8.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


8.1A 
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

Apply
MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:
 Mathematical problem situations within and between disciplines
 Everyday life
 Society
 Workplace
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Representing, applying, and analyzing proportional relationships
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 Making inferences from data
 TxCCRS:

8.1B 
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving process and the reasonableness of the solution
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Representing, applying, and analyzing proportional relationships
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 Making inferences from data
 TxCCRS:
 VIII. Problem Solving and Reasoning

8.1C 
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
Process Standard

Select
TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
Including, but not limited to:
 Appropriate selection of tool(s) and techniques to apply in order to solve problems
 Tools
 Real objects
 Manipulatives
 Paper and pencil
 Technology
 Techniques
 Mental math
 Estimation
 Number sense
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Representing, applying, and analyzing proportional relationships
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 Making inferences from data
 TxCCRS:
 VIII. Problem Solving and Reasoning

8.1D 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard

Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Representing, applying, and analyzing proportional relationships
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 Making inferences from data
 TxCCRS:
 IX. Communication and Representation

8.1E 
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

Create, Use
REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Representations of mathematical ideas
 Organize
 Record
 Communicate
 Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
 Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Representing, applying, and analyzing proportional relationships
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 Making inferences from data
 TxCCRS:
 IX. Communication and Representation

8.1F 
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

Analyze
MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Mathematical relationships
 Connect and communicate mathematical ideas
 Conjectures and generalizations from sets of examples and nonexamples, patterns, etc.
 Current knowledge to new learning
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Representing, applying, and analyzing proportional relationships
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 Making inferences from data
 TxCCRS:

8.1G 
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

Display, Explain, Justify
MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:
 Mathematical ideas and arguments
 Validation of conclusions
 Displays to make work visible to others
 Diagrams, visual aids, written work, etc.
 Explanations and justifications
 Precise mathematical language in written or oral communication
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Representing, applying, and analyzing proportional relationships
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 Making inferences from data
 TxCCRS:
 IX. Communication and Representation

8.8 
Expressions, equations, and relationships. The student applies mathematical process standards to use onevariable equations or inequalities in problem situations. The student is expected to:


8.8A 
Write onevariable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants.
Supporting Standard

Write
ONEVARIABLE EQUATIONS OR INEQUALITIES WITH VARIABLES ON BOTH SIDES THAT REPRESENT PROBLEMS USING RATIONAL NUMBER COEFFICIENTS AND CONSTANTS
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
 Variable – a letter or symbol that represents a number
 One variable on both sides of the equation or inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Decimals (positive or negative)
 Fractions (positive or negative)
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals (positive or negative)
 Fractions (positive or negative)
 Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
 Constraints or conditions
 Distinguishing between equations and inequalities
 Characteristics of equations
 Equates two expressions
 Equality of variable
 One solution
 Characteristics of inequalities
 Shows the relationship between two expressions in terms of >, <, ≥, ≤, or ≠
 Inequality of the variable
 One or more solutions
 Equality and inequality words and symbols
 Equal to, =
 Greater than, >
 Greater than or equal to, ≥
 Less than, <
 Less than or equal to, ≤
 Not equal to, ≠
 Relationship of order of operations within an equation or inequality
 Order of operations – the rules of which calculations are performed first when simplifying an expression
 Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
 Exponents: rewrite in standard numerical form and simplify from left to right
 Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
 Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
 Onevariable equations with variables on both sides from a problem situation
 Onevariable inequalities with variables on both sides from a problem situation
Note(s):
 Grade Level(s):
 Grade 7 wrote onevariable, twostep equations and inequalities to represent constraints or conditions within problems.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 TxCCRS:
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

8.8B 
Write a corresponding realworld problem when given a onevariable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants.
Supporting Standard

Write
A CORRESPONDING REALWORLD PROBLEM WHEN GIVEN A ONEVARIABLE EQUATION OR INEQUALITY WITH VARIABLES ON BOTH SIDES OF THE EQUAL SIGN USING RATIONAL NUMBER COEFFICIENTS AND CONSTANTS
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
 Variable – a letter or symbol that represents a number
 One variable on both sides of the equation or inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Decimals (positive or negative)
 Fractions (positive or negative)
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals (positive or negative)
 Fractions (positive or negative)
 Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
 Constraints or conditions
 Distinguishing between equations and inequalities
 Characteristics of equations
 Equates two expressions
 Equality of the variable
 One solution
 Characteristics of inequalities
 Shows the relationship between to expressions in terms of >, <, ≥, ≤, or ≠
 Inequality of the variable
 One or more solutions
 Equality and inequality words and symbols
 Equal to, =
 Greater than, >
 Greater than or equal to, ≥
 Less than, <
 Less than or equal to, ≤
 Not equal to, ≠
 Relationship of order of operations within an equation or inequality
 Order of operations – the rules of which calculations are performed first when simplifying an expression
 Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
 Exponents: rewrite in standard numerical form and simplify from left to right
 Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
 Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
 Corresponding realworld problem situation from a onevariable equation with variables on both sides of the equal sign
 Corresponding realworld problem situation from a onevariable inequality with variables on both sides of the inequality symbol
Note(s):
 Grade Level(s):
 Grade 7 wrote corresponding realworld problems given a onevariable, twostep equation or inequality.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 TxCCRS:
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

8.8C 
Model and solve onevariable equations with variables on both sides of the equal sign that represent mathematical and realworld problems using rational number coefficients and constants.
Readiness Standard

Model, Solve
ONEVARIABLE EQUATIONS WITH VARIABLES ON BOTH SIDES OF THE EQUAL SIGN THAT REPRESENT MATHEMATICAL AND REALWORLD PROBLEMS USING RATIONAL NUMBER COEFFICIENTS AND CONSTANTS
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Variable – a letter or symbol that represents a number
 One variable on both sides of the equation
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Decimals (positive or negative)
 Fractions (positive or negative)
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals (positive or negative)
 Fractions (positive or negative)
 Characteristics of equations
 Equates two expressions
 Equality of the variable
 One solution
 Equality words and symbol
 Relationship of order of operations within an equation
 Order of operations – the rules of which calculations are performed first when simplifying an expression
 Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
 Exponents: rewrite in standard numerical form and simplify from left to right
 Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
 Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
 Models to solve onevariable equations with variables on both sides of the equal sign (concrete, pictorial, algebraic)
 Solutions to onevariable equations with variables on both sides of the equal sign from mathematical and realworld problem situations
 Possible solutions
 One real solution
 No solution
 Infinite solutions (all real solutions)
Note(s):
 Grade Level(s):
 Grade 7 modeled and solved onevariable, twostep equations and inequalities.
 Algebra I will solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships, including the Pythagorean Theorem
 TxCCRS:
 I. Numeric Reasoning
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

8.12 
Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to:


8.12A 
Solve realworld problems comparing how interest rate and loan length affect the cost of credit.
Supporting Standard

Solve
REALWORLD PROBLEMS COMPARING HOW INTEREST RATE AND LOAN LENGTH AFFECT THE COST OF CREDIT
Including, but not limited to:
 Credit – buying or obtaining goods or services now with an agreement to pay in the future
 Annual percentage rate (APR) – annual percentage rate applied to the balance on a loan compounded monthly
 Principal of a loan – the original amount borrowed
 Interest
 Simple interest for a loan – interest that is calculated only on the principal amount of the loan
 Formula for simple interest from STAAR Grade 8 Mathematics Reference Materials
 I = Prt, where I represents the interest, P represents the principal amount borrowed, r represents the interest rate in decimal form, and t represents the number of years the principal amount is borrowed
 Compound interest for a loan – interest that is computed on the latest balance, including all compounded interest that has been added to the original loan principal
 Formula for compound interest from STAAR Grade 8 Mathematics Reference Material
 A = P(1+ r)^{t}, where A represents the total amount of money borrowed including the principal and accumulated compounded interest, P represents the principal amount borrowed, r represents the interest rate in decimal form, and t represents the number of years the pricipal amount is borrowed
 Generalizations about loans
 Longer the repayment period, usually the higher the interest rate
 Longer the repayment period, the lower the monthly payment
 Longer the repayment period, the greater the amount of money repaid over the life of the loan
 Realworld problem situations comparing interest rates, loan length, and/or cost of credit
Note(s):
 Grade Level(s):
 Grade 6 distinguished between debit cards and credit cards.
 Grade 7 calculated and compared simple interest and compound interest earnings.
 Grade 8 solves realworld problems comparing how interest rate and loan length affect the cost of credit.
 Algebra I will refer to 1 + r in the compound interest formula, A = P(1 + r)^{t}, as the factor and will be given the variable b.
 Mathematical Models with Applications will introduce analyzing compound interest for multiple compounding periods within a year.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

8.12B 
Calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator.

Calculate
THE TOTAL COST OF REPAYING A LOAN, INCLUDING CREDIT CARDS AND EASY ACCESS LOANS, UNDER VARIOUS RATES OF INTEREST AND OVER DIFFERENT PERIODS USING AN ONLINE CALCULATOR
Including, but not limited to:
 Credit – buying or obtaining goods or services now with an agreement to pay in the future
 Annual percentage rate (APR) – annual percentage rate applied to the balance on a loan compounded monthly
 Principal of a loan – the original amount borrowed
 Collateral – something which is pledged to secure repayment of a loan; in the event of default on the loan, the collateral is forfeited
 Interest
 Simple interest for a loan – interest that is calculated only on the principal amount of the loan
 Formula for simple interest from STAAR Grade 8 Mathematics Reference Materials
 I = Prt, where I represents the interest, P represents the principal amount borrowed, r represents the interest rate in decimal form, and t represents the number of years the principal amount is borrowed
 Compound interest for a loan – interest that is calculated on the latest balance, including all compounded interest that has been added to the original loan principal
 Formula for compound interest from STAAR Grade 8 Mathematics Reference Materials
 A = P(1+ r)^{t}, where A represents the total amount of money borrowed including the pricipal and accumulated compounded interest, P represents the principal amount borrowed, r represents the interest rate in decimal form, and t represents the number of years the principal amount is borrowed
 Generalizations about loans
 Longer the repayment period, the higher the interest rate
 Longer the repayment period, the lower the monthly payment
 Longer the repayment period, the higher the effective interest rate
 Various types of loans
 Easy access loan
 Payday loan – a highinterest, short term loan that is repaid when the borrower receives their next paycheck
 Car title loan – a highinterest, short term loan of cash for which an automobile title is required as collateral
 Credit card
 Tend to have higher interest rates than other types of loans
 Various fees may be associated
 Longer the repayment period, the higher the effective interest rate
 Calculates compound interest
 Online calculator to determine the costs of loans
Note(s):
 Grade Level(s):
 Grade 5 identified the advantages and disadvantages of different methods of payment, including check, credit card, and electronic payments.
 Grade 6 explained why it is important to establish a positive credit history.
 Grade 7 calculated and compared simple interest and compound interest earnings.
 Grade 8 introduces calculating and comparing interest on simple and compound on loans.
 Algebra I will refer to 1 + r in the compound interest formula, A = P(1 + r)^{t}, as the factor and will be given the variable b.
 Mathematical Models with Applications will introduce analyzing compound interest for multiple compounding periods within a year.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

8.12D 
Calculate and compare simple interest and compound interest earnings.
Readiness Standard

Calculate, Compare
SIMPLE INTEREST AND COMPOUND INTEREST EARNINGS
Including, but not limited to:
 Principal of an investment – the original amount invested
 Simple interest for an investment – interest paid on the original principal in an account, disregarding any previously earned interest
 Compound interest for an investment – interest that is calculated on the latest balance, including all compounded interest that has been added to the original principal investment
 Formulas for interest from STAAR Grade 8 Mathematics Reference Materials
 Simple interest
 I = Prt, where I represents the interest, P represents the principal amount deposited, r represents the interest rate in decimal form, and t represents the number of years the principal amount is deposited
 Compound interest
 A = P(1+ r)^{t}, where A represents the total accumulated amount including the principal and earned compounded interest, P represents the principal amount deposited, r represents the interest rate in decimal form, and t represents the number of years the principal amount is deposited
 Comparing simple and compound interest earnings
Note(s):
 Grade Level(s):
 Grade 7 calculated and compared simple interest and compound interest earnings.
 Grade 8 solves realworld problems comparing how interest rate and loan length affect the cost of credit.
 Algebra I will refer to 1 + r in the compound interest formula, A = P(1 + r)^{t}, as the factor and will be given the variable b.
 Mathematical Models with Applications will introduce analyzing compound interest for multiple compounding periods within a year.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections
