# MATH 6TH

Reporting Category 1: Numbers, Operations, and Quantitative Reasoning – The student will demonstrate an understanding of numbers, operations, and quantitative reasoning.

(6.1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to:

6.1 (A) Compare and order non-negative rational numbers. Supporting Standard (STAAR)

Fractions/Decimals

Exponential & Scientific Notation

Ordering Decimals

Compare and Order Fractions

Compare and Order Numbers

Ordering Fractions

Ordering Fractions

Fractions/Decimals

Less Than, Greater Than

Rational and Irrational Numbers

Exponents, Factors, and Fractions

6.1 (B) Generate equivalent forms of rational numbers including whole numbers, fractions, and decimals. Readiness Standard (STAAR)

Simplify Fractions

Percents

Mixed Numbers

Simplify Fractions

Subtracting Fractions

Percentage

Multiple Representation of Rational Numbers

Rational and Irrational Numbers

Exponents, Factors, and Fractions

Fraction Operations

Introduction to Percent

6.1 (D) Write prime factorizations using exponents. Supporting Standard (STAAR)

Number Patterns

Exponents, Factors, and Fractions

6.1 (E) Identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers. Supporting Standard (STAAR)

Common Factors

Number Patterns

Exponents, Factors and Fractions

(6.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to:

6.2 (A) Model addition and subtraction situations involving fractions with objects, pictures, words, and numbers. Supporting Standard (STAAR)

Subtracting Fractions

Fraction Operations

6.2 (B) Use addition and subtraction to solve problems involving fractions and decimals. Readiness Standard (STAAR)

Subtracting Fractions

Fraction Operations

6.2 (C) Use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates. Readiness Standard (STAAR)

Multiplication

Multiplication

Proportions/Equivalent Fractions

Distributive Property

Commutative/Associative Properties

Ratio

Division

Ratio

Division

Simple Proportions

Numerical Proportions

6.2 (D) Estimate and round to approximate reasonable results and to solve problems where exact answers are not required. Supporting Standard (STAAR)

Estimation

Estimation

6.2 (E) Use order of operations to simplify whole number expressions (without exponents) in problem solving situations. Readiness Standard (STAAR)

Order of Operations

Order of Operations

Using Integers

Reporting Category 2: Patterns, Relationships, and Algebraic Reasoning – The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning.

(6.3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to:

6.3 (A) Use ratios to describe proportional situations. Supporting Standard (STAAR)

Proportions/Equivalent Fractions

Ratio

Ratio

Simple Proportions

Numerical Proportions

6.3 (B) Represent ratios and percents with concrete models, fractions, and decimals. Supporting Standard (STAAR)

Proportions/Equivalent Fractions

Percents

Ratio

Ratio

Percentage

Simple Proportions

Multiple Representation of Rational Numbers

Numerical Proportions

Introduction to Percent

6.3 (C) Use ratios to make predictions in proportional situations. Readiness Standard (STAAR)

Proportions/Equivalent Fractions

Ratio

Ratio

Simple Proportions

Numerical Proportions

(6.4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to:

6.4 (A) Use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area. Readiness Standard (STAAR)

Proportions/Equivalent Fractions

Measurement

Ratio

Ratio

Simple Proportions

Numerical Proportions

Exploring Area and Surface Area

Reporting Category 3: Geometry and Spatial Reasoning – The student will demonstrate an understanding of geometry and spatial reasoning.

(6.6) Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to:

6.6 (A) Use angle measurements to classify angles as acute, obtuse, or right. Supporting Standard (STAAR)

Angles

Plane Figures: Lines and Angles

6.6 (C) Describe the relationship between radius, diameter, and circumference of a circle. Readiness Standard (STAAR)

Diameter of Circle

(6.7) Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions. The student is expected to:

6.7 (A) Locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. Supporting Standard (STAAR)

Plot Points

Coordinates

Plotting Points

Graphs and Tables

Area of Coordinate Polygons

Reporting Category 4: Measurement – The student will demonstrate an understanding of the concepts and uses of measurement.

(6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to:

6.8 (B) Select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight. Readiness Standard (STAAR)

Volume

Perimeter

Measurement

Formulas

Volume/Capacity

Measurement, Perimeter, and Circumference

6.8 (C) Measure angles. Supporting Standard (STAAR)

Angles

Plane Figures: Lines and Angles

6.8 (D) Convert measures within the same measurement system (customary and metric) based on relationships between units. Supporting Standard (STAAR)

Measurement

Reporting Category 5: Probability and Statistics – The student will demonstrate an understanding of probability and statistics.

(6.10) Probability and statistics. The student uses statistical representations to analyze data. The student is expected to:

6.10 (B) Identify mean (using concrete objects and pictorial models), median, mode, and range of a set of data. Supporting Standard (STAAR)

Statistics

Statistics

Data Analysis

Organizing Data

6.10 (C) Sketch circle graphs to display data. Supporting Standard (STAAR)

Data Analysis

6.10 (D) Solve problems by collecting, organizing, displaying, and interpreting data. Readiness Standard (STAAR)

Tables

Graphs

Data Analysis

(6.9) Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to:

6.9 (B) Find the probabilities of a simple event and its complement and describe the relationship between the two. Supporting Standard (STAAR)

Using Probability

Underlying Processes and Mathematical Tools: These skills will not be listed under a separate recording category. Instead, they will be incorporated into at least 75% of the test questions in reporting categories 1-5 and will be identified along with content standards.

(6.11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:

6.11 (D) Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. (STAAR)

Estimation

Estimation

(6.12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to:

6.12 (A) Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. (STAAR)

Multiplication

Exponents to Repeated Multiplication

Multiplication

Simplify Fractions

Place Value

Measurement

Proportions/Equivalent Fractions

Distributive Property

Fractions/Decimals

Exponential & Scientific Notation

Ordering Decimals

Compare and Order Fractions

Common Factors

Percents

Whole Numbers to Millions

Equivalent Fractions

Compare and Order Numbers

Whole Numbers to Trillions

Commutative/Associative Properties

Order of Operations

Percent, Rate, Base

Evaluate Exponents

Repeated Multiplication to Exponents

Ordering Fractions

Mixed Numbers

Multiply/Divide Fractions

Estimation

Exponents

Simplify Fractions

Estimation

Rounding

Ratio

Multiply Fractions

Number Patterns

Division

Probability

Patterns

Positive & Negative Integers

Ordering Fractions

Subtracting Fractions

Fractions/Decimals

Ratio

Division

Percentage

Simple Proportions

Less Than, Greater Than

Multiple Representation of Rational Numbers

Order of Operations

Using Integers

Rational and Irrational Numbers

Decimal Operations

Exponents, Factors and Fractions

Fraction Operations

Numerical Proportions

Introduction to Percent

Applying Percents

19 TAC Chapter 111. Texas Essential Knowledge and Skills for Mathematics

Subchapter B. Middle School