Mathematics Standards

Sixth Grade

B= Beginning D= Developing S= Secure

Problem Solving

Solves problems that arise in math and in other content areas:

• Builds new mathematical knowledge through problem solving  (D/S)
• Makes, investigates, and applies a variety of strategies to solve problems (D/S)
• Develops and evaluates inferences and predictions that are based on data  (D/S)
• Uses a Problem-Solving Plan  (D/S)
• Draws a Diagram  (D/S)
• Makes an organized list   (D/S)
• Solves a Simpler Problem and Look for a Pattern  (D/S)
• Tries, Checks, and Revises and Work Backward  (D/S)
• Maps and Scale Drawings (D/S)

Communicates mathematical thinking coherently and clearly:

• Uses mathematical language to express ideas   (D/S)
• Shows connections among mathematical ideas  (D/S)
• Creates and uses representations to organize, record, and communicate mathematical ideas   (D/S)
• Writes in Math to Explain   (D/S)
• Solves Mathematical equations using the customary system   (D/S)
• Creates circle, line, and bar graphs (D/S)

Number and Operations

Understands numbers, ways of representing numbers, relationships among numbers, and number systems:

• Understands Whole Numbers (D/S)
• Reads and Writes Decimals (D/S)
• Compares and Orders Decimals (D/S)
• Estimates with Decimals (D/S)
• Adds and Subtracts Decimals (D/S)
• Multiplies Decimals (D/S)
• Divides Decimals (D/S)
• Understands order of Operations (D/S)
• Demonstrates divisibility and Mental Math (D/S)
• Prime Numbers and Prime Factorization (D/S)
• Greatest Common Factor (D/S)
• Prime Numbers (D/S)
• Least Common Multiple (D/S)

Understands meanings of operations and how they relate to one another:

• Prime Factorization (D/S)
• Equivalent Fractions (D/S)
• Applies Decimals in Real World (D/S)
• Applies Pattern in Real World (D/S)
• Applies Fractions in Real World (D/S)
• Applies Mixed Numbers Real World (D/S)
• Applies Fractions Real World (D/S)
• Applies Rational Numbers (D/S)
• Applies Percents, Fractions, and Decimals (D/S)

Compute fluently and make reasonable estimates:

• Divisibility and Mental Math (D/S)
• Greatest Common Factor (D/S)
• Mixed Numbers (D/S)
• Compares and Orders Fractions (D/S)
• Fractions:  Estimating Sums and Differences (D/S)
• Fractions with Like and Unlike Denominators (D/S)
• Adds & Subtracts  Mixed Numbers (D/S)
• Multiplies fractions (D/S)
• Multiplies Mixed Numbers (D/S)
• Divides Fractions (D/S)
• Divides Mixed Numbers (D/S)
• Uses Cross Products (D/S)
• Exponents and Order of Operations (D/S)
• Compares and Orders Fractions (D/S)
• Estimates with Fractions and Mixed Numbers (D/S)

Algebra

Understands patterns, relations and functions:

• Describes a Pattern (D/S)
• Variable and Expressions (D/S)
• Writes Algebraic Expressions (D/S)
• Uses Number Sense to Solve One-Step Equations (D/S)
• Solves Addition and Subtraction Equations (D/S)
• Solves Multiplication and Division Equations (D/S)
• Uses cross products (D/S)
• Solves Two-Step equations   (D/S)
• Inequalities   (D/S)
• Solves one-step inequalities   (D/S)
• Explores square roots and rational numbers   (D/S)
• Introduces the Pythagorean Theorem   (D/S)
• Compares and Orders Integers (D/S)
• Adds and Subtracts Integers (D/S)
• Multiplies and Divides Integers (D/S)
• Order of Operations and the Distributive Property (D/S)
• Scientific Notation  (D/S)
• Prime Factorizations (D/S)
• Solves Proportions  (D/S)
• Solves Percent Problems Using Proportions  (D/S)
• Solves Percent Problems Using Equations (D/S)
• Applies  Percent  (D/S)

Represents and analyzes mathematical situations and structures using algebraic symbols:

• Writes an algebraic equation   (D/S)
• Graphs functions   (D/S)
• Graphs in  the coordinate plane   (D/S)
• Evaluates and Writes Algebraic Expressions  (D/S)
• Explores and Solves Two-Step Equations (D/S)

Uses mathematical models to represent and understand quantitative relationships:

• Makes a Table and Looks for a Pattern (D/S)
• Understands relationship between data and bar graphs (D/S)
• Uses Models to Solve Equations (D/S)
• Equations with fractions (D/S)
• Bar, line and circle graphs (D/S)
• Graphs in the coordinate plane   (D/S)
• Graphs and Writes Inequalities (D/S)

Geometry

Analyzes characteristics and properties of two-and three-dimensional geometric shapes and develops mathematical arguments about geometrical relationships:

• Points, Lines, Segments, and Rays   (D/S)
• Angles   (D/S)
• Congruent and Similar figures   (D/S)
• Lines and Planes (D/S)
• Estimates Length and Area (D/S)
• Areas of Parallelograms and Triangles (D/S)
• Areas of Other Figures (D/S)

Specifies locations and describes spatial relationships using coordinate geometry and other representational systems:

• Uses a Number line   (D/S)
• Adds  and subtracts integers   (D/S)
• Multiplies and divides integers   (D/S)
• Measures and Classifies Angles (D/S)
• Quadrilaterals and Other Polygons (D/S)
• Congruent Figures (D/S)
• Circumferences and Areas of Circles (D/S)
• Square Roots and Irrational Numbers (D/S)
• Three Dimensional Figures (D/S)

Applies transformations and uses symmetry to analyze mathematical situations:

• Line symmetry   (D/S)
• Transformations and Tessellations   (D/S)

Uses visualization, spatial reasoning, and geometric modeling to solve problems:

• Classifies triangles   (D/S)
• Classifies polygons   (D/S)
• Surface area of prisms and cylinders   (D/S)

• Three-Dimensional figures and spatial reasoning (D/S)

Measurement

Understands measurable attributes of objects and the units, systems, and processes of measurement:

• Measures Elapsed Time   (D/S)
• Metric Units of Length, Mass, and Capacity   (D/S)
• Perimeters and areas of rectangles   (D/S)
• Areas of Parallelograms, triangles   (D/S)
• Circles and Circumference   (D/S)
• Area of a circle   (D/S)
• Volumes of Rectangular Prisms and Cylinders   (D/S)
• Measurement:  Changing Units in the Customary System

Applies appropriate techniques, tools and formulas to determine measurements:

• Converts Units in the Metric Systems   (D/S)
• Applies geometry to real-world situations   (D/S)
• Applies measurement to real-world situations   (D/S)

Data Analysis and Probability

Formulates questions that can be addressed with data and collects, organizes, and displays relevant data to answer them:

• Mean, Median, and Mode   (D/S)
• Organizes and Displays Data   (D/S)
• Makes a graph using a spreadsheet   (D/S)
• Data analysis real world   (D/S)
• Understands probability   (D/S)
• Experimental probability   (D/S)
• Tree diagrams and the counting principle   (D/S)
• Unit Rates and Proportional Reasoning (D/S)

Selects and uses appropriate statistical method to analyze data:

• Stem-Leaf Plots  (D/S)
• Unit Rates   (D/S)
• Understanding Proportions   (D/S)
• Estimating and finding a percent of a number   (D/S)
• Ratios  (D/S)

Understands and applies basic concepts of probability:

• Makes predictions from data   (D/S)
• Simulates a problem using technology   (D/S)
• Independent activity using probability   (D/S)