Grade 8 Online Math Tutorial5 (hrs)
Sep 23, 2020 20201124 13:05Grade 8 Online Math Tutorial5 (hrs)
Grade 8 Online Math Tutorial5 (hrs)
Studentsâ€™ knowledge of operations on numbers is expanded to include operations on numbers in integer exponents. Learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence.Â Congruence has been taken to mean, intuitively, same size and same shape. Translations, reflections, and rotations are examples of rigid motions, which are, intuitively, rules of moving points in the plane in such a way that preserves distance.
Students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean theorem based on the angleangle criterion for similar triangles. Extend what they already know about unit rates and proportional relationships to linear equations and their graphs.
Students use their understanding of functions to model the relationships of bivariate data.Â This module is important in setting a foundation for studentsâ€™ work in Algebra I and also begins with work related to the Pythagorean theorem and right triangles.

Integer Exponents and Scientific Notation
 Exponential Notation
 Multiplication of Numbers in Exponential Form
 Numbers in Exponential Form Raised to a Power
 Numbers Raised to the Zeroth Power
 Negative Exponents and the Laws of Exponents
 Proofs of Laws of Exponents
 Magnitude
 Estimating Quantities
 Scientific Notation
 Operations with Numbers in Scientific Notation
 Efficacy of Scientific Notation
 Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology

The Concept of Congruence

Similarity

Linear Equations
 Writing Equations Using Symbols
 Linear and Nonlinear Expressions in đť‘Ą
 Solving a Linear Equation
 Solutions of a Linear Equation
 Linear Equations in Disguise
 An Application of Linear Equations
 Linear Equations in Two Variables
 The Graph of a Linear Equation in Two Variables
 The Graph of a Linear Equationâ€•Horizontal and Vertical Lines
 The Slope of a NonVertical Line
 The Computation of the Slope of a NonVertical Line
 The Line Joining Two Distinct Points of the Graph đť‘¦=đť‘šđť‘Ą+đť‘Ź Has Slope đť‘š

Examples of Functions from Geometry

Linear Functions
 Modeling Linear Relationships
 Interpreting Rate of Change and Initial Value
 Representations of a Line
 Increasing and Decreasing Functions
 Scatter Plots
 Patterns in Scatter Plots
 Informally Fitting a Line
 Determining the Equation of a Line Fit to Data
 Using Linear and Non Linear Models in a Data Context
 Summarizing Bivariate Categorical Data in a TwoWay Table
 Association Between Categorical Variables

Introduction to Irrational Numbers Using Geometry
 The Pythagorean Theorem
 Square Roots
 Existence and Uniqueness of Square Roots and Cube Roots
 Solving Equations with Radicals
 Finite and Infinite Decimals
 Infinite Decimals
 The Long Division Algorithm
 Decimal Expansions of Fractions
 Converting Repeating Decimals to Fractions
 The Decimal Expansion of Some Irrational Numbers
 Comparing Irrational Numbers