### 6.RP: Ratios and Proportional Relationships

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

6.RP.A.1: Understand the concept of a ratio and 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. Use rate language in the context of a ratio relationship.

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.

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

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.

6.RP.A.3.d: Use ratio reasoning to convert customary and metric measurement units (within the same system); manipulate and transform units appropriately when multiplying or dividing quantities.

### 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 contextual problems involving division of fractions by fractions (e.g., using visual fraction models and equations to represent the problem is suggested).

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

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

#### 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, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

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.

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.

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 position of two numbers on a number line diagram.

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

6.NS.C.7.c: Understand the absolute value of a rational number as its distance from 0 on the number line and distinguish comparisons of absolute value from statements about order in a real-world context.

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.

### 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.

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

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

6.EE.A.2.b: 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.

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).

6.EE.A.3: Apply the properties of operations (including, but not limited to, commutative, associative, and distributive properties) to generate equivalent expressions. The distributive property is prominent here.

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

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

6.EE.B.5: Understand solving an equation or inequality is carried out by determining if any of the values from a given set make the 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 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.

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

6.EE.B.8: Interpret and write an inequality of the form x > c or x < c which represents a condition or constraint in a real-world or mathematical problem. Recognize that inequalities have infinitely many solutions; represent solutions of inequalities on number line diagrams.

### 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; know and apply these techniques in the context of solving real-world and mathematical problems.

6.G.A.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or horizontal segments only). Know and apply these techniques in the context of solving real-world and mathematical problems.

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 in the context of solving real-world and mathematical problems.

### 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.

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 (mean, median, mode), spread (range), 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 describes how its values vary with a single number.

#### 6.SP.B: Summarize and describe distributions.

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

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

6.SP.B.5.c: Give quantitative measures of center (median and/or mean) and variability (range) as well as describing any overall pattern with reference to the context in which the data were gathered.

6.SP.B.5.d: Relate the choice of measures of center to the shape of the data distribution and the context in which the data were gathered.

Correlation last revised: 11/21/2018

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