### MA-08-1: 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-08-1.1: Number Sense

MA-08-1.1.1: Students will provide examples of and identify rational numbers and irrational numbers (square roots and pi only).

MA-08-1.1.2: Students will describe and provide examples of representations of numbers (rational, square roots, and pi) 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-08-1.1.3: Students will convert, compare and order multiple numerical representations (e.g., fractions, decimals, percentages) of rational numbers and irrational numbers (square roots and pi only).

#### MA-08-1.2: Estimation

MA-08-1.2.1: Students will estimate to solve real-world and mathematical problems with rational numbers, checking for reasonable and appropriate computational results.

#### MA-08-1.3: Number Operations

MA-08-1.3.1: Students will add, subtract, multiply and divide rational numbers to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions.

MA-08-1.3.2: Students will explain how operations (additions and subtraction; multiplication and division; squaring and taking the square root of a number) are inversely related.

#### MA-08-1.4: Ratios and Proportional Reasoning

MA-08-1.4.1: Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, constant rate of change, unit pricing, percent of increase or decrease).

#### MA-08-1.5: Properties of Numbers and Operations

MA-08-1.5.2: Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication, the identity properties for addition and multiplication, inverse properties and the distributive property of multiplication over addition and subtraction) to justify a given step in solving problems.

### MA-08-2: 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-08-2.1: Measuring Physical Attributes

MA-08-2.1.3: Students will evaluate the measures of angles by estimation, measurement with a protractor or angle ruler and determine angle measures in mathematical and/or real-world situations (e.g., supplementary, external, vertical).

MA-08-2.1.4: Students will apply formulas to determine the volume of right rectangular prisms in real-world problems.

MA-08-2.1.5: Students will use formulas to find surface area of right rectangular prisms in real-world and mathematical problems.

MA-08-2.1.6: Students will apply the Pythagorean theorem to determine the length of a hypotenuse.

#### MA-08-2.2: Systems of Measurement

MA-08-2.2.1: Students will convert units within the same measurement system and use these units to solve real-world problems.

### MA-08-3: 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-08-3.1: Shapes and Relationships

MA-08-3.1.1: Students will describe and provide examples of basic geometric elements that include points, segments, rays, lines, angles, and planes and will use these elements in real-world and mathematical problems.

MA-08-3.1.2: Students will identify and compare properties of two-dimensional figures (circles, triangles acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular/irregular polygons), and will apply these properties and figures to solve real-world and mathematical problems.

MA-08-3.1.4: Students will:

MA-08-3.1.4.a: provide examples of congruent and similar figures;

MA-08-3.1.4.b: apply congruent and similar figures to solve real-world and mathematical problems and

MA-08-3.1.4.c: apply proportional reasoning to solve problems involving scale drawings and proportional figures.

#### MA-08-3.2: Transformations of Shapes

MA-08-3.2.1: Students will describe, provide examples of, and apply to real-world and mathematical problems rotational symmetry (90º, 180º, 360º).

MA-08-3.2.2: Students will transform (translations, reflections, and dilations with the center of dilation at the origin) figures in a coordinate plane and determine the new coordinates of the image after the transformation.

MA-08-3.2.3: Students will identify rotations (clockwise or counterclockwise) of figures about the origin in a coordinate plane.

#### MA-08-3.3: Coordinate Geometry

MA-08-3.3.1: Students will identify and graph ordered pairs on a coordinate system, correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve real-world and mathematical problems.

### MA-08-4: 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-08-4.1: Representations of Data Sets

MA-08-4.1.1: 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, scatter plots, histograms, box-and-whiskers plots).

MA-08-4.1.4: Students will:

MA-08-4.1.4.a: construct data displays (Venn diagrams, tables, line graphs, stem-and-leaf plots, circle graphs, scatter plots);

MA-08-4.1.4.b: explain why the type of display is appropriate for the data and

MA-08-4.1.5: Students will construct box-and-whiskers plots.

#### MA-08-4.2: Characteristics of Data Sets

MA-08-4.2.1: Students will:

MA-08-4.2.1.a: determine the mean, median, mode, and range of a set of data;

MA-08-4.2.1.b: identify clusters, gaps, and outliers and

MA-08-4.2.1.c: apply these concepts to compare sets of data.

#### MA-08-4.3: Experiments and Samples

MA-08-4.3.1: Students will explain how data gathering, bias issues, and faulty data analysis can affect the results of data collection.

#### MA-08-4.4: Probability

MA-08-4.4.2: Students will:

MA-08-4.4.2.a: determine theoretical probabilities of simple events;

MA-08-4.4.2.b: determine probabilities based on the results of an experiment and

MA-08-4.4.3: Students will tabulate experimental results from simulations and explain how theoretical and experimental probabilities are related.

### MA-08-5: 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-08-5.1: Patterns, Relations and Functions

MA-08-5.1.2: Students will represent, analyze and generalize simple first and second degree relationships using tables, graphs, words and algebraic notations, and will apply the relationships to solve real-world and mathematical problems.

#### MA-08-5.2: Variables, Expressions and Operations

MA-08-5.2.1: Students will evaluate and simplify algebraic expressions applying the order of operations.

MA-08-5.2.2: Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems.

#### MA-08-5.3: Equations and Inequalities

MA-08-5.3.1: Students will model and solve single variable, first-degree real-world and mathematical problems (e.g., 5x + 2 = x + 22, x-4 < -60).

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.