AR.Math.Content.6.RP: Ratios and Proportional Relationships

AR.Math.Content.6.RP.A: Understand ratio concepts and use ratio reasoning to solve problems.

AR.Math.Content.6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Part-to-part and Part-to-whole Ratios

AR.Math.Content.6.RP.A.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

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

AR.Math.Content.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. Use and create tables to compare equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Solve unit rate problems including those involving unit pricing and constant speed. 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. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Household Energy Usage
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Points in the Coordinate Plane
Points, Lines, and Equations
Polling: Neighborhood
Real-Time Histogram
Road Trip (Problem Solving)
Slope
Time Estimation
Unit Conversions

AR.Math.Content.6.NS: The Number System

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

AR.Math.Content.6.NS.A.1: Interpret and compute quotients of fractions. Solve word problems involving division of fractions by fractions (e.g., by using various strategies, including but not limited to, visual fraction models and equations to represent the problem).

Dividing Fractions
Dividing Mixed Numbers

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

AR.Math.Content.6.NS.B.2: Use computational fluency to divide multi-digit numbers using a standard algorithm.

No Alien Left Behind (Division with Remainders)

AR.Math.Content.6.NS.B.3: Use computational fluency to add, subtract, multiply, and divide multi-digit decimals and fractions using a 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

AR.Math.Content.6.NS.B.4: Find the greatest common factor of two whole numbers less than or equal to 100 using prime factorization as well as other methods. Find the least common multiple of two whole numbers less than or equal to 12 using prime factorization as well as other methods. 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.

Finding Factors with Area Models
Pattern Flip (Patterns)

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

AR.Math.Content.6.NS.C.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values, explaining the meaning of 0. (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

AR.Math.Content.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. 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. 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. 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
Solving Algebraic Equations I

AR.Math.Content.6.NS.C.7: Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 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. Distinguish comparisons of absolute value from statements about order.

Absolute Value with Linear Functions
Comparing and Ordering Decimals
Estimating Population Size
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Points in the Coordinate Plane
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

AR.Math.Content.6.NS.C.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Use 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

AR.Math.Content.6.EE: Expressions and Equations

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

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

Order of Operations

AR.Math.Content.6.EE.A.2: Write, read, and evaluate expressions in which letters (variables) stand for numbers. Write expressions that record operations with numbers and with letters standing for numbers. 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. 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).

Compound Interest
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

AR.Math.Content.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

AR.Math.Content.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
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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

AR.Math.Content.6.EE.B.5: Understand solving an equation or inequality as a process of answering a question: Using substitution, which values from a specified set, if any, make the 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

AR.Math.Content.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 any number in a specified set.

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

AR.Math.Content.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

AR.Math.Content.6.EE.B.8: For real world or mathematical problems, write an inequality of the form x > c, x ≥ c, x < c, or x ≤ c to represent a constraint or condition, 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

AR.Math.Content.6.G: Geometry

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

AR.Math.Content.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

AR.Math.Content.6.G.A.2: Find the volume of a right rectangular prism including whole number and 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 V = l w h and V = B h to find volumes of right rectangular prisms including fractional edge lengths in the context of solving real-world and mathematical problems.

Prisms and Cylinders

AR.Math.Content.6.G.A.3: Apply the following techniques in the context of solving real-world and mathematical problems. 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.

Points in the Coordinate Plane

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

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

AR.Math.Content.6.SP: Statistics and Probability

AR.Math.Content.6.SP.A: Develop understanding of statistical variability.

AR.Math.Content.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)

AR.Math.Content.6.SP.A.2: Determine center, spread, and overall shape from a set of data.

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

AR.Math.Content.6.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number (such as mean, median, or mode), while a measure of variation (such as Interquartile Range or Mean Absolute Deviation) 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

AR.Math.Content.6.SP.B: Summarize and describe distributions.

AR.Math.Content.6.SP.B.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Box-and-Whisker Plots
Graphing Skills
Histograms
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

AR.Math.Content.6.SP.B.5: Summarize numerical data sets in relation to their context, such as by: Reporting the number of observations. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Calculate quantitative measures of center (including but not limited to median and/or mean) and variability (including but not limited to interquartile range and/or mean absolute deviation). Use the calculations to describe any overall pattern and any striking deviations (outliers) from the overall pattern with reference to the context in which the data were gathered. 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
Estimating Population Size
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