Gizmos for Arizona - Mathematics: 6th Grade (High Academic Standards for Students adopted 2016)

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

6.RP: Ratio and Proportion

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

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.

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 (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.)

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.NS: The Number System

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

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.

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 a standard algorithm.

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

6.NS.B.4: Use previous understanding of factors to find the greatest common factor and the least common multiple.

6.NS.C: Apply and extend previous understanding 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. Use positive and negative numbers to represent quantities in real-world context, explaining the meaning of 0 in each situation.

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

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.

6.EE: Expressions and Equations

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

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.3: Apply the properties of operations to generate equivalent expressions.

6.EE.A.4: Identify when two expressions are equivalent.

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 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.

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.

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.

6.EE.B.8: Write an inequality of the form 𝑥 > 𝑐, 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.

6.EE.C: Represent and analyze quantitative relationships between dependent and independent variables.

6.EE.C.9: Use variables to represent two quantities that change in relationship to one another to solve mathematical problems and problems in real-world context. Write an equation to express one quantity (the dependent variable) in terms of the other quantity (the independent variable). Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

6.G: Geometry

6.G.A: Solve mathematical problems and problems in real-world context 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 to solve mathematical problems and problems in real-world context.

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.

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.

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 variability in the answers.

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.

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.

6.SP.B: Summarize and describe distributions.

6.SP.B.4: Display and interpret numerical data by creating plots on a number line including histograms, dot plots, and box plots.

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

Correlation last revised: 4/13/2026

Arizona - Mathematics: 6th Grade

High Academic Standards for Students | Adopted: 2016

6.RP: Ratio and Proportion

6.NS: The Number System

6.EE: Expressions and Equations

6.G: Geometry

6.SP: Statistics and Probability