
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.

5.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


5.1A 
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 an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 Understanding and generating expressions and equations to solve problems
 Representing and solving problems with perimeter, area, and volume
 Organizing, representing, and interpreting sets of data
 TxCCRS:

5.1B 
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 an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 Understanding and generating expressions and equations to solve problems
 Representing and solving problems with perimeter, area, and volume
 Organizing, representing, and interpreting sets of data
 TxCCRS:
 VIII. Problem Solving and Reasoning

5.1C 
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 an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 Understanding and generating expressions and equations to solve problems
 Representing and solving problems with perimeter, area, and volume
 Organizing, representing, and interpreting sets of data
 TxCCRS:
 VIII. Problem Solving and Reasoning

5.1D 
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 an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 Understanding and generating expressions and equations to solve problems
 Representing and solving problems with perimeter, area, and volume
 Organizing, representing, and interpreting sets of data
 TxCCRS:
 IX. Communication and Representation

5.1E 
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 an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 Understanding and generating expressions and equations to solve problems
 Representing and solving problems with perimeter, area, and volume
 Organizing, representing, and interpreting sets of data
 TxCCRS:
 IX. Communication and Representation

5.1F 
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 an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 Understanding and generating expressions and equations to solve problems
 Representing and solving problems with perimeter, area, and volume
 Organizing, representing, and interpreting sets of data
 TxCCRS:

5.1G 
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 an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 Understanding and generating expressions and equations to solve problems
 Representing and solving problems with perimeter, area, and volume
 Organizing, representing, and interpreting sets of data
 TxCCRS:
 IX. Communication and Representation

5.3 
Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to:


5.3E 
Solve for products of decimals to the hundredths, including situations involving money, using strategies based on placevalue understandings, properties of operations, and the relationship to the multiplication of whole numbers.
Readiness Standard

Solve
FOR PRODUCTS OF DECIMALS TO THE HUNDREDTHS, INCLUDING SITUATIONS INVOLVING MONEY, USING STRATEGIES BASED ON PLACEVALUE UNDERSTANDINGS, PROPERTIES OF OPERATIONS, AND THE RELATIONSHIP TO THE MULTIPLICATION OF WHOLE NUMBERS
Including, but not limited to:
 Decimals (positive decimals less than one and greater than one to the tenths, hundredths, and thousandths)
 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
 Multiplication
 Product – the total when two or more factors are multiplied
 Factor – a number multiplied by another number to find a product
 Products of decimals limited to threedigit factors by twodigit factors with products to the hundredths
 Multiply tenths by tenths (e.g., 0.3 × 0.7 = 0.21, 1.2 × 1.2 = 1.44, 14.3 × 1.3 = 18.59, etc.)
 Multiply tenths by hundredths or vice versa (e.g., 0.5 × 0.12 = 0.06, 1.4 × 0.15 = 0.21, 21.4 × 0.45 = 9.63, etc.)
 Multiply tenths by thousandths or vice versa (e.g., 0.4 × 0.125 = 0.05, 0.125 × 8.4 = 1.05, etc.)
 Multiply whole numbers by tenths, hundredths, and thousandths or vice versa (e.g., 3 × 1.3 = 3.9, 42 × 7.45 = 312.9, 7.02 × 78 = 547.56, 6 × 0.125 = 0.75, etc.)
 Multiplying by a lesser factor results in lesser products.
 Connections between whole number multiplication and decimal multiplication
 Base10 place value system
 A number system using ten digits 0 – 9
 Relationships between places are based on multiples of 10.
 Moving left across the places, the values are 10 times the position to the right.
 Moving right across the places, the values are onetenth the value of the place to the left.
 Place value relationships to determine products
 Properties of operations
 Commutative property of multiplication – if the order of the factors are changed, the product will remain the same
 a × b = c; therefore, b × a = c
 Associative property of multiplication – if three or more factors are multiplied, they can be grouped in any order, and the product will remain the same
 a × b × c = (a × b) × c = a × (b × c)
 Distributive property of multiplication – if multiplying a number by a sum of numbers, the product will be the same as multiplying the number by each addend and then adding the products together
 a × (b + c) = (a × b) + (a × c)
 Recognition of multiplication in mathematical and realworld problem situations
 Strategies for multiplication
 Distributive property for partial products
 Doubling and halving
 Relate multiplication (associative property) to numerical notation
 Ratio tables
 Equation(s) to reflect solution process
Note(s):
 Grade Level(s):
 Grade 5 introduces solving for products of decimals to the hundredths, including situations involving money, using strategies based on placevalue understandings, properties of operations, and the relationship to the multiplication of whole numbers.
 Grade 6 will multiply and divide positive rational numbers fluently.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

5.3G 
Solve for quotients of decimals to the hundredths, up to fourdigit dividends and twodigit whole number divisors, using strategies and algorithms, including the standard algorithm.
Readiness Standard

Solve
FOR QUOTIENTS OF DECIMALS TO THE HUNDREDTHS, UP TO FOURDIGIT DIVIDENDS AND TWODIGIT WHOLE NUMBER DIVISORS, USING STRATEGIES AND ALGORITHMS, INCLUDING 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}
 Decimals (positive decimals less than one and 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
 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 decimals limited to fourdigit dividends and twodigit whole number divisors, with quotients to the hundredths
 Dividend to the tenths and whole number divisor (e.g., 1.2 ÷ 24 = 0.05, 358.8 ÷ 23 = 15.6, 721.7 ÷ 14 = 51.55, etc.)
 Dividend to the hundredths and whole number divisor (e.g., 8.68 ÷ 4 = 2.17, 8.25 ÷ 15 = 0.55, 62.76 ÷ 12 = 5.23, etc.)
 Whole number dividends and whole number divisors that yield quotients to the hundredths (e.g., 3 ÷ 4 = 0.75, 10 ÷ 8 = 1.25, 1000 ÷ 16 = 62.5, etc.)
 Relationships between multiplication and division to help in solution process
 Connections between division of whole numbers and division with decimals
 Decimal quotients will have the same digits as whole number quotients when the number of digits in the dividend and number of digits in the divisor of both the decimal problem and whole number problem are the same.
 Base10 place value system
 A number system using ten digits 0 – 9
 Relationships between places are based on multiples of 10.
 Moving left across the places, the values are 10 times the position to the right.
 Moving right across the places, the values are onetenth the value of the place to the left.
 Place value relationships to determine quotients
 Recognition of division in mathematical and realworld problem situations
 Division structures
 Partitive division
 Total amount known
 Number of groups known
 Size or measure of each group unknown
 Quotative division (also known as Measurement division)
 Total amount known
 Size or measure of each group known
 Number of groups unknown
 Decomposing division problems into partial quotients
 Standard algorithm using the distributive method
 Record steps that relate to the algorithm used including distributing the value in the quotient according to place value.
 Standard algorithm
 Remainder dependent upon the mathematical and realworld problem situation
 Various ways to record remainder
 Ignore the remainder
 Add one to the quotient
 Remainder is written as a decimal
 Remainder is the answer
 Conversion of remainder into smaller units
 Equation(s) to reflect solution process
Note(s):
 Grade Level(s):
 Grade 5 introduces solving for quotients of decimals to the hundredths, up to fourdigit dividends and twodigit whole number divisors, using strategies and algorithms, including the standard algorithm.
 Grade 6 will multiply and divide decimals fluently.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

5.3I 
Represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models.
Supporting Standard

Represent, Solve
MULTIPLICATION OF A WHOLE NUMBER AND A FRACTION THAT REFERS TO THE SAME WHOLE USING OBJECTS AND PICTORIAL MODELS, INCLUDING AREA MODELS
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}
 Fractions (positive proper, improper, or mixed numbers)
 Fraction – a number in the form where a and b are whole numbers and b is not equal to zero. A fraction can be used to name part of an object, part of a set of objects, to compare two quantities, or to represent division
 Proper fraction – a number in the form where a and b are whole numbers and a < b where b is not equal to zero
 Improper fraction –a number in the form where a and b are whole numbers and a > b where b is not equal to zero
 Mixed number – a number that is composed of a whole number and a fraction
 Multiplication
 Product – the total when two or more factors are multiplied
 Factor – a number multiplied by another number to find a product
 Products limited to a whole number and a fraction that refers to the same whole
 Fractional relationships
 Relationship between the whole and the part
 Numerator – the part of a fraction written above the fraction bar that tells the number of fractional parts specified or being considered
 Denominator – the part of a fraction written below the fraction bar that tells the total number of equal parts in a whole or set
 Referring to the same whole
 Fractions are relationships, and the size or the amount of the whole matters.
 Equivalent fractions to simplify solutions
 Recognition of multiplication in mathematical and realworld problem situations
 Concrete objects and pictorial models
 Pattern blocks and other shapes
 Skip counting
 Fraction bars
 Number lines
 Area models
 Strip diagrams
 Strip diagram – a linear model used to illustrate number relationships
 Equation(s) to reflect solution process
Note(s):
 Grade Level(s):
 Grade 5 introduces representing and solving multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models.
 Grade 6 will multiply and divide positive rational numbers fluently.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation

5.3K 
Add and subtract positive rational numbers fluently.
Readiness Standard

Add, Subtract
POSITIVE RATIONAL NUMBERS FLUENTLY
Including, but not limited to:
 Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
 Various forms of positive rational 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}
 Decimals (positive decimals less than one and greater than one to the tenths, hundredths, and thousandths)
 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
 Fractions (positive proper, improper, or mixed numbers with equal or unequal denominators)
 Fraction – a number in the form where a and b are whole numbers and b is not equal to zero. A fraction can be used to name part of an object, part of a set of objects, to compare two quantities, or to represent division.
 Proper fraction – a number in the form where a and b are whole numbers and a < b where b is not equal to zero
 Improper fraction – a number in the form where a and b are whole numbers and a > b where b is not equal to zero
 Mixed number – a number that is composed of a whole number and a fraction
 Unit fraction – a fraction in the form representing the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a nonzero whole number
 Fluency – efficient application of procedures with accuracy
 Addition
 Sums of whole numbers
 Sums of decimals up to the thousandths
 Sums of fractions with equal and unequal denominators
 Subtraction
 Differences of whole numbers
 Differences of decimals with values limited to the thousandths
 Differences of fractions with equal and unequal denominators
 Fractional relationships
 Equivalent fractions to determine common denominator prior to adding or subtracting fractions
 Least common denominator (LCD) – the least common multiple of the denominators of two or more fractions
 Equivalent fractions to simplify solutions
 Recognition of addition and/or subtraction in mathematical and realworld problem situations
Note(s):
 Grade Level(s):
 Grade 4 evaluated the reasonableness of sums and differences of fractions using benchmark fractions 0, and 1 referring to the same whole.
 Grade 7 will add, subtract, multiply, and divide rational numbers fluently.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 TxCCRS:
 I. Numeric Reasoning
 X. Communication and Representation

5.3L 
Divide whole numbers by unit fractions and unit fractions by whole numbers.
Readiness Standard

Divide
WHOLE NUMBERS BY UNIT FRACTIONS AND UNIT FRACTIONS BY 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}
 Fractions (positive unit fractions)
 Fraction – a number in the form where a and b are whole numbers and b is not equal to zero. A fraction can be used to name part of an object, part of a set of objects, to compare two quantities, or to represent division.
 Unit fraction – a fraction in the form representing the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a nonzero whole number
 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 fractions where dividend and divisors are limited to whole numbers by unit fractions and unit fractions by whole numbers
 Fractional relationships
 Relationship between the whole and the part
 Numerator – the part of a fraction written above the fraction bar that tells the number of fractional parts specified or being considered
 Denominator – the part of a fraction written below the fraction bar that tells the total number of equal parts in a whole or set
 Referring to the same whole
 Fractions are relationships, and the size or the amount of the whole matters.
 Recognition of division in mathematical and realworld problem situations
 Division structures
 Partitive division
 Total amount known
 Number of groups known
 Size or measure of each group unknown
 Quotative division (also known as Measurement division)
 Total amount known
 Size or measure of each group known
 Number of groups unknown
 Division strategies
Note(s):
 Grade Level(s):
 Grade 5 introduces dividing whole numbers by unit fractions and unit fractions by whole numbers.
 Grade 6 will multiply and divide positive rational numbers fluently.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation

5.4 
Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:


5.4F 
Simplify numerical expressions that do not involve exponents, including up to two levels of grouping.
Readiness Standard

Simplify
NUMERICAL EXPRESSIONS THAT DO NOT INVOLVE EXPONENTS, INCLUDING UP TO TWO LEVELS OF GROUPING
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}
 Decimals (positive decimals less than one and greater than one to the tenths, hundredths, and thousandths)
 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
 Fractions (positive proper, improper, or mixed numbers with equal or unequal denominators)
 Fraction – a number in the form where a and b are whole numbers and b is not equal to zero. A fraction can be used to name part of an object, part of a set of objects, to compare two quantities, or to represent division.
 Proper fraction – a number in the form where a and b are whole numbers and a < b where b is not equal to zero
 Improper fraction – a number in the form where a and b are whole numbers and a > b where b is not equal to zero
 Mixed number – a number that is composed of a whole number and a fraction
 Unit fraction – a fraction in the form representing the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a nonzero whole number
 Addition
 Sums of whole numbers
 Sums of decimals up to the thousandths
 Sums of fractions with equal and unequal denominators
 Subtraction
 Differences of whole numbers
 Differences of decimals with values limited to the thousandths
 Differences of fractions with equal and unequal denominators
 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 threedigit factors by twodigit factors
 Products of decimals limited to threedigit factors by twodigit factors with products to the hundredths
 Multiply tenths by tenths (e.g., 0.3 × 0.7 = 0.21, 1.2 × 1.2 = 1.44, 14.3 × 1.3 = 18.59, etc.)
 Multiply tenths by hundredths or vice versa (e.g., 0.5 × 0.12 = 0.06, 1.4 × 0.15 = 0.21, 21.4 × 0.45 = 9.63, etc.)
 Multiply tenths by thousandths or vice versa (e.g., 0.4 × 0.125 = 0.05, 0.125 × 8.4 = 1.05, etc.)
 Multiply whole numbers by tenths, hundredths, and thousandths or vice versa (e.g., 3 × 1.3 = 3.9, 42 × 7.45 = 312.9, 7.02 × 78 = 547.56, 6 × 0.125 = 0.75, etc.)
 Products of fractions where factors are limited to a fraction and a whole number
 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
 Whole numbers with quotients up to fourdigit dividends and twodigit divisors
 Quotients of decimals limited to fourdigit dividends and twodigit whole number divisors, with quotients to the hundredths
 Dividend to the tenths and whole number divisor (e.g., 1.2 ÷ 24 = 0.05, 358.8 ÷ 23 = 15.6, 721.7 ÷ 14 = 51.55, etc.)
 Dividend to the hundredths and whole number divisor (e.g., 8.68 ÷ 4 = 2.17, 8.25 ÷ 15 = 0.55, 62.76 ÷ 12 = 5.23, etc.)
 Whole number dividends and whole number divisors that yield quotients to the hundredths (e.g., 3 ÷ 4 = 0.75, 10 ÷ 8 = 1.25, 1000 ÷ 16 = 62.5, etc.)
 Quotients of fractions where dividend and divisors are limited to whole numbers by unit fractions and unit fractions by whole numbers
 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)
 Numerical expressions without exponents
 Grouping symbols – symbols to show a group of terms and/or expressions within a mathematical expression
 Parentheses ( )
 Brackets [ ]
 Up to two levels of grouping
 Grouping symbols within grouping symbols
 Two sets of grouping symbols
 Order of operations – the rules of which calculations are performed first when simplifying an expression
 Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
 Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
 Various indicators of multiplication include ×, •, or grouping symbols without a multiplication symbol.
 Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
 Recognition of expressions in realworld problem situations
Note(s):
 Grade Level(s):
 Grade 5 introduces simplifying numerical expressions that do not involve exponents, including up to two levels of grouping.
 Grade 6 will generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization.
 Grade 6 will simplify numerical expressions that may include a division bar instead of the division symbol.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and generating expressions and equations to solve problems
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation
