
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.
 A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.

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 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
 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

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


5.4C 
Generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph.
Readiness Standard

Generate
A NUMERICAL PATTERN WHEN GIVEN A RULE IN THE FORM y = ax OR y = x + a AND GRAPH
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
 Addition
 Sums of whole numbers
 Sums of decimals up to the thousandths
 Sums 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
 Mathematical and realworld numerical relationships
 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 numerical patterns
 Input represented as x
 Output represented as y
 Numerical patterns from rules
 Replace the input (x) with a set of numbers to generate a related output (y).
 Input values must be sequential.
 List of output values creates numerical pattern
 Multiplicative rule in the form y = ax
 Additive rule in the form y = x + a
Graph
A NUMERICAL PATTERN WHEN GIVEN A RULE IN THE FORM y = ax OR y = x + a
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
 Addition
 Sums of whole numbers
 Sums of decimals up to the thousandths
 Sums 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
 Graphs of numerical patterns
 Limited to Quadrant I of the coordinate plane
 Horizontal axis represents an input (x)
 Vertical axis represents the related output (y)
 Ordered pairs written in the form (x, y) where x represents the input (xcoordinate) and y represents the output (ycoordinate)
 Numerical patterns from the rule y = ax create a graph of points that lie in a straight line and pass through the origin (0, 0).
 Numerical patterns from the rule y = x + a create a graph of points that lie in a straight line and do not pass through the origin (0, 0).
 Generating a set of ordered pairs from a rule using an inputoutput table
 Substitute values of x in the rule as the input to produce a related values of y as the output to create an ordered pair (x, y), including when x = 0.
 Multiplicative rule in the form y = ax
 Additive rule in the form y = x + a
 Process for graphing ordered pairs of numbers in the first quadrant
 To locate the xcoordinate, begin at the origin and move to the right along the xaxis the appropriate number of units according to the xcoordinate in the ordered pair.
 To locate the ycoordinate, begin at the origin and move up along the yaxis the appropriate number of units according to the ycoordinate in the ordered pair.
 The point of intersection of both the parallel movements on the xaxis and the yaxis is the location of the ordered pair.
 Mathematical and realworld numerical relationships
 Graphing ordered pairs from a numerical rule on a coordinate plane
 Multiplicative rule in the form y = ax
 Additive rule in the form y = x + a
Note(s):
 Grade Level(s):
 Grade 4 represented 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.
 Grade 6 will compare the two rules verbally, numerically, graphically, symbolically in the form y = ax or y = a + x in order to differentiate between additive and multiplicative relationships.
 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
 II.D. Algebraic Reasoning – Representations
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

5.4D 
Recognize the difference between additive and multiplicative numerical patterns given in a table or graph.
Supporting Standard

Recognize
THE DIFFERENCE BETWEEN ADDITIVE AND MULTIPLICATIVE NUMERICAL PATTERNS GIVEN IN A TABLE OR GRAPH
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
 Addition
 Sums of whole numbers
 Sums of decimals up to the thousandths
 Sums 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
 Additive numerical pattern – a pattern that occurs when a constant nonzero value is added to an input value to determine the output value (y = x + a)
 Multiplicative numerical pattern – a pattern that occurs when a constant nonzero value is multiplied by an input value to determine the output value (y = ax)
 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 tables of numerical patterns
 x is the input.
 y is the output.
 Additive numerical patterns exist in a table when a constant nonzero value is added to each input value to result in a respective output value.
 Multiplicative numerical patterns exist in a table when a constant nonzero value is multiplied by each input value to result in a respective output value.
 Graphs of numerical patterns
 Limited to Quadrant I of the coordinate plane
 Horizontal axis represents an input (x)
 Vertical axis represents the related output (y)
 Ordered pairs written in the form (x, y) where x represents the input (xcoordinate) and y represents the output (ycoordinate)
 Additive numerical patterns exist in a graph when the points lie in a straight line that does not pass through the origin (0, 0).
 Multiplicative numerical patterns exist in a graph when the points lie in a straight line that passes through the origin (0, 0).
 Relationship between numerical patterns in tables and graphs
 An additive numerical pattern exists when each value of x is added to a constant nonzero value of a to result in a set of respective values of y and will result in a set of ordered pairs which, when graphed, lie on a straight line that does not pass through the origin (0, 0).
 A multiplicative numerical pattern exists when each value of x is multiplied by a constant nonzero value of a to result in a set of respective values of y and will result in a set of ordered pairs which, when graphed, lie on a straight line that passes through the origin (0, 0).
Note(s):
 Grade Level(s):
 Grade 4 represented 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.
 Grade 6 will compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships.
 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
 II.D. Algebraic Reasoning – Representations
 IX. Communication and Representation

5.8 
Geometry and measurement. The student applies mathematical process standards to identify locations on a coordinate plane. The student is expected to:


5.8A 
Describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the xcoordinate, the first number in an ordered pair, indicates movement parallel to the xaxis starting at the origin; and the ycoordinate, the second number, indicates movement parallel to the yaxis starting at the origin.
Supporting Standard

Describe
THE KEY ATTRIBUTES OF THE COORDINATE PLANE, INCLUDING PERPENDICULAR NUMBER LINES (AXES) WHERE THE INTERSECTION (ORIGIN) OF THE TWO LINES COINCIDES WITH ZERO ON EACH NUMBER LINE AND THE GIVEN POINT (0, 0); THE XCOORDINATE, THE FIRST NUMBER IN AN ORDERED PAIR, INDICATES MOVEMENT PARALLEL TO THE XAXIS STARTING AT THE ORIGIN; AND THE YCOORDINATE, THE SECOND NUMBER, INDICATES MOVEMENT PARALLEL TO THE YAXIS STARTING AT THE ORIGIN
Including, but not limited to:
 Coordinate plane (coordinate grid) – a twodimensional plane on which to plot points, lines, and curves
 Perpendicular lines – lines that intersect at right angles to each other to form square corners
 Axes – the vertical and horizontal lines that act as a reference when plotting points on a coordinate plane
 Intersecting lines – lines that meet or cross at a point
 Origin – the starting point in locating points on a coordinate plane
 Quadrants – any of the four areas created by dividing a plane with an xaxis and yaxis
 Attributes of the coordinate plane
 Two number lines intersect perpendicularly to form the axes, which are used to locate points on the plane.
 The horizontal number line is called the xaxis.
 The vertical number line is called the yaxis.
 The xaxis and the yaxis cross at 0 on both number lines and that intersection is called the origin.
 The ordered pair of numbers corresponding to the origin is (0, 0).
 Four quadrants are formed by the intersection of the x and yaxes and are labeled counterclockwise with Roman numerals beginning with Quadrant I that includes the positive x and yvalues.
 The first quadrant plots positive rational numbers.
 Positive numbers on the xaxis are located to the right of the origin.
 Positive numbers on the yaxis are located above the origin.
 Iterated units are labeled and shown on both axes to show scale.
 Intervals may or may not be increments of one.
 Intervals may or may not include decimal or fractional amounts.
 Relationship between ordered pairs and attributes of the coordinate plane
 A pair of ordered numbers names the location of a point on a coordinate plane.
 Ordered pairs of numbers are indicated within parentheses and separated by a comma (x, y).
 When graphing in Quadrant I, the first number in the ordered pair represents the parallel movement on the xaxis, starting at the origin and moving right.
 When graphing in Quadrant I, the second number in the ordered pair represents the parallel movement on the yaxis, starting at the origin and moving up.
Note(s):
 Grade Level(s):
 Grade 3 represented fractions of halves, fourths, and eighths as distances from zero on a number line.
 Grade 6 will graph points in all four quadrants using ordered pairs of rational numbers.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Organizing, representing, and interpreting sets of data
 TxCCRS:
 IX. Communication and Representation

5.8B 
Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane.
Supporting Standard

Describe
THE PROCESS FOR GRAPHING ORDERED PAIRS OF NUMBERS IN THE FIRST QUADRANT OF THE COORDINATE PLANE
Including, but not limited to:
 Coordinate plane (coordinate grid) – a twodimensional plane on which to plot points, lines, and curves
 Axes – the vertical and horizontal lines that act as a reference when plotting points on a coordinate plane
 Intersecting lines – lines that meet or cross at a point
 Origin – the starting point in locating points on a coordinate plane
 Quadrants – any of the four areas created by dividing a plane with an xaxis and yaxis
 Attributes of the coordinate plane
 Two number lines intersect perpendicularly to form the axes, which are used to locate points on the plane.
 The horizontal number line is called the xaxis.
 The vertical number line is called the yaxis.
 The xaxis and the yaxis cross at 0 on both number lines and that intersection is called the origin.
 The ordered pair of numbers corresponding to the origin is (0, 0).
 Four quadrants are formed by the intersection of the x and yaxes and are labeled counterclockwise with Roman numerals beginning with Quadrant I that includes the positive x and yvalues.
 Relationship between ordered pairs and attributes of the coordinate plane
 A pair of ordered numbers names the location of a point on a coordinate plane.
 Ordered pairs of numbers are indicated within parentheses and separated by a comma (x, y).
 When graphing in Quadrant I, the first number in the ordered pair represents the parallel movement on the xaxis, starting at the origin and moving right.
 When graphing in Quadrant I, the second number in the ordered pair represents the parallel movement on the yaxis, starting at the origin and moving up.
 Limited to the first quadrant for graphing ordered pairs of positive rational numbers
 Various forms of positive rational numbers as ordered pairs
 Counting (natural) numbers
 Decimals (positive decimals less than one and greater than one to the tenths, hundredths, and thousandths)
 Fractions (positive proper, improper, or mixed numbers with equal or unequal denominators)
 Process for graphing ordered pairs of numbers in the first quadrant
 To locate the xcoordinate, begin at the origin and move to the right along the xaxis the appropriate number of units according to the xcoordinate in the ordered pair.
 To locate the ycoordinate, begin at the origin and move up along the yaxis the appropriate number of units according to the ycoordinate in the ordered pair.
 The point of intersection of both the parallel movements on the xaxis and the yaxis is the location of the ordered pair.
 Multiple ordered pairs may be graphed on the same coordinate plane.
Note(s):
 Grade Level(s):
 Grade 3 represented fractions of halves, fourths, and eighths as distances from zero on a number line.
 Grade 6 will graph points in all four quadrants using ordered pairs of rational numbers.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Organizing, representing, and interpreting sets of data
 TxCCRS:
 IX. Communication and Representation

5.8C 
Graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and realworld problems, including those generated by number patterns or found in an inputoutput table.
Readiness Standard

Graph
IN THE FIRST QUADRANT OF THE COORDINATE PLANE ORDERED PAIRS OF NUMBERS ARISING FROM MATHEMATICAL AND REALWORLD PROBLEMS, INCLUDING THOSE GENERATED BY NUMBER PATTERNS OR FOUND IN AN INPUTOUTPUT TABLE
Including, but not limited to:
 Coordinate plane (coordinate grid) – a twodimensional plane on which to plot points, lines, and curves
 Axes – the vertical and horizontal lines that act as a reference when plotting points on a coordinate plane
 Intersecting lines – lines that meet or cross at a point
 Origin – the starting point in locating points on a coordinate plane
 Quadrants – any of the four areas created by dividing a plane with an xaxis and yaxis
 Attributes of the coordinate plane
 Two number lines intersect perpendicularly to form the axes, which are used to locate points on the plane.
 The horizontal number line is called the xaxis.
 The vertical number line is called the yaxis.
 The xaxis and the yaxis cross at 0 on both number lines and that intersection is called the origin.
 The coordinate pair of numbers corresponding to the origin is (0, 0).
 Four quadrants are formed by the intersection of the x and yaxes and are labeled counterclockwise with Roman numerals beginning with Quadrant I that includes the positive x and yvalues.
 Relationship between ordered pairs and attributes of the coordinate plane
 A pair of ordered numbers names the location of a point on a coordinate plane.
 Ordered pairs of numbers are indicated within parentheses and separated by a comma (x, y).
 When graphing in Quadrant I, the first number in the ordered pair represents the parallel movement on the xaxis, starting at the origin and moving right.
 When graphing in Quadrant I, the second number in the ordered pair represents the parallel movement on the yaxis, starting at the origin and moving up.
 Limited to the first quadrant for graphing ordered pairs of positive rational numbers
 Various forms of positive rational numbers as ordered pairs
 Counting (natural) numbers
 Decimals (positive decimals less than one and greater than one to the tenths, hundredths, and thousandths)
 Fractions (positive proper, improper, or mixed numbers with equal or unequal denominators)
 Process for graphing ordered pairs of numbers in the first quadrant
 To locate the xcoordinate, begin at the origin and move to the right along the xaxis the appropriate number of units according to the xcoordinate in the ordered pair.
 To locate the ycoordinate, begin at the origin and move up along the yaxis the appropriate number of units according to the ycoordinate in the ordered pair.
 The point of intersection of both the parallel movements on the xaxis and the yaxis is the location of the ordered pair.
 Multiple ordered pairs may be graphed on the same coordinate plane.
 Ordered pairs in mathematical and realworld problem situations
 Ordered pairs generated from number patterns or those found in an inputoutput table
Note(s):
 Grade Level(s):
 Grade 3 represented fractions of halves, fourths, and eighths as distances from zero on a number line.
 Grade 4 represented fractions and decimals to the tenths or hundredths as distances from zero on a number line.
 Grade 6 will graph points in all four quadrants using ordered pairs of rational numbers.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Organizing, representing, and interpreting sets of data
 TxCCRS:
 IX. Communication and Representation
