6.4

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

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 8³, 8 is the base and 3 is the exponent (e.g., 8³ = 8 ∙ 8 ∙ 8).

Any real number other than zero raised to the zero power is 1. Zero to the zero power (0⁰) is undefined.

A perfect square is a whole number whose square root is an integer (e.g., 36 = 6 ∙ 6 = 6²). Zero (a whole number) is a perfect square.

Any real number raised to the zero power is 1. The only exception to this rule is zero itself. Zero raised to the zero power is undefined.

Identify the perfect squares from 0 to 400. (d)

The square root of a whole number that is not a perfect square is an irrational number (e.g., √2 is an irrational number). An irrational number cannot be expressed exactly as a fraction 𝑎/𝑏 where 𝑏 does not equal 0.

A number written in scientific notation is the product of two factors — a decimal greater than or equal to 1 but less than 10, and a power of 10 (e.g., 3.1 x 10⁵= 310,000 and 2.85 x 10-⁴ = 0.000285).

The positive and negative square root of any whole number other than a perfect square lies between two consecutive integers (e.g., √57 lies between 7 and 8 since 7² = 49 and 8² = 64; −√11 lies between −4 and −3 since (−4)² = 16 and (−3)² = 9).