4.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


4.1A 
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:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:

4.1B 
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:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 VIII. Problem Solving and Reasoning

4.1C 
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:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 VIII. Problem Solving and Reasoning

4.1D 
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:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 IX. Communication and Representation

4.1E 
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:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 IX. Communication and Representation

4.1F 
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:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:

4.1G 
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:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 IX. Communication and Representation

4.4 
Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. The student is expected to:


4.4A 
Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm.
Readiness Standard

Add, Subtract
WHOLE NUMBERS AND DECIMALS TO THE HUNDREDTHS PLACE USING THE STANDARD ALGORITHM
Including, but not limited to:
 Whole numbers
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Addition and subtraction of whole numbers
 Connection between place value and the standard algorithm
 Standard algorithm
 Decimals (less than or greater than one to the tenths and hundredths)
 Decimal number – a number in the base10 place value system used to represent a quantity that may include part of a whole and is recorded with a decimal point separating the whole from the part
 Addition and subtraction of decimals
 Relate addition and subtraction of decimals to the hundredths place using concrete objects and pictorial models to the standard algorithm for adding and subtracting decimals.
 Trailing zeros – a sequence of zeros in the decimal part of a number that follow the last nonzero digit, and whether recorded or deleted, does not change the value of the number
Note(s):
 Grade Level(s):
 Grade 3 solved with fluency onestep and twostep problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
 Grade 4 extends adding and subtracting of whole numbers from 1,000 to 1,000,000 and introduces adding and subtracting decimals, including tenths and hundredths.
 Grade 5 will estimate to determine solutions to mathematical and realworld problems involving addition, subtraction, multiplication, or division.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Understanding decimals and addition and subtraction of decimals
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

4.4H 
Solve with fluency one and twostep problems involving multiplication and division, including interpreting remainders.
Readiness Standard

Solve
WITH FLUENCY ONE AND TWOSTEP PROBLEMS INVOLVING MULTIPLICATION AND DIVISION, INCLUDING INTERPRETING REMAINDERS
Including, but not limited to:
 Whole numbers
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Fluency – efficient application of procedures with accuracy
 Standard algorithms for the four operations
 Automatic recall of basic facts
 Multiplication
 Product – the total when two or more factors are multiplied
 Factor – a number multiplied by another number to find a product
 Products of twodigit factors by twodigit factors and up to fourdigit factors by onedigit factors
 Division
 Quotient – the size or measure of each group or the number of groups when the dividend is divided by the divisor
 Dividend – the number that is being divided
 Divisor – the number the dividend is being divided by
 Quotients up to fourdigit dividends by onedigit divisors
 Quotients may include remainders
 Remainder dependent upon the mathematical or realworld situation
 Various ways to record remainder
 Ignore the remainder
 Add one to the quotient
 Remainder is the answer
 Remainder recorded as a fraction
 One and twostep problem situations
 Onestep problems
 Recognition of multiplication and division in mathematical and realworld problem situations
 Twostep problems
 Twostep problems must have onestep in the problem that involves multiplication and/or divison; however, the other step in the problem can involve addition and/or subtraction.
 Recognition of multiplication and division in mathematical and realworld problem situations
 Equation(s) to reflect solution process
Note(s):
 Grade Level(s):
 Grade 4 introduces solving with fluency one and twostep problems involving multiplication and division, including interpreting remainders.
 Grade 5 will multiply with fluency a threedigit number by a twodigit number using the standard algorithm.
 Grade 5 will solve with proficiency for quotients of up to a fourdigit dividend by a twodigit divisor using strategies and the standard algorithm.
 Various mathematical process standards will be applied to this student expectation as appropriate
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

4.8 
Geometry and measurement. The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement. The student is expected to:


4.8C 
Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.
Readiness Standard

Solve
PROBLEMS THAT DEAL WITH INTERVALS OF TIME AND MONEY USING ADDITION, SUBTRACTION, MULTIPLICATION, OR DIVISION AS APPROPRIATE
Including, but not limited to:
 Whole numbers (0 – 1,000,000,000)
 Products of twodigit factors by twodigit factors and up to fourdigit factors by onedigit factors
 Quotients up to fourdigit dividends by onedigit divisors
 Decimals (greater than one and less than one)
 Addition and subtraction of money amounts up to hundredths
 Conversions limited to multiples of halves (e.g., 0.5, 1.5, 4.5, etc.)
 Determined using reasoning that half of any value is that value divided by 2
 Fractions (proper, improper, and mixed numbers)
 Addition and subtraction of fractions with like denominators
 Conversions limited to multiples of halves (e.g., etc.)
 Determined using reasoning that half of any value is that value divided by 2
 Problem situations that deal with intervals of time (clocks: hours, minutes, seconds)
 Addition and subtraction of time intervals in minutes
 Such as a 1 hour and 45minute event minus a 20minute event equals 1 hour 25 minutes
 Time intervals given
 Pictorial models and tools
 Measurement conversion tables
 Analog clock with gears, digital clock, stop watch, number line, etc.
 Time conversions
 1 hour = 60 minutes; 1 minute = 60 seconds
 Fractional values of time limited to multiples of halves
 Elapsed time
 Finding the end time
 Finding the start time
 Finding the duration
 Problem situations that deal with intervals of time (calendar: years, months, weeks, days)
 Time conversions
 1 year = 12 months; 1 year = 52 weeks; 1 week = 7 days; 1 day = 24 hours
 Fractional values of time limited to multiples of halves
 Problem situations that deal with money
 Addition and subtraction may include whole number or decimal amounts
 Multiplication and division limited to amounts expressed as cents or dollars with no decimal values
 Comparison of money amounts
 Making change
 Range of dollar amounts
Note(s):
 Grade Level(s):
 Grade 3 determined solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15minute event plus a 30minute event equals 45 minutes.
 Grade 4 introduces solving problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.
 Grade 5 will solve problems by calculating conversions within a measurement system, customary or metric.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

4.10 
Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:


4.10A 
Distinguish between fixed and variable expenses.
Supporting Standard

Distinguish
BETWEEN FIXED AND VARIABLE EXPENSES
Including, but not limited to:
 Expense – payment for goods and services
 Fixed expenses – expenses that are consistent from month to month
 Allows for greater planning in spending
 Often associated with necessary spending
 Often reflects needs
 Sometimes reflects wants
 Variable expenses – expenses that vary in cost from month to month
 Allows for greater personal control in spending
 Often associated with discretionary spending
 Often reflects wants
 Sometimes reflects needs
 Relationship between fixed and variable expenses
 Some expenses do not change from month to month and some expenses do change each month
 Some expenses that may be fixed for you may be variable for others depending on the situation
Note(s):
 Grade Level(s):
 Grade 3 explained the connection between human capital/labor and income.
 Grade 5 will define income tax, payroll tax, sales tax, and property tax.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 IX. Communication and Representation
 X. Connections

4.10B 
Calculate profit in a given situation.
Supporting Standard

Calculate
PROFIT IN A GIVEN SITUATION
Including, but not limited to:
 Whole numbers
 Decimals (less than or greater than one to the tenths and hundredths)
 Addition
 Sums of whole numbers
 Sums of decimals up to the hundredths
 Subtraction
 Differences of whole numbers
 Differences of decimals with values limited to the hundredths
 Multiplication
 Products of whole numbers up to twodigit factors by twodigit factors and up to fourdigit factors by onedigit factors
 Division
 Quotients of whole numbers up to fourdigit dividends by onedigit divisors
 Income – money earned or received
 Income in a business also called revenue
 Expense – payment for goods and services
 Expenses in a business also called costs
 Profit – money that is made in a business after all the costs and expenses are paid
 Profit is calculated by subtracting expenses (costs) from income (revenue).
 Income – expenses = profit
 Revenue – costs = profit
 Determining profit from a single source for income and/or expenses
 Determining profit from multiple sources for incomes and/or expenses
 Relationship between income, expenses, and profit
 When income is greater than expenses there is a profit.
 When income is less than expenses, there is no profit or the costs exceed the income.
Note(s):
 Grade Level(s):
 Grade 3 described the relationship between the availability or scarcity of resources and how that impacts cost.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

4.10C 
Compare the advantages and disadvantages of various savings options.

Compare
THE ADVANTAGES AND DISADVANTAGES OF VARIOUS SAVINGS OPTIONS
Including, but not limited to:
 Savings – money set aside for future use
 Interest – money received for saving money in a bank account; money paid for borrowing money or making purchases on credit
 Interest earned from saving
 Used to encourage people to put money in a bank or credit union or to invest money
 Factors that affect the interest earned in a savings account
 Amount of money deposited in the account
 Interest rate
 Length of time the money is in the account
 Interest rate – price paid for using someone else’s money; the price paid to you for someone else to use your money
 Savings options (choices)
 Piggy bank
 Advantages of saving using a piggy bank
 Disadvantages of piggy bank
 Does not earn interest
 Low risk of theft or loss
 Interest bearing account – a bank or credit union account in which the money deposited earns interest so there will be more money in the future than originally deposited
 Saving accounts
 Advantages of savings accounts
 Money is easy to access and withdrawal usually does not incur a penalty
 No risk
 Earns interest
 Disadvantages of savings accounts
 Interest rate is usually low
 Certificates of deposit (CDs) and bonds are common types of investment accounts
 Advantages of CDs and bonds
 Low to almost no risk
 Interest rate is usually slightly higher than a savings account
 Earns interest
 Disadvantages of CDs and bonds
 Access to money without penalty occurs on maturity date
 Withdrawal prior to maturity date usually incurs a penalty
 Investing – purchasing something of value (e.g., stocks, bonds, real estate, etc.) with the goal of earning money over time if the value increases
 Advantages of investing
 Potential for profit is higher than an interest bearing account
 Disadvantages of investing
 Money is sometimes hard to access and/or a penalty is charged for withdrawal
 Low to high risk depending on the type of investment
 Potential loss due to economic situations
Note(s):
 Grade Level(s):
 Grade 3 listed reasons to save and explained the benefit of a savings plan, including for college.
 Grade 7 will calculate and compare simple interest and compound interest earning.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 IX. Communication and Representation
 X. Connections

4.10D 
Describe how to allocate a weekly allowance among spending; saving, including for college; and sharing.

Describe
HOW TO ALLOCATE A WEEKLY ALLOWANCE AMONG SPENDING; SAVING, INCLUDING FOR COLLEGE; AND SHARING
Including, but not limited to:
 Process to allocate (assign or distribute) weekly allowance
 Set a goal every week for both spending and saving.
 Calculate fixed and variable expenses for each week.
 Calculate the desired amount for savings each week.
 The remaining money, after expenses and savings, is allocated for personal spending and/or sharing.
 Reasons to allocate (assign or distribute) weekly allowance
 Predetermined spending amounts
 Ability to earn interest on savings
 Saving to pay for college
 Saving to purchase future wants and needs
 Saving to cover unexpected future expenses
Note(s):
 Grade Level(s):
 Grade 2 distinguished between a deposit and a withdrawal.
 Grade 5 will develop a system for keeping and using financial records.
 Grade 8 will estimate the cost of a twoyear and fouryear college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 IX. Communication and Representation
 X. Connections

4.10E 
Describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending.
Supporting Standard

Describe
THE BASIC PURPOSE OF FINANCIAL INSTITUTIONS, INCLUDING KEEPING MONEY SAFE, BORROWING MONEY, AND LENDING
Including, but not limited to:
 Financial institution – an establishment that focuses on dealing with financial transactions such as investments, loans, and deposits
 Purposes of financial institutions
 Take in funds (deposits), pool that money, and lend that money to those who need funds.
 Keep deposits safe and regulate accounts and transactions according to federal and/or state laws.
 Provide a place where individuals, businesses, and governments can deposit and borrow money.
 Serve as agents for depositors (who lend money to the bank) and borrowers (to whom the bank lends money).
 Depositors and borrowers can be individuals and households, financial and nonfinancial firms, or national and local governments.
 Keep individual funds available on demand (e.g., checking accounts) or with some restrictions (e.g., savings or investments).
 Process payments to and from account holders and other financial institutions.
Note(s):
 Grade Level(s):
 Grade 3 explained that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest.
 Grade 5 will identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 IX. Communication and Representation
 X. Connections
