### MA-06-1: Middle grades students understand fractions, decimals, percents and integers, compare them and locate their relative positions on a number line. They develop and use proportional reasoning to solve problems. They work with large numbers and small numbers. They use factors, multiples and prime factorizations. They perform arithmetic operations with fractions, decimals and integers, use properties in computation, develop fluency and develop strategies to estimate the result of operations on rational numbers.

#### MA-06-1.1: Number Sense

MA-06-1.1.1: Students will provide examples of and identify fractions, decimals and percents.

MA-06-1.1.2: Students will describe and provide examples of representations of numbers (whole numbers, fractions in simplest form, mixed numbers, decimals, percents) and operations in a variety of equivalent forms using models, diagrams, and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences), based on real-world and mathematical problems.

MA-06-1.1.3: Students will convert between any two of the following numbers: fractions, decimals, and percents (less than or equal to 100%); and will compare and order these numbers.

#### MA-06-1.2: Estimation

MA-06-1.2.1: Students will estimate to solve real-world and mathematical problems with whole numbers, fractions, decimals and percents, checking for reasonable and appropriate computational results.

#### MA-06-1.3: Number Operations

MA-06-1.3.2: Students will explain how operations (addition and subtraction; multiplication and division) are inversely related.

#### MA-06-1.4: Ratios and Proportional Reasoning

MA-06-1.4.1: Students will describe and apply ratios to solve real-world problems.

#### MA-06-1.5: Properties of Numbers and Operations

MA-06-1.5.1: Students will identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve real-world and mathematical problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]).

MA-06-1.5.2: Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication and the identity properties for addition and multiplication) to simplify numerical expressions.

### MA-06-2: Students continue to measure and estimate measurements including fractions and decimals. They use formulas to find perimeter, area, circumference and volume. They use rulers and protractors. They use US Customary and metric units of measurement.

#### MA-06-2.1: Measuring Physical Attributes

MA-06-2.1.3: Students will explain how measurements and measurement formulas are related or different (perimeter and area of rectangles).

#### MA-06-2.2: Systems of Measurement

MA-06-2.2.1: Students will convert units within the same measurement system and use these units to solve real-world problems.

MA-6-3.1.1: Students will describe and provide examples of the basic geometric elements (points, rays, lines, segments, angles [acute, right, obtuse], planes, radius, diameter, circumference).

### MA-06-3: Middle grades students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality. They use the Pythagorean theorem.

#### MA-06-3.1: Shapes and Relationships

MA-06-3.1.2: Students will describe, and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles, quadrilaterals, regular polygons), and will apply these elements and figures to solve real-world and mathematical problems.

MA-06-3.1.3: Students will describe, provide examples of, and identify elements (e.g., vertices, angles, faces, edges, congruent parts) of common three-dimensional figures (spheres, cones, cylinders, prisms, and pyramids).

#### MA-06-3.2: Transformations of Shapes

MA-06-3.2.1: Students will describe, provide examples of, and apply line symmetry to real-world and mathematical problems.

#### MA-06-3.3: Coordinate Geometry

MA-06-3.3.1: Students will identify and graph ordered pairs on a positive coordinate system (Quadrant I), correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve real-world and mathematical problems.

### MA-06-4: Middle grades students extend the early development of data representations and examine the appropriateness of graphs and representations of data. They examine central tendencies and dispersion. They develop organized approaches to counting and use experimental and theoretical probabilities.

#### MA-06-4.1: Representations of Data Sets

MA-06-4.1.1: Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots).

MA-06-4.1.2: Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related.

MA-06-4.1.4: Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs), and will explain why the type of display is appropriate for the data.

#### MA-06-4.2: Characteristics of Data Sets

MA-06-4.2.1: Students will determine and apply the mean, median, mode and range of a set of data.

#### MA-06-4.4: Probability

MA-06-4.4.1: Students will describe or determine (e.g., tables, tree diagrams) the sample space of an event for a real-world or mathematical situation.

MA-06-4.4.3: Students will explore the theoretical probability of simple events.

### MA-06-5: Middle grades students extend pattern work to include arithmetic sequences. They use linear functions and linear equations. They plot rational number pairs in the Cartesian plane. They simplify algebraic and numeric expressions. They explore the effects of change on related variables. They use and solve two-step single variable equations and inequalities.

#### MA-06-5.1: Patterns, Relations and Functions

MA-06-5.1.1: Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems.

MA-06-5.1.3: Students will describe, define, provide examples of, and apply to real-world and mathematical problems functions using tables, graphs and verbal rules.

MA-06-5.1.4: Students will explain how tables, graphs and patterns relate to each other.

MA-06-5.1.5: Students will explain how the change in one quantity affects change in another quantity (e.g., in tables or graphs, input/output tables).

#### MA-06-5.2: Variables, Expressions and Operations

MA-06-5.2.2: Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems.

#### MA-06-5.3: Equations and Inequalities

MA-06-5.3.1: Students will model and solve real-world and mathematical problems with simple equations and inequalities (e.g., 8x = 4, x + 2 > 5).

Correlation last revised: 5/11/2018

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