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, 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.
 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

4.2 
Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to:


4.2D 
Round whole numbers to a given place value through the hundred thousands place.
Supporting Standard

Round
WHOLE NUMBERS TO A GIVEN PLACE VALUE THROUGH THE HUNDRED THOUSANDS PLACE
Including, but not limited to:
 Whole numbers (0 – 1,000,000,000)
 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}
 Rounding – a type of estimation with specific rules for determining the closest value
 Nearest 10; 100; 1,000; 10,000; or 100,000
 Number lines
 Proportionally scaled number lines (predetermined intervals)
 Open number lines (no marked intervals)
 Relative magnitude of a number describes the size of a number and its relationship to another number.
 Rounding to the nearest 10 on a number line
 Determine the two consecutive multiples of 10 that the number being rounded falls between.
 Begin with the value of the original tens place within the number and then identify the next highest value in the tens place.
 Determine the halfway point between the consecutive multiples of 10.
 Locate the position of the number being rounded on the number line.
 Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 10 on the number line.
 If the number being rounded is before the halfway point on the number line, round to the value of the original tens place.
 If the number being rounded is past the halfway point on the number line, round to the value of the next highest tens place.
 If the number being rounded is on the halfway point on the number line, round to the value of the next highest tens place.
 Rounding to the nearest 100 on a number line
 Determine the two consecutive multiples of 100 that the number being rounded falls between.
 Begin with the value of the original hundreds place within the number and then identify the next highest value in the hundreds place.
 Determine the halfway point between the consecutive multiples of 100.
 Locate the position of the number being rounded on the number line.
 Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 100 on the number line.
 If the number being rounded is before the halfway point on the number line, round to the value of the original hundreds place.
 If the number being rounded is past the halfway point on the number line, round to the value of the next highest hundreds place.
 If the number being rounded is on the halfway point on the number line, round to the value of the next highest hundreds place.
 Rounding to the nearest 1,000 on a number line
 Determine the two consecutive multiples of 1,000 that the number being rounded falls between.
 Begin with the value of the original thousands place within the number and then identify the next highest value in the thousands place.
 Determine the halfway point between the consecutive multiples of 1,000.
 Locate the position of the number being rounded on the number line.
 Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 1,000 on the number line.
 If the number being rounded is before the halfway point on the number line, round to the value of the original thousands place.
 If the number being rounded is past the halfway point on the number line, round to the value of the next highest thousands place.
 If the number being rounded is on the halfway point on the number line, round to the value of the next highest thousands place.
 Rounding to the nearest 10,000 on a number line
 Determine the two consecutive multiples of 10,000 that the number being rounded falls between.
 Begin with the value of the original ten thousands place within the number and then identify the next highest value in the ten thousands place.
 Determine the halfway point between the consecutive multiples of 10,000.
 Locate the position of the number being rounded on the number line.
 Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 10,000 on the number line.
 If the number being rounded is before the halfway point on the number line, round to the value of the original ten thousands place.
 If the number being rounded is past the halfway point on the number line, round to the value of the next highest ten thousands place.
 If the number being rounded is on the halfway point on the number line, round to the value of the next highest ten thousands place.
 Rounding to the nearest 100,000 on a number line
 Determine the two consecutive multiples of 100,000 that the number being rounded falls between.
 Begin with the value of the original hundred thousands place within the number and then identify the next highest value in the hundred thousands place.
 Determine the halfway point between the consecutive multiples of 100,000.
 Locate the position of the number being rounded on the number line.
 Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 100,000 on the number line.
 If the number being rounded is before the halfway point on the number line, round to the value of the original hundred thousands place.
 If the number being rounded is past the halfway point on the number line, round to the value of the next highest hundred thousands place.
 If the number being rounded is on the halfway point on the number line, round to the value of the next highest hundred thousands place.
 Round a given number to the closest multiple of 10; 100; 1,000; 10,000; or 100,000 on a number line.
 Round a given number to the higher multiple of 10; 100; 1,000; 10,000; or 100,000 if it falls exactly halfway between the multiples on a number line.
 Rounding numerically based on place value
 Find the place to which you are rounding.
Look at the digit of the next lowest place value, the digit to the right of which you are rounding. If the digit in that place is less than 5, then the digit in the rounding place remains the same. If the digit in that place is greater than or equal to 5, then the digit in the rounding place increases by 1. The digit(s) to the right of the place of which you are rounding is replaced with “0”.
Note(s):
 Grade Level(s):
 Grade 3 introduced rounding to the nearest 10 or 100 or using compatible numbers to estimate solutions to addition and subtraction problems.
 Grade 5 will round decimals to the tenths or hundredths.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding decimals and addition and subtraction of decimals
 TxCCRS:
 I. Numeric Reasoning
 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

4.4G 
Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers.
Supporting Standard

Round
TO THE NEAREST 10, 100, OR 1,000 TO ESTIMATE SOLUTIONS INVOLVING WHOLE NUMBERS
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
 Subtraction
 Differences of whole numbers
 Recognition of operations in mathematical and realworld problem situations
 Estimation – reasoning to determine an approximate value
 Rounding – a type of estimation with specific rules for determining the closest value
 To the nearest 10; 100; or 1,000
 Number lines
 Proportionally scaled number lines (predetermined intervals)
 Open number line (no marked intervals)
 Relative magnitude of a number describes the size of a number and its relationship to another number.
 Rounding to the nearest 10 on a number line
 Determine the two consecutive multiples of 10 that the number being rounded falls between.
 Begin with the value of the original tens place within the number and then identify the next highest value in the tens place.
 Determine the halfway point between the consecutive multiples of 10.
 Locate the position of the number being rounded on the number line.
 Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 10 on the number line.
 If the number being rounded is before the halfway point on the number line, round to the value of the original tens place.
 If the number being rounded is past the halfway point on the number line, round to the value of the next highest tens place.
 If the number being rounded is on the halfway point on the number line, round to the value of the next highest tens place.
 Rounding to the nearest 100 on a number line
 Determine the two consecutive multiples of 100 that the number being rounded falls between.
 Begin with the value of the original hundreds place within the number and then identify the next highest value in the hundreds place.
 Determine the halfway point between the consecutive multiples of 100.
 Locate the position of the number being rounded on the number line.
 Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 100 on the number line.
 If the number being rounded is before the halfway point on the number line, round to the value of the original hundreds place.
 If the number being rounded is past the halfway point on the number line, round to the value of the next highest hundreds place.
 If the number being rounded is on the halfway point on the number line, round to the value of the next highest hundreds place.
 Rounding to the nearest 1,000 on a number line
 Determine the two consecutive multiples of 1,000 that the number being rounded falls between.
 Begin with the value of the original thousands place within the number and then identify the next highest value in the thousands place.
 Determine the halfway point between the consecutive multiples of 1,000.
 Locate the position of the number being rounded on the number line.
 Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 1,000 on the number line.
 If the number being rounded is before the halfway point on the number line, round to the value of the original thousands place.
 If the number being rounded is past the halfway point on the number line, round to the value of the next highest thousands place.
 If the number being rounded is on the halfway point on the number line, round to the value of the next highest thousands place.
 Round a given number to the closest multiple of 10; 100; or 1,000 on a number line.
 Round a given number to the higher multiple of 10; 100; or 1,000 if it falls exactly halfway between the multiples on a number line.
 Round numbers to a common place then compute.
 If not designated, find the greatest common place value of all numbers in the problem to determine the place value to which you are rounding (e.g., round to the nearest 10 if only twodigit numbers are being considered in the problem; round to the nearest 100 if only threedigit numbers are being considered in the problem; round to the nearest 1,000 if only fourdigit numbers are being considered; round to the nearest 10 if both twodigit and threedigit numbers are being considered in the problem; round to the nearest 100 if both threedigit and fourdigit numbers are being considered; etc.).
 Vocabulary indicating estimation in mathematical and realworld problem situations (e.g., about, approximately, estimate, etc.)
 Vocabulary descriptors of the effects of the adjustment on the estimation compared to the actual solution (e.g., about, close, little more/little less, around, approximately, estimated, etc.)
 Variation of the estimate from the actual solution is dependent upon the magnitude of the adjustment(s) of the actual numbers.
 Rounding numerically based on place value
 Find the place to which you are rounding.
Look at the digit of the next lowest place value, the digit to the right of which you are rounding. If the digit in that place is less than 5, then the digit in the rounding place remains the same. If the digit in that place is greater than or equal to 5, then the digit in the rounding place increases by 1. The digit(s) to the right of the place of which you are rounding is replaced with “0”.
 Round numbers to a common place then compute.
 If not designated, find the greatest common place value of all numbers in the problem to determine the place value to which you are rounding (e.g., round to the nearest 10 if only twodigit numbers are being considered in the problem; round to the nearest 100 if only threedigit numbers are being considered in the problem; round to the nearest 1,000 if only fourdigit numbers are being considered; round to the nearest 10 if both twodigit and threedigit numbers are being considered in the problem; round to the nearest 100 if both threedigit and fourdigit numbers are being considered; etc.).
 Vocabulary indicating estimation in mathematical and realworld problem situations (e.g., about, approximately, estimate, etc.)
 Vocabulary descriptors of the effects of the adjustment on the estimation compared to the actual solution (e.g., about, close, little more/little less, around, approximately, estimated, etc.)Variation of the estimate from the actual solution is dependent upon the magnitude of the adjustment(s) of the actual numbers.
 Variation of the estimate from the actual solution is dependent upon the magnitude of the adjustment(s) of the actual numbers.
Use
COMPATIBLE NUMBERS TO ESTIMATE SOLUTIONS INVOLVING WHOLE NUMBERS
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
 Subtraction
 Differences of whole numbers
 Recognition of operations in mathematical and realworld problem situations
 Estimation – reasoning to determine an approximate value
 Compatible numbers – numbers that are slightly adjusted to create groups of numbers that are easy to compute mentally
 Determine compatible numbers then compute.
 Vocabulary indicating estimation in mathematical and realworld problem situations (e.g., about, approximately, estimate, etc.)
 Vocabulary descriptors of the effects of the adjustment on the estimation compared to the actual solution (e.g., about, close, little more/little less, around, approximately, estimated, etc.)
 Variation of the estimate from the actual solution is dependent upon the magnitude of the adjustment(s) of the actual numbers.
Note(s):
 Grade Level(s):
 Grade 3 rounded to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems.
 Grade 5 will round decimals to tenths or hundredths.
 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

4.10 
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:


4.10B 
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
 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

4.10E 
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
