M.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


M.1A 
Apply mathematics to problems arising in everyday life, society, and the workplace.

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.
 TxCCRS:
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld situation.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
 IX.A.2. Connect mathematics to the study of other disciplines.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.
 IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
 IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.

M.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.

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.
 TxCCRS:
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.1. Use estimation to check for errors and reasonableness of solutions.
 V.A. Statistical Reasoning – Design a study
 V.A.1. Formulate a statistical question, plan an investigation, and collect data.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 VII.A.2. Formulate a plan or strategy.
 VII.A.3. Determine a solution.
 VII.A.4. Justify the solution.
 VII.A.5. Evaluate the problemsolving process.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.2. Evaluate the problemsolving process.

M.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.

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.
 TxCCRS:
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.1. Use estimation to check for errors and reasonableness of solutions.
 V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
 V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.

M.1D 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Graphs
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxCCRS:
 II.D. Algebraic Reasoning – Representing relationships
 II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
 II.D.2. Convert [among multiple representations of equations, inequalities, and relationships.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
 VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
 VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
 VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

M.1E 
Create and use representations to organize, record, and communicate mathematical ideas.

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.
 TxCCRS:
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.

M.1F 
Analyze mathematical relationships to connect and communicate mathematical ideas.

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.
 TxCCRS:
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
 VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
 VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
 VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
 IX.A.2. Connect mathematics to the study of other disciplines.

M.1G 
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

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.
 TxCCRS:
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.4. Justify the solution.
 VII.B. Problem Solving and Reasoning – Proportional reasoning
 VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
 VII.C. Problem Solving and Reasoning – Logical reasoning
 VII.C.1. Develop and evaluate convincing arguments.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.

M.4 
Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:


M.4A 
Analyze and compare coverage options and rates in insurance.

Analyze, Compare
COVERAGE OPTIONS IN INSURANCE
Including, but not limited to:
 Insurance policy – a contract between an insurance company and customer that states the terms of the coverage, the limitations, and the premiums
 Insurance coverage – the total or maximum amount by the insurance company a consumer will be paid in the event of a loss
 Types of insurance
 Auto insurance
 Most common types of auto coverage
 Liability (required by law) coverage pays for damage(s) to property and/or medical costs for persons injured by the insured in an accident or other occurrence.
 Collision coverage pays for damage(s) to automobile caused by a collision.
 Comprehensive coverage pays for damage(s) from an event other than a collision, including damage from weather events, theft, vandalism, etc.
 Rental coverage pays for rental of a vehicle for use while insured's vehicle is being repaired under an insured incident.
 Homeowner's and property insurance
 Most common types of property coverage
 Fire, storm, natural disaster (required by lenders) coverage pays the property owner for damages due to almost any natural phenomenon other than flood or rising water.
 Flood (may be required by lenders especially if house is located in a flood plain) coverage is available to property owners whose property is located in a place vulnerable to flooding and/or rising water.
 Burglary/Theft coverage pays for damage and loss due to theft from burglary on insured property, theft of personal belongings at places away from insured property, and personal robbery.
 Liability coverage protects the homeowner by paying for damages to personal property or personal injury to guests while on insured property.
 Renter's insurance coverage pays for damage to personal property such as furnishings and personal effects while living in a rented property.
 Health insurance
 Most common types of health coverage
 Medical
 Physician
 Hospital
 Laboratory and testing
 Prescription drugs
 Dental
 Vision
 Personal insurance
 Most common types of personal insurance
 Life insurance
 Term life insurance offers coverage for a limited period of time that provides a death benefit for the family of the insured if that person dies during that time period. Term policies generally do not accumulate cash value.
 Permanent (Whole) life insurance offers coverage that is usually lifetime and provides cash value in addition to death benefits to the family of the insured
 Total and permanent disability insurance provides a onetime payment if the insured is injured or becomes sick and is no longer able to work permanently.
 Critical illness insurance provides a onetime payment if the insured suffers a serious injury or illness as specified by the policy agreement.
 Income protection insurance replaces a portion of the insured's income during periods of time of economic stress due to lack of income.
Analyze, Compare
RATES IN INSURANCE
Including, but not limited to:
 Premiums – the amount of money paid by the customer to the insurance company for specified coverage as stated in the policy.
 Insurance rates – premiums for different aspects of insurance that vary with amount of coverage, deductibles, and various risk factors.
 Homeowner's and property insurance
 Factors that increase homeowner’s and property insurance rates may include age of home, poor construction, high risk location, previous claims, risk factors on property such as pools, low credit score, etc.
 Factors that lower homeowner’s and property insurance rates may include newer home, sturdy construction meeting updated codes, low risk location, no major claims, no risk factors on property, and high credit score.
 Auto insurance
 Factors that increase auto insurance rates may include traffic tickets, accident claims, location, driving habits, new vehicle, male under the age of 25, lapses in coverage, auto theft, low credit score, etc.
 Factors that lower auto insurance rates may include clean driving record (no tickets or accidents), location, married, used or less expensive vehicle, age between 50 and 65, no lapses in coverage, high credit score, etc.
Note(s):
 Grade Level(s)
 Grade 5 studied the multiplication of decimals.
 Grade 8 identified and explained the advantages and disadvantages of different payment methods.
 Algebra I studied the linear parent function f(x) = x.
 Mathematical Models with Applications introduces insurance, premiums and making decisions about coverage.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxCCRS
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 VII.B. Problem Solving and Reasoning – Proportional reasoning
 VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
 VII.C. Problem Solving and Reasoning – Logical reasoning
 VII.C.2. Understand attributes and relationships with inductive and deductive reasoning.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.2. Connect mathematics to the study of other disciplines.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.
 IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.

M.4B 
Investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans.

Investigate, Compare
INVESTMENT OPTIONS, INCLUDING STOCKS, BONDS, ANNUITIES, CERTFICATES OF DEPOSIT, AND RETIREMENT PLANS
Including, but not limited to:
 Stocks – shares or pieces of a corporation's assets and earnings
 Bonds – investments made as a loan to a government entity, company, nonprofit organization, for a stated amount of time and on which the investor (bond buyer) receives interest. Interest is usually paid periodically over the predetermined time.
 Annuities – contracts sold, usually by insurance companies, for which the buyer pays regular premiums for a specified time, and then receives a stated amount of money per month or year for life, usually beginning with the time of retirement
 Certificates of deposit (CD) – a specified amount deposited with a bank for a specified amount of time that earns interest at a set rate. At the end of the specified time, on the maturity date, the deposited amount accrues the interest for the entire time.
 Savings account – a bank or credit union account in which the money deposited earns interest on the principal over time. The owner of the account can make deposits and withdrawals at any time without penalty.
 Retirement plans
 Employer pension programs – a retirement plan through which an employer puts a portion of an employee's earnings into an investment account set aside to grow for the employee's retirement. These funds are usually tax exempt at the time of deposit.
 Individual retirement account (Traditional IRA)
 Individual Roth IRA
Note(s):
 Grade Level(s)
 Algebra I studied the linear parent function, f(x) = x and the exponential parent function f(x) = ab^{x}.
 Mathematical Models with Applications introduces investment and savings options and decisions.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxCCRS
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 VII.B. Problem Solving and Reasoning – Proportional reasoning
 VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
 VII.C. Problem Solving and Reasoning – Logical reasoning
 VII.C.2. Understand attributes and relationships with inductive and deductive reasoning.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.2. Connect mathematics to the study of other disciplines.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.
 IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.

M.4C 
Analyze types of savings options involving simple and compound interest and compare relative advantages of these options.

Analyze
TYPES OF SAVINGS OPTIONS INVOLVING SIMPLE AND COMPOUND INTEREST
Including, but not limited to:
 Simple interest – interest paid on the original principal in an account, disregarding any previously earned interest
 Simple interest formula: A = P(1 + rt), where A represents the total accumulated amount (principal and interest), P represents the original principal amount, r represents the rate of interest per year, and t represents the number of years.
 Compound interest – interest that is calculated on the latest balance, including all previously accumulated interest that has been added to the original principal
 Compound interest formula: A = P, where A represents the total accumulated amount including principal and earned compount interest, P represents the original amount deposited, r presents the interest rate per year, n represents the number of times per year the interest is paid (the compounding interval), and t represents the number of years. The more often interest is compounded, the faster the balance grows.
 Quarterly (four times per year): A = P
 Monthly (12 times per year): A = P
 Daily (365 times per year): A = P
Compare
RELATIVE ADVANTAGES OF SAVINGS OPTIONS
Including, but not limited to:
 Savings account – a bank or credit union account in which the money deposited earns interest on the principal over time. The owner of the account can make deposits and withdrawals at any time without penalty.
 Certificates of deposit (CD) – a specified amount deposited with a bank for a specified amount of time that earns interest at a set rate. At the end of the specified time, on the maturity date, the deposited amount accrues the interest for the entire time.
 Money market account – a savings account that pays interest based on current interest rates. Money market accounts pay higher interest rates than other savings options and usually require a higher minimum balance.
 Annual percentage yield (APY) – the effective annual rate of return taking into account the effect of compounding interest
 Simple and compound interest
 Bank service fees – bank charges for different services for different types of accounts
 Available balance – the amount available in an account for a person, business, or organization to spend. Some types of savings accounts have limitations on time and amount of withdrawals allowed without penalty.
Note(s):
 Grade Level(s)
 Grade 7 calculated and compared simple interest and compound interest earnings.
 Grade 8 introduced the compound interest formula without using multiple compounding in a year.
 Algebra I studied the exponential parent function f(x) = ab^{x}.
 Mathematical Models with Applications introduces students to investment and savings options and decisions.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxCCRS
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 VII.B. Problem Solving and Reasoning – Proportional reasoning
 VII. B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
 VII.C. Problem Solving and Reasoning – Logical reasoning
 VII.C.2. Understand attributes and relationships with inductive and deductive reasoning.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.2. Connect mathematics to the study of other disciplines.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.
 IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
