mathispower4u

Grade 6 Common Core Math Lessons  
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6.RP Ratios & Proportional Relationships

6.RP.A.1 — Ratio concepts & language

1. Introduction to Ratios

6.RP.A.2 — Unit rates (a/b for a:b)

1. Unit Rates

6.RP.A.3 — Solve with ratio/reasoning (tables, diagrams, equations)

o 6.RP.A.3a — Equivalent ratios; tables; plot & compare

1. Determining if Rates are Equivalent
2. Solving Problems Using Ratios and Tape Diagrams

o 6.RP.A.3b — Unit-rate problems (pricing, speed, etc.)

1. Unit Rates and Problem Solving (Table)

o 6.RP.A.3c — Percent problems (part, whole, %; discount/markup/tax/tip; % change)

1. Preliminary Skill
   1. Write Fractions as Percents Using Equivalent Fractions with Denominators of 100
   2. Write Fractions as Percent Using Division and Denominator of 100
2. The Percent Proportion to Solve Percent Problems (No Cross Multiplication)
3. Introduction to Proportions and Cross Products
4. The Percent Proportion to Solve Percent Problems (Cross Multiplication)
5. Solve a Percent Problem Using a Double Number Line

o 6.RP.A.3d — Convert measurement units using ratios

1. Unit Conversions Using Equivalent Ratios
2. Video: Unit Conversions using Unit Factors
   1. Example 1: Convert Meters to Millimeters
   2. Example 2: Convert Grams to Kilograms
   3. Example 3: Convert Miles Per Hour to Feet Per Second

6.NS The Number System

6.NS.A.1 — Interpret & compute fraction ÷ fraction; word problems

1. What Does Dividing by a Fraction Mean? Whole Number Divided by Fraction
2. What Does Dividing by a Fraction Mean? Fraction Divided by Fraction
3. What Does Dividing by a Fraction Mean? Fraction Divided by Fraction (Compare to Trad Method)
4. Fraction Division Application: Number of Batches from a Recipe

6.NS.B.2 — Fluently divide multi-digit whole numbers (standard algorithm)

1. Long Division: 4 Digit Divided by 2 Digit – No Remainder
2. Long Division: 4 Digit Divided by 2 Digit – With Remainder

6.NS.B.3 — Fluently add/subtract/multiply/divide decimals

1. Add and Subtract Decimals
2. Decimal Division: Decimal Divided by a Decimal with Whole Number Quotient
3. Decimal Division: Decimal Divided by a Decimal with a Decimal Quotient
4. Decimal App: Find a Total Cost (Multiply and Add Decimals)
5. Decimal Division App: Determine the Length of Pieces of Rope (Decimal Divided by a Whole Number)

6.NS.B.4 — GCF & LCM; use distributive property with common factors

1. Determining GCF and LCM
2. Factor a Sum Using GCF and Distributive Property
3. Factor a Difference Using GCF and the Distributive Property
4. Application of Factoring a Sum – Gift Bags

6.NS.C.5 — Use positive & negative numbers in context; meaning of 0

1. Positive/Negative Integer and Absolute Value App: Vertical Distance Between a Submarine and Bird
2. Positive/Negative Integer and Absolute Value App: Rise in Temperature

6.NS.C.6 — Rational numbers on the number line & coordinate plane

o 6.NS.C.6a — Opposite signs → opposite directions; 0 as origin

1. Introduction to Opposite Integers
2. Using Opposite Integers to Represent Situations and Determining Sums of Opposites

o 6.NS.C.6b — Quadrants; reflections across axes

1. Reflecting Points Across the x-axis and y-axis on the Coordinate Plane

o 6.NS.C.6c — Locate/plot rational numbers & ordered pairs

1. Plotting Decimals on the Number Line
2. Ordering Fractions from Least to Greatest by Plotting Fractions on the Number Line
3. Identify Coordinates of Points on the Coordinate Plane
4. Plotting Points with Integer Coordinates on the Coordinate Plane
5. Plotting Points on the Coordinate Plane with Rational Coordinates 1
6. Plotting Points on the Coordinate Plane with Rational Coordinates 2

6.NS.C.7 — Order & absolute value of rational numbers

o 6.NS.C.7a — Inequalities as positions on a number line

1. Compare the Absolute Value of Integers Using Inequality Symbols
2. Compare Integers and Signed Decimals Using Inequality Symbols
3. Compare Negative Fractions and Mixed Numbers Using Inequality Symbols

o 6.NS.C.7b — Order statements in real-world contexts

1. Compare Two Negative Account Balances

o 6.NS.C.7c — Absolute value as distance/magnitude; interpret in context

1. Determine the Difference of a Negative and Positive Account Balance using Absolute Value
2. Determine the Difference of Two Negative Temperatures using Absolute Value

o 6.NS.C.7d — Distinguish order vs. absolute-value comparisons

1. Write, Compare, and Determine Absolute Value of Integers that Represent Depths Below Sea Level

6.NS.C.8 — Graph in all four quadrants; use absolute value for distances

1. Plot Points on the Coordinate Plane and Determine the Distance from the Axes
2. Plot Points on the Coordinate Plane and Determine the Horizontal and Vertical Distance Between the Points

6.EE Expressions & Equations

6.EE.A.1 — Evaluate numerical expressions with whole-number exponents

1. Evaluate Numerical Expressions with Whole Number Exponents
2. Evaluate Numerical Expressions Using the Order of Operations

6.EE.A.2 — Write/read/evaluate expressions with variables

o 6.EE.A.2a — Translate words ↔ expressions

1. Writing Variable Expressions from Words

o 6.EE.A.2b — Name parts (term, factor, coefficient)

1. Variable Expression Vocabulary

o 6.EE.A.2c — Evaluate at given values; formulas; order of operations

1. Evaluating Variable Expressions
2. Formulas: Determine the Perimeter of a Rectangle

6.EE.A.3 — Use properties to create equivalent expressions

1. The Associative Property of Addition and Multiplication
2. The Commutative Property of Addition and Multiplication
3. Use the Distributive Property to Write Equivalent Expressions
4. Simplifying Variable Expressions

6.EE.A.4 — Identify when expressions are equivalent

1. Determining if Two Expressions are Equivalent

6.EE.B.5 — What it means to solve; test solutions (substitution)

1. Solving Basic Equations and Inequalities by Inspection Only
2. Determining if Values are Solutions to Equations and Inequalities
3. Determining if Values are Solutions to Equations

6.EE.B.6 — Use variables for unknowns or varying quantities

1. Writing Variable Expressions for Situations

6.EE.B.7 — Solve x + p = q and px = q (nonnegative rationals)

1. Solving One Step Equations with Whole Numbers and Decimals
2. Writing and Solving Equations for Real Life Situations

6.EE.B.8 — Write one-variable inequalities; graph solution sets

1. Write and Graph Inequalities that Represent Situations

6.EE.C.9 — Dependent & independent variables; relate tables/graphs to an Equation

1. Write an Equation, Make a Table, and Graph to Model a Situation: Earnings
2. Write an Equation, Make a Table, and Graph to Model a Situation: Plant Growth

6.G Geometry

6.G.A.1 — Areas of triangles, special quadrilaterals, polygons (compose/decompose)

1. Determine the Area of a Pentagon on the Coordinate Plane – Decompose Area
2. Determine the Area of a Rhombus on the Coordinate Plane – Decompose Area

6.G.A.2 — Volume of right rectangular prisms (incl. fractional edges); V=lwhV=\ell w h, V=BhV=Bh

1. Determine the Volume of a Rectangular Prism (Box)

6.G.A.3 — Polygons in the coordinate plane; side lengths parallel to axes

1. Determine the Perimeter of a Polygon on the Coordinate Plane Given the Vertices

6.G.A.4 — Nets of prisms/pyramids; surface area

1. Determine the Surface Area of a Right Rectangular Prism (Box)

6.SP Statistics & Probability

6.SP.A.1 — Statistical questions (variability)

1. Statistical and Non-Statistical Questions

6.SP.A.2 — Distributions described by center, spread, shape

1. Describing Data Distributions: Center, Spread, and Shape

6.SP.A.3 — Center vs. variability—what each summarizes

1. Data with Similar Centers and Different Variability

6.SP.B.4 — Dot plots, histograms, box plots

1. Create a Dot Plot from Data and Find Mode, Range, Median, and Mean
2. Create a Histogram and Analyze Data

6.SP.B.5 — Summarize data in context

o 6.SP.B.5a — Number of observations

o 6.SP.B.5b — Attribute measured & units

1. Determine the Number of Data Value, Attribute, and Unit from a Data Set

o 6.SP.B.5c — Mean/median; IQR/MAD; patterns & outliers

1. Create a Box Plot without Outliers
2. Create a Box Plot with an Outlier

o 6.SP.B.5d — Choose center/variability measures based on shape & context

1. Determine the Best Measure of Center and Variability for Skewed Data
2. Determine the Best Measure of Center and Variability for Symmetric Data