocabulary terms are denoted by asterisks*)

*Absolute Value: The distance of a number from zero on a number line; shown by ∣ ∣.

Base: When a number is raised to a power, the number that is used as a factor is the base.

Coefficient: The number that is multiplied by the variable in an algebraic expression.

Constant: A value that does not change.

Cubed: Raising a number to the third power

*Decimal Expansion: a fraction written in base-10

Equivalent: equal or same

Exponent: The number that indicates how many times the base is used as a factor.

*Exponential Notation: A number written with a base and an exponent.

Inequality: A mathematical sentence that shows the relationship between quantities that are not equivalent.

*Inverse Operation: Operations that undo each other: addition and subtraction, or multiplication and division.

*Irrational Numbers: numbers that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal.

*Linear Equation: An equation whose solutions form a straight line on a coordinate plane.

*Magnitude: The size of a mathematical object, a property by which the object can be compared as larger or smaller than other objects of the same kind. An object's magnitude is the displayed result of an ordering (or ranking) of the class of objects to which it belongs.

One Solution: A value or values that make an equation true.

Perfect Square: A square of a whole number.

Power: A number produced by raising a base to an exponent.

*Properties of Integer Exponents:

Proportional Relationships: A relationship between two quantities in which the ratio of one quantity to the other quantity is constant.

Radical: The symbol √ used to represent the non-negative square root of a number.

Rational Number: repeating or terminating decimals; any number that can be expressed as a ratio of two integers.

*Real Number System: The field of all rational and irrational numbers

Roots: The root of a number x is another number, which when multiplied by itself a given number of times, equals x.

Scientific Notation: A method of writing very large or very small numbers by using powers of 10.

Square Root: A number that is multiplied by itself to form a product is called a square root of that product.

*Symbol Notation: letters or symbolic expressions that are used as stand-ins for unspecified numeric quantities (i.e. an - both a and n are letters representing unspecified quantities).

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