6.RP: Ratios and Proportional Relationships

6.RP.A: Understand ratio and rate concepts and use ratio and rate reasoning to solve problems.

6.RP.A.1: Understand the concept of a ratio including the distinctions between part:part and part:whole and the value of a ratio; part/part and part/whole. Use ratio language to describe a ratio relationship between two quantities.

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

6.RP.A.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship, including the use of units.

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

6.RP.A.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 diagrams, or equations.

6.RP.A.3.a: Make tables of equivalent ratios relating quantities with whole-number measurements. Find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

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

6.RP.A.3.b: Solve unit rate problems, including those involving unit pricing, and constant speed.

Household Energy Usage
Road Trip (Problem Solving)

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

Unit Conversions

6.NS: The Number System

6.NS.A: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Dividing Fractions
Dividing Mixed Numbers

6.NS.B: Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.B.2: Fluently divide multi-digit numbers using the standard algorithm.

No Alien Left Behind (Division with Remainders)

6.NS.B.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

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.B.4: Use prime factorization to 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 relatively prime numbers.

Finding Factors with Area Models
Pattern Flip (Patterns)

6.NS.C: Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.C.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, and positive/negative electric charge). Use positive and negative numbers (whole numbers, fractions, and decimals) to represent quantities in real-world contexts, explaining the meaning of zero in each situation.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Integers, Opposites, and Absolute Values
Multiplying with Decimals
Percents, Fractions, and Decimals
Sums and Differences with Decimals

6.NS.C.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.6.a: 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 zero is its own opposite.

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.C.6.b: Understand signs of numbers in ordered pairs as indicating 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.C.6.c: 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 and Subtracting Integers
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.C.7: Understand ordering and absolute value of rational numbers.

6.NS.C.7.a: Interpret statements of inequality as statements about the relative positions 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.C.7.b: 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.C.7.c: Understand 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.C.7.d: Distinguish comparisons of absolute value from statements about order.

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

6.NS.C.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

6.EE.A: Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Order of Operations

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

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

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

6.EE.A.2.c: 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.A.3: Apply the properties of operations 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.EE.A.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

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

6.EE.B: Reason about and solve one-variable equations and inequalities.

6.EE.B.5: 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
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

6.EE.B.6: 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.B.7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

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

6.EE.B.8: 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

6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.A.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.G.A.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas ?? = ?????? and ?? = ???? to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Prisms and Cylinders

6.G.A.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Points in the Coordinate Plane

6.G.A.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface areas 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

6.SP.A: Develop understanding of statistical variability.

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

Polling: City
Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)

6.SP.A.2: Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center (median, mean, and/or mode), spread (range, interquartile range), and overall shape.

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.A.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.SP.B: Summarize and describe distributions.

6.SP.B.4: Display numerical data in plots on a number line, 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.SP.B.4.a: Read and interpret circle graphs.

Graphing Skills

6.SP.B.5: Summarize numerical data sets in relation to their context, such as by:

6.SP.B.5.b: 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.B.5.c: Giving quantitative measures of center (median, and/or mean) 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.B.5.d: Relating the choice of measures of center and variability to the shape of the data distribution and 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)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)