#### Math - 2017-18

# 6.5 and *6.4 - Exponents and Squares

**6.5 ** The student will **investigate** and **describe
**concepts of positive exponents and perfect squares.

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

**Bloom's Level: ** Analyze, Understand

*Adopted: 2009*

### 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

- 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
^{3}, 8 is the base and 3 is the exponent. - A power of a number represents repeated
multiplication of the number by itself (e.g., 8
^{3}= 8 x 8 x 8 and is read “8 to the third power”). - Any real number other than zero raised to the
zero power is 1. Zero to the zero power (0) is undefined.
- Perfect squares are the numbers that result from
multiplying any whole number by itself (e.g., 36 = 6 x 6 = 6
^{2}). - Perfect squares can be represented geometrically
as the areas of squares the length of whose sides are whole numbers (e.g., 1 x 1, 2 x 2, or 3 x
3). This can be modeled with grid paper, tiles, geoboards and virtual
manipulatives.

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 = 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**

6.5_{1} **Recognize**
and **describe** patterns with exponents
that are natural numbers by using a calculator.

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

6.5_{2} **Recognize**
and **describe** patterns of perfect
squares not to exceed 20^{2}, by using grid paper, square tiles, tables, and
calculators.

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

6.5_{3} **Recognize**
power of 10 by examining patterns in a place value chart: 10^{4} = 10,000, 10^{3} =
1,000, 10^{2} = 100, 10^{1} = 10, 10^{0} = 1.

·
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 27, 2017*