#### Math - 2018-19

# 6.4 - Exponents and Squares

6.4The student willrecognizeandrepresentpatterns with whole number exponents and perfect squares.

*Adopted: 2016*

### 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

· 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 = 5
^{4}. - 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**

·
6.4_{1} **Recognize**
and **represent** patterns with bases
and exponents that are whole numbers.

·
6.4_{2} **Recognize**
and **represent** patterns of perfect
squares not to exceed,
by using grid paper, square tiles, tables, and calculators.

·
6.4_{3} **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*