6.RP: Ratios and Proportional Relationships

1.1: Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.2: Use unit rate language (“for each one”, “for every one” and “per”) and unit rate notation to demonstrate understanding the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0.

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

6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagram, or using calculations).

6.RP.3a: Make tables of equivalent ratios relating quantities with whole-number measurements, find the missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed.

Function Machines 2 (Functions, Tables, and Graphs)
Household Energy Usage
Points, Lines, and Equations
Road Trip (Problem Solving)
Slope

6.RP.3b: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Polling: Neighborhood
Real-Time Histogram
Time Estimation

6.RP.3c: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Unit Conversions

6.NS: The Number System

2.1: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, requiring multiple exposures connecting various concrete and abstract models.

Dividing Fractions
Dividing Mixed Numbers

2.2: Compute fluently (efficiently, accurately, and flexibly) with multi-digit numbers and find common factors and multiples.

6.NS.3: Fluently (efficiently, accurately, and flexibly) add, subtract, multiply, and divide multi-digit decimals using an efficient algorithm for each operation.

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

6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Pattern Flip (Patterns)

2.3: Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.5: Understand positive and negative numbers to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge);

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

6.NS.5a: Use positive and negative numbers to represent quantities in real-world contexts,

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

6.NS.5b: Explaining the meaning of 0 in each situation.

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

6.NS.6: Understand a rational number as a point on the number line and a coordinate pair as a location on a coordinate plane.

6.NS.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, (e.g., -(-3) = 3,) and that 0 is its own opposite.

Adding and Subtracting Integers
Adding on the Number Line
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.NS.6b: Recognize signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Points in the Coordinate Plane

6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Adding on the Number Line
City Tour (Coordinates)
Elevator Operator (Line Graphs)
Fraction Garden (Comparing Fractions)
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

6.NS.7: Understand ordering and absolute value of rational numbers.

6.NS.7a: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

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

6.NS.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts.

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

6.NS.7c: Explain the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

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

6.NS.7d: Distinguish comparisons of absolute value from statements about order.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.NS.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

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

6.EE: Expressions and Equations

3.1: Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.1: Write and evaluate numerical expressions involving whole-number exponents.

Order of Operations

6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.2a: Write expressions that record operations with numbers and with letters standing for numbers.

Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

6.EE.2b: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

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

6.EE.2c: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

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

6.EE.3: Apply the properties of operations and combine like terms, with the conventions of algebraic notation, to identify and generate equivalent expressions.

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

3.2: Reason about and solve one-variable equations and inequalities.

6.EE.4: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Compound Inequalities
Linear Inequalities in Two Variables
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

6.EE.5: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

6.EE.7: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

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.G: Geometry

4.1: Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.1: Find the area of all triangles, special quadrilaterals (including parallelograms, kites and trapezoids), and polygons whose edges meet at right angles (rectilinear figure 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.G.2: Find the volume of a right rectangular prism with fractional edge lengths by applying the formulas ?? = ????? and ?? = ??? (?? is the area of the base and ? is the height) to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (Builds on the 5th grade concept of packing unit cubes to find the volume of a rectangular prism with whole number edge lengths.)

Prisms and Cylinders

6.G.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

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

6.SP: Statistics and Probability

5.1: Develop concepts of statistical measures of center and variability and an informal understanding of outlier.

6.SP.1: Recognize and generate a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)

6.SP.2: Analyze a set of data collected to answer a statistical question with a distribution which can be described by its center (mean, median and/or mode), spread (range and/or interquartile range), and overall shape (cluster, peak, gap, symmetry, skew (data) and/or outlier).

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
Sight vs. Sound Reactions
Stem-and-Leaf Plots

6.SP.3: Recognize that a measure of center (mean, median and/or mode) for a numerical data set summarizes all of its values with a single number, while a measure of variation (range and/or interquartile range) 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)
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

5.2: Summarize and describe distributions.

6.SP.4: Display numerical data on dot plots, histograms, stem-and-leaf plots, 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.SP.5: Summarize numerical data sets in relation to their context, such as by:

6.SP.5b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Box-and-Whisker Plots
Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

6.SP.5c: Giving quantitative measures of center (mean, median and/or mode) and variability (range and/or interquartile range), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

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.SP.5d: Relating the choice of measures of center and variability to the distribution of the data.

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)