Math - 2018-19
6.4 - Exponents and Squares
6.4 The student will recognize and represent patterns with whole number exponents and perfect squares.
I can find diagonal distance between opposite street corners and I can determine what size TV to purchase if I know length and width of the space where it goes.
- I will
realize that an exponent is a short way to write repeated multiplication and
understand the relationship between a perfect square and a geometric square.
UNDERSTANDING THE STANDARD
· The symbol can be used in grade six in place of “x” to indicate multiplication.
· In exponential notation, the base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. In , 8 is the base and 3 is the exponent (e.g., ).
· Any real number other than zero raised to the zero power is 1. Zero to the zero power () is undefined.
· A perfect square is a whole number whose square root is an integer (e.g., ). Zero (a whole number) is a perfect square.
· Perfect squares may be represented geometrically as the areas of squares the length of whose sides are whole numbers (e.g., , etc.). This can be modeled with grid paper, tiles, geoboards and virtual manipulatives.
· The examination of patterns in place value of the powers of 10 in grade six leads to the development of scientific notation in grade seven.
- What does exponential form represent? Exponential form is a short way to write repeated multiplication of a common factor such as 5 x 5 x 5 x 5 = 54.
- What is the relationship between perfect squares and a geometric square? A perfect square is the area of a geometric square whose side length is a whole number.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
and represent patterns with bases
and exponents that are whole numbers.
and represent patterns of perfect
squares not to exceed,
by using grid paper, square tiles, tables, and calculators.
· 6.43 Recognize powers of 10 with whole number exponents by examining patterns in place value.