Academic Standards

6.RP.A.1: Understand the concept of a ratio as comparing two quantities multiplicatively or joining/composing the two quantities in a way that preserves a multiplicative relationship. 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 (e.g., for every, for each, for each 1, per) in the context of a ratio relationship. (Complex fraction notation is not an expectation for unit rates in this grade level.)

Beam to Moon (Ratios and Proportions)

Household Energy Usage

Road Trip (Problem Solving)

6.RP.A.3: Use ratio and rate reasoning to solve mathematical problems and problems in real-world context (e.g., by reasoning about data collected from measurements, tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

6.RP.A.3a: 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.

Function Machines 2 (Functions, Tables, and Graphs)

Points, Lines, and Equations

Slope

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

Household Energy Usage

Road Trip (Problem Solving)

6.RP.A.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity). Solve percent problems with the unknown in all positions of the equation.

Percent of Change

Percents and Proportions

Percents, Fractions, and Decimals

Polling: Neighborhood

Real-Time Histogram

Time Estimation

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

6.NS.A.1: Interpret and compute quotients of fractions to solve mathematical problems and problems in real-world context involving division of fractions by fractions using visual fraction models and equations to represent the problem.

Dividing Fractions

Dividing Mixed Numbers

6.NS.B.3: Fluently add, subtract, multiply, and divide multi-digit decimals 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

6.NS.C.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real-world context, 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.C.6: Understand a rational number can be represented 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.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 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.C.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.C.7: Understand ordering and absolute value of rational numbers.

6.NS.C.7a: Interpret statements of inequality as statements about the relative position of two numbers on a 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.C.7b: Write, interpret, and explain statements of order for rational numbers in real-world context.

Estimating Population Size

Integers, Opposites, and Absolute Values

Modeling Decimals (Area and Grid Models)

6.NS.C.7c: 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 real-world context.

Absolute Value with Linear Functions

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

6.NS.C.7d: Distinguish comparisons of absolute value from statements about order in mathematical problems and problems in real-world context.

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

6.NS.C.8: Solve mathematical problems and problems in real-world context 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.A.1: Write and evaluate numerical expressions involving whole-number exponents.

6.EE.A.2: Write, read, and evaluate algebraic expressions.

6.EE.A.2a: Write expressions that record operations with numbers and variables.

Solving Equations on the Number Line

Using Algebraic Equations

Using Algebraic Expressions

6.EE.A.2b: 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

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Equations

Using Algebraic Expressions

6.EE.A.2c: Evaluate expressions given specific values of their variables. Include expressions that arise from formulas used to solve mathematical problems and problems in real-world context. 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).

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.

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Modeling the Factorization of *x*^{2}+*bx*+*c*

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

6.EE.B.5: Understand solving an equation or inequality as a process of reasoning to find the value(s) of the variables that make that 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.B.6: Use variables to represent numbers and write expressions when solving mathematical problems and problems in real-world context; understand that a variable can represent an unknown number or any number in a specified set.

Solving Equations on the Number Line

Using Algebraic Equations

Using Algebraic Expressions

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

Absolute Value Equations and Inequalities

Solving Equations on the Number Line

6.EE.B.8: Write an inequality of the form x > x, x < c, x >= c, or x <= c to represent a constraint or condition to solve mathematical problems and problems in real-world context. Recognize that inequalities have infinitely many solutions; represent solutions of such inequalities on number lines.

Absolute Value Equations and Inequalities

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Solving Linear Inequalities in One Variable

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 to solve mathematical problems and problems in real-world context.

Area of Parallelograms

Area of Triangles

Fido's Flower Bed (Perimeter and Area)

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 to solve mathematical problems and problems in a real-world context.

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 area of these figures. Apply these techniques to solve mathematical problems and problems in real-world context.

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

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

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 whose general characteristics can be described by its center, spread, 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

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 uses a single number to describe the spread of the 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)

Real-Time Histogram

Stem-and-Leaf Plots

6.SP.B.4: Display and interpret numerical data by creating plots on a number line including histograms, dot 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.B.5: Summarize numerical data sets in relation to their context by:

6.SP.B.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.B.5c: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), 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.5d: 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)

6.1.1: Mathematically proficient students explain to themselves the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. While engaging in productive struggle to solve a problem, they continually ask themselves, “Does this make sense?' to monitor and evaluate their progress and change course if necessary. Once they have a solution, they look back at the problem to determine if the solution is reasonable and accurate. Mathematically proficient students check their solutions to problems using different methods, approaches, or representations. They also compare and understand different representations of problems and different solution pathways, both their own and those of others.

Biconditional Statements

Conditional Statements

Estimating Population Size

6.2.1: Mathematically proficient students make sense of quantities and their relationships in problem situations. Students can contextualize and decontextualize problems involving quantitative relationships. They contextualize quantities, operations, and expressions by describing a corresponding situation. They decontextualize a situation by representing it symbolically. As they manipulate the symbols, they can pause as needed to access the meaning of the numbers, the units, and the operations that the symbols represent. Mathematically proficient students know and flexibly use different properties of operations, numbers, and geometric objects and when appropriate they interpret their solution in terms of the context.

Estimating Population Size

Using Algebraic Expressions

6.3.1: Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.

6.4.1: Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Estimating Population Size

Using Algebraic Expressions

6.6.1: Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.

Biconditional Statements

Using Algebraic Expressions

6.7.1: Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

6.8.1: Mathematically proficient students look for and describe regularities as they solve multiple related problems. They formulate conjectures about what they notice and communicate observations with precision. While solving problems, students maintain oversight of the process and continually evaluate the reasonableness of their results. This informs and strengthens their understanding of the structure of mathematics which leads to fluency.

Correlation last revised: 4/4/2018

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