### PR: Proportional Reasoning

#### 1.1: Develop an understanding of ratio concepts and use reasoning about ratios to solve problems.

PR.1: Students will… Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

PR.2: Students will… Use unit rates to represent and describe ratio relationships.

PR.3: Students will… Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

### NO: Number Systems and Operations

#### 2.1: Use prior knowledge of multiplication and division to divide fractions.

NO.4: Students will… Interpret and compute quotients of fractions using visual models and equations to represent problems.

NO.4.a: Use quotients of fractions to analyze and solve problems.

#### 2.2: Compute multi-digit numbers fluently and determine common factors and multiples.

NO.5: Students will… Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.

NO.6: Students will… Add, subtract, multiply, and divide decimals using a standard algorithm.

NO.7: Students will… Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

NO.8: Students will… Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

NO.8.a: Use factors and multiples to determine prime factorization.

#### 2.3: Apply knowledge of the number system to represent and use rational numbers in a variety of forms.

NO.9: Students will… Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.

NO.10: Students will… Locate integers and other rational numbers on a horizontal or vertical line diagram.

NO.10.a: Define opposites as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

NO.10.b: Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

NO.11: Students will… Find the position of pairs of integers and other rational numbers on the coordinate plane.

NO.11.a: Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

NO.11.b: Identify (a, b) and (a, –b) as reflections across the x-axis.

NO.11.c: Identify (a, b) and (–a, b) as reflections across the y-axis.

NO.11.d: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

NO.12: Students will… Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts.

NO.13: Students will… Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.

### AF: Algebra and Functions

#### 3.1: Apply knowledge of arithmetic to read, write, and evaluate algebraic expressions.

AF.14: Students will… Write, evaluate, and compare expressions involving whole number exponents.

AF.15: Students will… Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

AF.15.a: Interpret a variable as an unknown value for any number in a specified set, depending on the context.

AF.15.b: Write expressions to represent verbal statements and real-world scenarios.

AF.15.c: Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

AF.15.d: Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.

AF.16: Students will… Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.

AF.17: Students will… Determine whether two expressions are equivalent and justify the reasoning.

#### 3.2: Use equations and inequalities to represent and solve real-world or mathematical problems.

AF.18: Students will… Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.

AF.19: Students will… Write and solve an equation in the form of x + p = q or px = q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematical problems.

AF.19.a: Interpret the solution of an equation in the context of the problem.

AF.20: Students will… Write and solve inequalities in the form of x > c, x < c, x >= c, or x <= c to represent a constraint or condition in a real-world or mathematical problem.

AF.20.a: Interpret the solution of an inequality in the context of a problem.

AF.20.b: Represent the solutions of inequalities on a number line and explain that the solution set may contain infinitely many solutions.

#### 3.3: Identify and analyze relationships between independent and dependent variables.

AF.21: Students will… Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.

AF.21.a: Use tables, graphs, and equations to represent the relationship between independent and dependent variables.

### DSP: Data Analysis, Statistics, and Probability

#### 4.1: Use real-world and mathematical problems to analyze data and demonstrate an understanding of statistical variability and measures of center.

DSP.22: Students will… Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.

DSP.23: Students will… Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.

DSP.23.a: Determine which measure of center best represents a real-world data set.

DSP.23.b: Interpret the measures of center and variability in the context of a problem.

DSP.24: Students will… Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.

DSP.24.a: Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).

DSP.24.b: Use graphical representations of real-world data to describe the context from which they were collected.

### GM: Geometry and Measurement

#### 5.1: Graph polygons in the coordinate plane to solve real-world and mathematical problems.

GM.25: Students will… Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems.

GM.25.a: Determine missing vertices of a rectangle with the same x-coordinate or the same y-coordinate when graphed in the coordinate plane.

GM.25.b: Use coordinates to find the length of a side between points having the same x-coordinate or the same y-coordinate.

#### 5.2: Solve real-world and mathematical problems to determine area, surface area, and volume.

GM.26: Students will… Calculate the area of triangles, special quadilaterals, and other polygons by composing and decomposing them into known shapes.

GM.26.a: Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.

GM.27: Students will… Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems.

GM.28: Students will… Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

GM.28.a: Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.

Correlation last revised: 3/2/2020

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