6.NS: The Number System

6.NS.1: Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations).

Dividing Fractions
Dividing Mixed Numbers

6.NS.2: Fluently divide multi-digit whole numbers using a standard algorithmic approach.

No Alien Left Behind (Division with Remainders)

6.NS.3: Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Square Roots
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

6.NS.4: Find common factors and multiples using two whole numbers.

6.NS.4.a: Compute the greatest common factor (GCF) of two numbers both less than or equal to 100.

Pattern Flip (Patterns)

6.NS.4.b: Compute the least common multiple (LCM) of two numbers both less than or equal to 12.

Pattern Flip (Patterns)

6.NS.4.c: Express sums of two whole numbers, each less than or equal to 100, using the distributive property to factor out a common factor of the original addends.

Pattern Flip (Patterns)

6.NS.5: Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Integers, Opposites, and Absolute Values

6.NS.6: Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane.

6.NS.6.a: Understand the concept of opposite numbers, including zero, and their relative locations on the number line.

Adding and Subtracting Integers
Adding on the Number Line
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Solving Algebraic Equations I

6.NS.6.b: Understand that the signs of the coordinates in ordered pairs indicate their location on an axis or in a quadrant on the coordinate plane.

Points in the Coordinate Plane

6.NS.6.c: Recognize when ordered pairs are reflections of each other on the coordinate plane across one axis, both axes, or the origin.

Points in the Coordinate Plane
Rotations, Reflections, and Translations

6.NS.6.d: Plot rational numbers on number lines and ordered pairs on coordinate planes.

Adding and Subtracting Integers
Adding on the Number Line
City Tour (Coordinates)
Elevator Operator (Line Graphs)
Fraction Garden (Comparing Fractions)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Points in the Coordinate Plane
Points, Lines, and Equations
Rational Numbers, Opposites, and Absolute Values
Slope

6.NS.7: Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers.

6.NS.7.a: Interpret statements using equal to (=) and not equal to (≠).

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.NS.7.b: Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

6.NS.7.c: Use concepts of equality and inequality to write and to explain real-world and mathematical situations.

Comparing and Ordering Decimals
Estimating Population Size
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)

6.NS.7.d: Understand that absolute value represents a number’s distance from zero on the number line and use the absolute value of a rational number to represent real-world situations.

Absolute Value with Linear Functions
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.NS.7.e: Recognize the difference between comparing absolute values and ordering rational numbers. For negative rational numbers, understand that as the absolute value increases, the value of the negative number decreases.

Integers, Opposites, and Absolute Values
Points in the Coordinate Plane
Rational Numbers, Opposites, and Absolute Values

6.NS.8: Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers.

6.NS.8.a: Plot points in all four quadrants to represent the problem.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

6.NS.8.b: Find the distance between two points when ordered pairs have the same x-coordinates or same y-coordinates.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

6.NS.8.c: Relate finding the distance between two points in a coordinate plane to absolute value using a number line.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

6.NS.9: Investigate and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100.

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

6.RP: Ratios and Proportional Relationships

6.RP.1: Interpret the concept of a ratio as the relationship between two quantities, including part to part and part to whole.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

6.RP.2: Investigate relationships between ratios and rates.

6.RP.2.a: Translate between multiple representations of ratios (i.e., a/b, a:b, a to b, visual models).

Beam to Moon (Ratios and Proportions)
Household Energy Usage
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

6.RP.2.b: Recognize that a rate is a type of ratio involving two different units.

Beam to Moon (Ratios and Proportions)
Household Energy Usage
Road Trip (Problem Solving)

6.RP.2.c: Convert from rates to unit rates.

Beam to Moon (Ratios and Proportions)
Household Energy Usage
Road Trip (Problem Solving)

6.RP.3: Apply the concepts of ratios and rates to solve real-world and mathematical problems.

6.RP.3.a: Create a table consisting of equivalent ratios and plot the results on the coordinate plane.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Points in the Coordinate Plane
Slope

6.RP.3.c: Use two tables to compare related ratios.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Points in the Coordinate Plane
Slope

6.RP.3.d: Apply concepts of unit rate to solve problems, including unit pricing and constant speed.

Household Energy Usage
Road Trip (Problem Solving)

6.RP.3.e: Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages.

Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Polling: Neighborhood
Real-Time Histogram
Time Estimation

6.RP.3.f: Solve one-step problems involving ratios and unit rates (e.g., dimensional analysis).

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Household Energy Usage
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)
Unit Conversions

6.EEI: Expressions, Equations, and Inequalities

6.EEI.1: Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of Operations.

Order of Operations

6.EEI.2: Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers.

6.EEI.2.a: Translate between algebraic expressions and verbal phrases that include variables.

Improper Fractions and Mixed Numbers
Multiplying with Decimals
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

6.EEI.2.b: Investigate and identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and factor.

Compound Interest
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Equations
Using Algebraic Expressions

6.EEI.2.c: Evaluate real-world and algebraic expressions for specific values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to whole-numbers.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Solving Equations on the Number Line

6.EEI.3: Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

6.EEI.4: Apply mathematical properties (e.g., commutative, associative, distributive) to justify that two expressions are equivalent.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

6.EEI.5: Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.

Circles
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

6.EEI.6: Write expressions using variables to represent quantities in real-world and mathematical situations. Understand the meaning of the variable in the context of the situation.

Equivalent Algebraic Expressions I
Solving Algebraic Equations II
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

6.EEI.7: Write and solve one-step linear equations in one variable involving nonnegative rational numbers for real-world and mathematical situations.

Absolute Value Equations and Inequalities
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations on the Number Line

6.EEI.8: Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations.

6.EEI.8.a: Write an inequality of the form x > c or x < c and graph the solution set on a number line.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

6.EEI.8.b: Recognize that inequalities have infinitely many solutions.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

6.EEI.9: Investigate multiple representations of relationships in real-world and mathematical situations.

6.EEI.9.c: Translate among graphs, tables, and equations.

Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Introduction to Functions
Points, Lines, and Equations

6.GM: Geometry and Measurement

6.GM.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

6.GM.2: Use visual models (e.g., model by packing) to discover that the formulas for the volume of a right rectangular prism (V = lwh, V = Bh) are the same for whole or fractional edge lengths. Apply these formulas to solve real-world and mathematical problems.

Prisms and Cylinders

6.GM.3: Apply the concepts of polygons and the coordinate plane to real-world and mathematical situations.

6.GM.3.a: Given coordinates of the vertices, draw a polygon in the coordinate plane.

Points in the Coordinate Plane

6.GM.3.b: Find the length of an edge if the vertices have the same x-coordinates or same y-coordinates.

Points in the Coordinate Plane

6.GM.4: Unfold three-dimensional figures into two-dimensional rectangles and triangles (nets) to find the surface area and to solve real-world and mathematical problems.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

6.DS: Data Analysis and Statistics

6.DS.1: Differentiate between statistical and non-statistical questions.

Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Polling: City
Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

6.DS.2: Use center (mean, median, mode), spread (range, interquartile range, mean absolute value), and shape (symmetrical, skewed left, skewed right) to describe the distribution of a set of data collected to answer a statistical question.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

6.DS.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

6.DS.4: Select and create an appropriate display for numerical data, including dot plots, histograms, and box plots.

Box-and-Whisker Plots
Histograms
Mascot Election (Pictographs and Bar Graphs)
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

6.DS.5: Describe numerical data sets in relation to their real-world context.

6.DS.5.a: State the sample size.

Polling: City
Polling: Neighborhood
Populations and Samples

6.DS.5.b: Describe the qualitative aspects of the data (e.g., how it was measured, units of measurement).

Box-and-Whisker Plots
Movie Reviewer (Mean and Median)
Polling: City
Polling: Neighborhood
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

6.DS.5.c: Give measures of center (median, mean).

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

6.DS.5.d: Find measures of variability (interquartile range, mean absolute deviation) using a number line.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

6.DS.5.e: Describe the overall pattern (shape) of the distribution.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

6.DS.5.f: Justify the choices for measure of center and measure of variability based on the shape of the distribution.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

6.DS.5.g: Describe the impact that inserting or deleting a data point has on the measures of center (median, mean) for a data set.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots