Grade 6 Online Math Tutorial5 (hrs)
Sep 15, 2020 20201124 13:07Grade 6 Online Math Tutorial5 (hrs)
Grade 6 Online Math Tutorial5 (hrs)
Students are introduced to the concepts of ratio and rate. Their previous experience solving problems involving multiplicative comparisons serves as the conceptual foundation for understanding ratios as a multiplicative comparison of two or more numbers used in quantities or measurements. Students develop fluidity in using multiple forms of ratio language and ratio notation. They construct viable arguments and communicate reasoning about ratio equivalence as they solve ratio problems in realworld contexts.
Students complete their understanding of the four operations as they study division of whole numbers, division by a fraction, and operations on multidigit decimals. This expanded understanding serves to complete their study of the four operations with positive rational numbers, thereby preparing students for understanding, locating, and ordering negative rational numbers and algebraic expressions.
Students extend their arithmetic work to include using letters to represent numbers. Students determine that letters are used to represent specific but unknown numbers and are used to make statements or identities that are true for all numbers or a range of numbers.
Students move from building arrays to using arrays to find area and eventually move to decomposing threedimensional shapes into layers that are arrays of cubes. Utilize their previous experiences in shape composition and decomposition in order to understand and develop formulas for area, volume, and surface area. Students used bar graphs and line plots to represent data and then solved problems using the information presented in the plots. Move from simply representing data into analyzing data.

Ratios and Unit Rates

Collections of Equivalent Ratios
 Tables of Equivalent Ratios
 The Structure of Ratio Tables—Additive and Multiplicative
 Comparing Ratios Using Ratio Tables
 From Ratio Tables to Double Number Line Diagrams
 From Ratio Tables to Equations Using the Value of a Ratio
 From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
 A Synthesis of Representations of Equivalent Ratio Collections

Arithmetic Operations Including Division of Fractions
 Interpreting Division of a Fraction by a Whole Number—Visual Models
 Interpreting Division of a Whole Number by a Fraction—Visual Models
 Interpreting and Computing Division of a Fraction by a Fraction—More Models
 Creating Division Stories
 More Division Stories
 The Relationship Between Visual Fraction Models and Equations
 Dividing Fractions and Mixed Numbers
 Sums and Differences of Decimals
 The Distributive Property and the Products of Decimals
 Fraction Multiplication and the Products of Decimals
 Estimating Digits in a Quotient
 Dividing MultiDigit Numbers Using the Algorithm
 The Division Algorithm—Converting Decimal Division into Whole Number Division Using Fractions
 The Division Algorithm—Converting Decimal Division into Whole Number Division Using Mental Math

Rational Numbers
 Positive and Negative Numbers on the Number Line—Opposite Direction and Value
 RealWorld Positive and Negative Numbers and Zero
 The Opposite of a Number
 The Opposite of a Number’s Opposite
 Rational Numbers on the Number Line
 Ordering Integers and Other Rational Numbers
 Comparing Integers and Other Rational Numbers
 Writing and Interpreting Inequality Statements Involving Rational Numbers
 Absolute Value—Magnitude and Distance
 The Relationship Between Absolute Value and Order
 Ordered Pairs
 Locating Ordered Pairs on the Coordinate Plane
 Symmetry in the Coordinate Plane
 Drawing the Coordinate Plane and Points on the Plane
 Distance on the Coordinate Plane
 Problem Solving and the Coordinate Plane

Expressions and Equations
 The Relationship of Addition and Subtraction
 The Relationship of Multiplication and Division
 The Relationship of Multiplication and Addition
 The Relationship of Division and Subtraction
 Exponents
 The Order of Operations
 Replacing Letters with Numbers
 Replacing Numbers with Letters
 Writing Addition and Subtraction Expressions
 Writing and Expanding Multiplication Expressions
 Factoring Expressions
 Distributing Expressions
 Writing Division Expressions
 Read Expressions in Which Letters Stand for Numbers

Area, Surface Area, and Volume Problems
 The Area of Parallelograms Through Rectangle Facts
 The Area of Right Triangles
 The Area of Acute Triangles Using Height and Base
 The Area of All Triangles Using Height and Base
 The Area of Polygons Through Composition and Decomposition
 Distance on the Coordinate Plane
 Drawing Polygons in the Coordinate Plane
 Determining Perimeter and Area of Polygons on the Coordinate Plane
 Volume with Fractional Edge Lengths and Unit Cubes
 From Unit Cubes to the Formulas for Volume
 The Formulas for Volume
 Representing ThreeDimensional Figures Using Nets
 Constructing Nets
 From Nets to Surface Area

Statistics
 Posing Statistical Questions
 Displaying a Data Distribution
 Creating a Dot Plot
 Creating a Histogram
 Describing a Distribution Displayed in a Histogram
 Describing the Center of a Distribution Using the Mean
 The Mean as a Balance Point
 Variability in a Data Distribution
 The Mean Absolute Deviation (MAD)
 Describing Distributions Using the Mean and MAD
 Describing the Center of a Distribution Using the Median
 Describing Variability Using the Interquartile Range (IQR)
 Summarizing a Distribution Using a Box Plot
 Understanding Box Plots
 Developing a Statistical Project
 Connecting Graphical Representations and Numerical Summaries