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

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

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 on the Number Line
 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

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.

 Rotations, Reflections, and Translations

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

 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)
 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

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
 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

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

 Points in the Coordinate Plane

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.

 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)
 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.

 Household Energy Usage

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

 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.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.

 Percent of Change
 Percents and Proportions
 Percents, Fractions, and Decimals
 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)

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
 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.

 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
 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.

 Solving Equations on the Number Line
 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.

 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
 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.

 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 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
 Pythagorean Theorem with a Geoboard

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.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)
 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)
 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
 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).

 Polling: City
 Polling: Neighborhood
 Populations and Samples

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)
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)
 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

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

Correlation last revised: 1/19/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.