
Legend:  Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
 Student Expectations (TEKS) identified by TEA are in bolded, black text.
 Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
 Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
 Student Expectations (TEKS) are labeled Process standards as identified by TEA of the assessed curriculum.
 Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a
strikethrough.

Legend:  Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
 Unitspecific clarifications are in italicized, blue text.
 Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.

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

4.4 
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

4.5 
Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:


4.5A 
Represent multistep problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity.
Readiness Standard

Represent
MULTISTEP PROBLEMS INVOLVING THE FOUR OPERATIONS WITH WHOLE NUMBERS USING STRIP DIAGRAMS AND EQUATIONS WITH A LETTER STANDING FOR THE UNKNOWN QUANTITY
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
 Multiplication
 Product – the total when two or more factors are multiplied
 Factor – a number multiplied by another number to find a product
 Products of whole numbers up to 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 of whole numbers up to fourdigit dividends by onedigit divisors
 Quotients may include remainders
 Representations of an unknown quantity in an equation
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Any single letter to represent the unknown quantity (e.g., 24 – 8 = y, etc.)
 Equal sign at beginning or end and unknown in any position
 Multistep problem situations involving the four operations in a variety of problem structures
 Recognition of addition, subtraction, multiplication, and/or division in mathematical and realworld problem situations
 Representation of problem situations with strip diagrams and equations with a letter standing for the unknown
 Strip diagram – a linear model used to illustrate number relationships
 Relationship between quantities represented and problem situation
Note(s):
 Grade Level(s):
 Grade 3 represented one and twostep problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations.
 Grade 3 represented and solved one and twostep multiplication and division problems within 100 using arrays, strip diagrams, and equations.
 Grade 3 determined the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product.
 Grade 5 will represent and solve multistep problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity.
 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
 II.D. Algebraic Reasoning – Representations
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

4.5B 
Represent problems using an inputoutput table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence.
Readiness Standard

Represent
PROBLEMS USING AN INPUTOUTPUT TABLE AND NUMERICAL EXPRESSIONS TO GENERATE A NUMBER PATTERN THAT FOLLOWS A GIVEN RULE REPRESENTING THE RELATIONSHIP OF THE VALUES IN THE RESULTING SEQUENCE AND THEIR POSITION IN THE SEQUENCE
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
 Multiplication
 Product – the total when two or more factors are multiplied
 Factor – a number multiplied by another number to find a product
 Products of whole numbers up to 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 of whole numbers up to fourdigit dividends by onedigit divisors
 Data sets of whole numbers
 Sets may or may not begin with 1
 Sets may or may not be listed in sequential order
 Sequence – a list of numbers or a collection of objects in a specific order that follows a particular pattern or rule
 Expression – a mathematical phrase, with no equal sign or comparison symbol, that may contain a number(s), an unknown(s), and/or an operator(s)
 Rule – an expression describing the relationship between the input and output values in a pattern or sequence
 Various representations of problem situations
 Inputoutput table – a table which represents how the application of a rule on a value, input, results in a different value, output
 Relationship between inputoutput tables and number patterns
 When the input is the position in the sequence, then the output is the value in the sequence.
 When the input is the value in the sequence, then the output is the position in the sequence.
 Relationship between values in a number pattern
 Additive numerical pattern – a pattern that occurs when a constant nonzero value is added to an input value to determine the output value
 Multiplicative numerical pattern – a pattern that occurs when a constant nonzero value is multiplied by an input value to determine the output value
 Relationship between numerical expressions and rules to create inputoutput tables representing the relationship between each position in the sequence and the value in the sequence
Note(s):
 Grade Level(s):
 Grade 3 represented realworld relationships using number pairs in a table and verbal descriptions.
 Grade 5 will generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph.
 Grade 5 will recognize the difference between additive and multiplicative numerical patterns given in a table or graph.
 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
 II.D. Algebraic Reasoning – Representations
 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:


4.10A 
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
