# MATH 7TH

Reporting Category 1: Numbers, Operations, and Quantitative Reasoning –

The student will demonstrate an understanding of numbers, operations, and quantitative reasoning.

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

7.1 (A) Compare and order integers and positive rational numbers. Supporting Standard (STAAR)

Fractions/Decimals

Ordering Fractions

Rational and Irrational Numbers

Exponents, Factors, and Fractions

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7.1 (B) Convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator. Readiness Standard (STAAR)

Mixed Numbers

Simplify Fractions

Percentage

Multiple Representation of Rational Numbers

Rational and Irrational Numbers

Exponents,

Factors and Fractions

Fraction Operations

Introduction to Percent Numbers and Percents

7.1 (C) Represent squares and square roots using geometric models. Supporting Standard (STAAR)

Order of Operations

Rational and Irrational Numbers

The Pythagorean Theorem

Real numbers

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

7.2 (A) Represent multiplication and division situations involving fractions and decimals with models, including concrete objects, pictures, words, and numbers. Supporting Standard (STAAR)

Multiply/Divide Fractions

Multiply Fractions

Decimal Operations

Fraction Operations

7.2 (B) Use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals. Readiness Standard (STAAR)

Multiply/Divide Fractions

Multiply Fractions

Decimal Operations

Fraction Operations

Rational numbers and operations

7.2 (C) Use models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms. Supporting Standard (STAAR)

Using Integers

Integer operations

7.2 (D) Use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio. Supporting Standard (STAAR)

Numerical Proportions

Ratios, proportions, and Percents

7.2 (E) Simplify numerical expressions involving the order of operations and exponents. Supporting Standard (STAAR)

Exponents to Repeated Multiplication

Order of Operations

Evaluate Exponents

Repeated Multiplication to Exponents

Exponents

Using Integers

Polynomials and Exponents

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

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

7.3 (A) Estimate and find solutions to application problems involving percent. Readiness Standard (STAAR)

Applying Percents

7.3 (B) Estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units. Readiness Standard (STAAR)

Geometric Proportions

Ratios, proportions and percents

Similarity and scale

(7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to:

7.4 (A) Generate formulas involving unit conversions within the same system (customary and metric), perimeter, area, circumference, volume, and scaling. Supporting Standard (STAAR)

Volume

Diameter of Circle

Area Measurement Formulas

Area of Coordinate Polygons

Area and Circumference of Circles

Measurement,

Perimeter and Circumference

Perimeter and area

(7.5) Patterns, relationships, and algebraic thinking. The student uses equations to solve problems. The student is expected to:

7.5 (A) Use concrete and pictorial models to solve equations and use symbols to record the actions. Supporting Standard (STAAR)

Order of Operations

Formulas One & Two-Step Equations

Simple Algebra

Algebraic Equations

Introduction to Algebra

Equations and Inequalities

Algebraic Equations

Algebraic Inequalities

Introduction to Functions

Nonlinear Functions and Set Theory

Equations and inequalities

Using graphs to analyze data Polynomials and Exponents

Solving linear equations

Solving equations and inequalities

Linear equations

Linear relationships

Sequences

Functions

7.5 (B) Formulate problem situations when given a simple equation and formulate an equation when given a problem situation. Readiness Standard (STAAR)

Simple Algebra

Introduction to Algebra

Solving linear equations

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

(7.6) Geometry and spatial reasoning. The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. The student is expected to:

7.6 (A) Use angle measurements to classify pairs of angles as complementary or supplementary. Supporting Standard (STAAR)

Finding Volume

7.6 (B) Use properties to classify triangles and quadrilaterals. Supporting Standard (STAAR)

Plane Figures: Lines and Angles

7.6 (C) Use properties to classify three-dimensional figures, including pyramids, cones, prisms, and cylinders. Supporting Standard (STAAR)

Finding Volume

Three dimensional geometry

Measurement

7.6 (D) Use critical attributes to define similarity. Readiness Standard (STAAR)

Geometric Proportions

Ratios, proportions and percents

Similarity and scale

(7.7) Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane. The student is expected to:

7.7 (A) Locate and name points on a coordinate plane using ordered pairs of integers. Supporting Standard (STAAR)

Coordinates

Plotting Points

Area of Coordinate Polygons

Using graphs to analyze data

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

(7.9) Measurement. The student solves application problems involving estimation and measurement. The student is expected to:

7.9 (B) Connect models for volume of prisms (triangular and rectangular) and cylinders to formulas of prisms (triangular and rectangular) and cylinders. Supporting Standard (STAAR)

Volume

Finding Volume

Three dimensional geometry/Measurement

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

(7.10) Probability and statistics. The student recognizes that a physical or mathematical model (including geometric) can be used to describe the experimental and theoretical probability of real-life events. The student is expected to:

7.10 (B) Find the probability of independent events. Supporting Standard (STAAR)

Using Probability

Theoretical probability and counting

(7.11) Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation. The student is expected to:

7.11 (A) Select and use an appropriate representation for presenting and displaying relationships among collected data, including line plot, line graph, bar graph, stem and leaf plot, circle graph, and Venn diagrams, and justify the selection. Supporting Standard (STAAR)

Using graphs to analyze data

(7.12) Probability and statistics. The student uses measures of central tendency and variability to describe a set of data. The student is expected to:

7.12 (A) Describe a set of data using mean, median, mode, and range. Supporting Standard (STAAR)

Statistics

Organizing Data Using graphs to analyze data

Collecting and describing data

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.

(7.13) Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:

7.13 (A) Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. (STAAR)

Mathematical processes

7.13 (B) Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. (STAAR)

Mathematical processes

7.13 (C) Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. (STAAR)

Mathematical processes

7.13 (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

(7.14) Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to:

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

Multiplication

Exponents to Repeated Multiplication

Proportions/Equivalent Fractions

Distributive Property

Fractions/Decimals

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

Multiply Fractions

Number Patterns

Division Ratio Percentage

Simple Proportions

Multiple Representation of Rational Numbers Using Integers

Rational and Irrational Numbers

Decimal Operations

Exponents, Factors and Fractions Fraction Operations

Numerical Proportions

Introduction to Percent

Applying Percents

Integer operations

Rational numbers and operations

Real numbers

Ratios, proportions and percents

Numbers and percents

Applications of percent

(7.15) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:

7.15 (A) Make conjectures from patterns or sets of examples and nonexamples. (STAAR)

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

Subchapter B. Middle School