PreAlgebra GT (Grade 6)
1: The Number System and Exponents (8.NS/8.EE)
In this unit, students will know that there are numbers that are not rational, and approximate them by rational numbers. Students should know that numbers that are not rational are called irrational and understand that every number has a decimal expansion. For rational numbers students should show that the decimal expansion repeats eventually. Students should also use rational approximations of irrational numbers to compare the size of irrational numbers and approximately locate them on a number line diagram. Students will apply properties of the law of exponents to simplify expressions. Students will understand the meaning behind square root and cubed root symbols. Numbers will be expressed in scientific notation so students can compare very large and very small quantities and compute with those numbers.
What will my child learn?
Students will:
Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
8.NS.A.2
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π^2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Work with radicals and integer exponents.
8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^5 = 3^3 = 1/3^3 = 1/27.
8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
8.EE.A.3
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10^8 and the population of the world as 7 times 10^9, and determine that the world population is more than 20 times larger.
8.EE.A.4
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology
Students will:
Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
 Check for Understanding: Converting 1Digit Repeating Decimals to Fractions  Converting Decimals to Fractions 2  Converting MultiDigit Repeating Decimals to Fractions  Recognizing Rational and Irrational Numbers  Writing Fractions As Repeating Decimals
 Review/Rewind: Intro to Rational and Irrational Numbers  Converting a Fraction to a Repeating Decimal  Converting Repeating Decimals to Fractions
 Enrichment Tasks: Identifying Rational Numbers  Converting Repeating Decimals to Fractions
8.NS.A.2
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π^2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
 Check for Understanding: Approximating Irrational Numbers
 Review/Rewind: Approximating Square Roots to Hundredths
 Enrichment Tasks: Comparing Rational and Irrational Numbers  Irrational Numbers on the Number Line
Work with radicals and integer exponents.
8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^5 = 3^3 = 1/3^3 = 1/27.
 Check for Understanding: Positive and Negative Exponents  Properties of Exponents  Using Exponent Rules to Evaluate Expressions
 Review/Rewind: Negative Exponents  Exponent Rules Part 1  Exponent Rules Part 2
 Enrichment Tasks: Extending the Definitions of Exponents, Variation 1
8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
 Check for Understanding: Square Roots of Perfect Squares  Cube Roots
 Review/Rewind: Intro to Square Roots  Intro to Cube Roots
8.EE.A.3
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10^8 and the population of the world as 7 times 10^9, and determine that the world population is more than 20 times larger.
 Check for Understanding: Orders of Magnitude
 Review/Rewind: Approximating with Powers of 10
 Enrichment Tasks: Ant vs Elephant  Orders of Magnitude
8.EE.A.4
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology
 Check for Understanding: Scientific Notation  Adding and Subtracting in Scientific Notation  Computing in Scientific Notation  Multiplying and Dividing Scientific Notation
 Review/Rewind: Subtracting in Scientific Notation Multiplying and Dividing in Scientific Notation
 Enrichment Tasks: Giantburgers  Ants vs Humans
What are some signs of student mastery?

Tools & Technology
PickaPath (NCTM) Practice calculations starting at level 4 with fractions, level 5 metric units, level 6 fraction and decimal operations, and level 7 exponent operations. http://illuminations.nctm.org/pickapath/ Patterning the Powers of 10 (Learn Alberta) Practice identifying patterns in powers of 10 by matching the tiles. Exploring Laws of Exponents (Learn Alberta) Practice multiplying and dividing exponents in this paleontological dig. Additional print resources available 
Source: HCPSS Office of Secondary Mathematics
