# 6.4 - Exponents and Squares

6.4  The student will recognize and represent patterns with whole number exponents and perfect squares.

### BIG IDEAS

• 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

2016 VDOE Curriculum Framework - 6.4 Understanding

·  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.

### ESSENTIALS

• 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

·  6.41  Recognize and represent patterns with bases and exponents that are whole numbers.

·  6.42  Recognize 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.

### KEY VOCABULARY

base, power, exponent, squared, cubed, square root, perfect square, squaring a number, exponential form, standard form, area of squares

Updated: Nov 20, 2018