
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.

7.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


7.1A 
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 rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:

7.1B 
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 rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VIII. Problem Solving and Reasoning

7.1C 
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 rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VIII. Problem Solving and Reasoning

7.1D 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard

Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.1E 
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 rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.1F 
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 rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:

7.1G 
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 rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.8 
Expressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is expected to:


7.8A 
Model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas.

Model
THE RELATIONSHIP BETWEEN THE VOLUME OF A RECTANGULAR PRISM AND A RECTANGULAR PYRAMID HAVING BOTH CONGRUENT BASES AND HEIGHTS AND CONNECT THAT RELATIONSHIP TO THE FORMULAS
Including, but not limited to:
 Threedimensional figure – a figure that has measurements including length, width (depth), and height
 Edge – where the sides of two faces meet on a threedimensional figure
 Vertex (vertices) in a threedimensional figure – the point (corner) where three or more edges of a threedimensional figure meet
 Face – a flat surface of a threedimensional figure
 Bases of a rectangular prism – any two congruent, opposite, and parallel faces shaped like rectangles; exactly 3 possible sets
 Height of a rectangular prism – the length of a side that is perpendicular to both bases
 Base of a rectangular pyramid – a rectangular face opposite the common vertex (apex) where the 4 triangular faces meet
 Height of a rectangular pyramid – the length of a perpendicular line segment from the vertex of the pyramid to the base
 Prism – a threedimensional figure containing two congruent and parallel faces that are polygons
 Rectangular prism, including a cube or square prism
 6 rectangular faces (2 parallel rectangular faces [bases], 4 rectangular faces)
 12 edges
 8 vertices
 Pyramid – a threedimensional figure containing a base that is a polygon and triangular faces that share a common vertex, also known as an apex
 Rectangular pyramid, including a square pyramid
 5 faces (1 rectangular face [base], 4 triangular faces)
 8 edges
 5 vertices (1 apex, 4 vertices)
 Volume – the measurement attribute of the amount of space occupied by matter
 One way to measure volume is a threedimensional cubic measure
 Congruent – of equal measure, having exactly the same size and same shape
 Various models to represent the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights
 Filling the rectangular pyramid with a measurable unit (e.g., rice, sand, water, etc.) and emptying the contents into the rectangular prism until the rectangular prism is completely full
 The contents of the rectangular pyramid will need to be emptied three times in order to fill the rectangular prism completely.
 Creating a replica of the rectangular pyramid and rectangular prisms with clay and comparing their masses
 The mass of the rectangular prism will be three times the mass of the rectangular pyramid, whereas the mass of the rectangular pyramid is the mass of the rectangular prism.
 Generalizations from models used to represent the relationship between the volume of a rectangular prism and a rectangular pyramid having congruent bases and heights
 The volume of a rectangular prism is three times the volume of a rectangular pyramid.
 The volume of a rectangular pyramid is the volume of a rectangular prism.
 Connections between models to represent volume of a rectangular prism and rectangular pyramid having both congruent bases and heights to the formulas for volume
 Formulas for volume from STAAR Grade 7 Mathematics Reference Materials
 Prism
 V = Bh, where B represents the base area and h represents the height of the prism which is the number of times the base area is repeated or layered
 Rectangular prism
 The base of a rectangular prism is a rectangle whose area may be found with the formula, A = bh or A = lw, meaning the base area, B, may be found with the formula B = bh or B = lw; therefore, the volume of a rectangular prism may be found using V = Bh or V =(bh)h or V = (lw)h.
 Pyramid
 V = Bh, where B represents the base area and h represents the height of the pyramid
 Rectangular pyramid
 The base of a rectangular pyramid is a rectangle whose area may be found with the formula, A = bh or A = lw, meaning the base area, B, may be found with the formula B = bh or B = lw; therefore, the volume of a rectangular pyramid may be found using V = Bh or V = (bh)h or V = (lw)h.
Note(s):
 Grade Level(s):
 Grade 6 modeled area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes.
 Grade 8 will describe the volume formula V = Bh of a cylinder in terms of its base area and its height.
 Grade 8 will model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 IV. Measurement Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

7.8B 
Explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas.

Explain
VERBALLY AND SYMBOLICALLY THE RELATIONSHIP BETWEEN THE VOLUME OF A TRIANGULAR PRISM AND A TRIANGULAR PYRAMID HAVING BOTH CONGRUENT BASES AND HEIGHTS AND CONNECT THAT RELATIONSHIP TO THE FORMULAS
Including, but not limited to:
 Threedimensional figure – a figure that has measurements including length, width (depth), and height
 Edge – where the sides of two faces meet on a threedimensional figure
 Vertex (vertices) in a threedimensional figure – the point (corner) where three or more edges of a threedimensional figure meet
 Face – a flat surface of a threedimensional figure
 Bases of a triangular prism – the two congruent, opposite, and parallel faces shaped like triangles
 Height of a triangular prism – the length of a side that is perpendicular to both bases
 Base of a triangular pyramid – a triangular face opposite the common vertex (apex) where the 3 triangular faces meet
 Height of a triangular pyramid – the length of a perpendicular line segment from the vertex of the pyramid to the base
 Prism – a threedimensional figure containing two congruent and parallel faces that are polygons
 Triangular prism
 5 faces (2 triangular faces [bases], 3 rectangular faces)
 9 edges
 6 vertices
 Pyramid – a threedimensional figure containing a base that is a polygon and the faces are triangles that share a common vertex, also known as an apex
 Triangular pyramid
 4 faces (1 triangular face [base], 3 triangular faces)
 6 edges
 4 vertices (1 apex, 4 vertices)
 Volume – the measurement attribute of the amount of space occupied by matter
 One way to measure volume is a threedimensional cubic measure
 Congruent – of equal measure, having exactly the same size and same shape
 Generalizations of the relationship between the volume of a triangular prism and a triangular pyramid having congruent bases and heights
 The volume of a triangular prism is three times the volume of a triangular pyramid.
 The volume of a triangular pyramid is the volume of a triangular prism.
 Connections between models to represent volume of a triangular prism and triangular pyramid having both congruent bases and heights to the formulas for volume
 Formulas for volume from STAAR Grade 7 Mathematics Reference Materials
 Prism
 V = Bh, where B represents the base area and h represents the height of the prism which is the number of times the base area is repeated or layered)
 Triangular prism
 The base of a triangular prism is a triangle whose area may be found with the formula, A = bh, meaning the base area, B, may be found using B = bh; therefore, the volume of a triangular prism may be found using V = Bh or V = .
 Pyramid
 V = Bh, where B represents the base area and h represents the height of the pyramid
 Triangular pyramid
 The base of a triangular pyramid is a triangle whose area may be found with the formula, A = bh, meaning the base area, B, may be found using B = bh; therefore, the volume of a triangular pyramid may be found using V = Bh or V = or V = .
Note(s):
 Grade Level(s):
 Grade 7 introduces explaining verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connecting that relationship to the formulas.
 Grade 8 will model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 I. Numeric Reasoning
 IV. Measurement Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

7.9 
Expressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is expected to:


7.9A 
Solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids.
Readiness Standard

Solve
PROBLEMS INVOLVING THE VOLUME OF RECTANGULAR PRISMS, TRIANGULAR PRISMS, RECTANGULAR PYRAMIDS, AND TRIANGULAR PYRAMIDS
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
 Decimals
 Fractions
 Threedimensional figure – a figure that has measurements including length, width (depth), and height
 Prism – a threedimensional figure containing two congruent and parallel faces that are polygons
 Rectangular prism, including a cube or square prism
 Pyramid – a threedimensional figure containing a base that is a polygon and the faces are triangles that share a common vertex, also known as an apex
 Rectangular pyramid, including a square pyramid
 Volume – the measurement attribute of the amount of space occupied by matter
 One way to measure volume is a threedimensional cubic measure
 Positive rational number side lengths
 Recognition of volume embedded in mathematical and realworld problem situations
 Formulas for volume from STAAR Grade 7 Mathematics Reference Materials
 Prism
 V = Bh, where B represents the base area and h represents the height of the prism which is the number of times the base area is repeated or layered)
 Rectangular prism
 The base of a rectangular prism is a rectangle whose area may be found with the formula, A = bh or A = lw, meaning the base area, B, may be found with the formula B = bh or B = lw; therefore, the volume of a rectangular prism may be found using V = Bh or V = (bh)h or V = (lw)h.
 Triangular prism
 The base of a triangular prism is a triangle whose area may be found with the formula, A = bh, meaning the base area, B, may be found using B = bh; therefore, the volume of a triangular prism may be found using V = Bh or V = .
 Pyramid
 V = Bh, where B represents the base area and h represents the height of the pyramid
 Rectangular pyramid
 The base of a rectangular pyramid is a rectangle whose area may be found with the formula, A = bh or A = lw, meaning the base area, B, may be found with the formula B = bh or B = lw; therefore, the volume of a rectangular pyramid may be found using V = Bh or V = (bh)h or V = (lw)h.
 Triangular pyramid
 The base of a triangular pyramid is a triangle whose area may be found with the formula, A = bh, meaning the base area, B, may be found using B = bh; therefore, the volume of a triangular pyramid may be found using V = Bh or V = or V = .
Note(s):
 Grade Level(s):
 Grade 6 determined solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
 Grade 8 will solve problems involving the volume of cylinders, cones, and spheres.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 I. Numeric Reasoning
 III.C. Geometric Reasoning – Connections between geometry and other mathematical content strands
 IV. Measurement Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

7.9D 
Solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net.
Supporting Standard

Solve
PROBLEMS INVOLVING THE LATERAL AND TOTAL SURFACE AREA OF A RECTANGULAR PRISM, RECTANGULAR PYRAMID, TRIANGULAR PRISM, AND TRIANGULAR PYRAMID BY DETERMINING THE AREA OF THE SHAPE'S NET
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
 Decimals
 Fractions
 Threedimensional figure – a figure that has measurements including length, width (depth), and height
 Edge – where the sides of two faces meet on a threedimensional figure
 Vertex (vertices) in a threedimensional figure – the point (corner) where three or more edges of a threedimensional figure meet
 Face – a flat surface of a threedimensional figure
 Bases of a rectangular prism – any two congruent, opposite, and parallel faces shaped like rectangles; exactly 3 possible sets
 Height of a rectangular prism – the length of a side that is perpendicular to both bases
 Bases of a triangular prism – the two congruent, opposite, and parallel faces shaped like triangles
 Height of a triangular prism – the length of a side that is perpendicular to both bases
 Base of a rectangular pyramid – a rectangular face opposite the common vertex (apex) where the 4 triangular faces meet
 Height of a rectangular pyramid – the length of a perpendicular line segment from the vertex of the pyramid to the base
 Base of a triangular pyramid – a triangular face opposite the common vertex (apex) where the 3 triangular faces meet
 Height of a triangular pyramid – the length of a perpendicular line segment from the vertex of the pyramid to the base
 Prism – a threedimensional figure containing two congruent and parallel faces that are polygons
 Rectangular prism, including a cube or square prism
 6 rectangular faces (2 parallel rectangular faces [bases], 4 rectangular faces)
 12 edges
 8 vertices
 Triangular prism
 5 faces (2 triangular faces [bases], 3 rectangular faces)
 9 edges
 6 vertices
 Pyramid – a threedimensional figure containing a base that is a polygon and the faces are triangles that share a common vertex, also known as an apex
 Rectangular pyramid, including a square pyramid
 5 faces (1 rectangular face [base], 4 triangular faces)
 8 edges
 5 vertices
 Triangular pyramid
 4 faces (1 triangular face [base], 3 triangular faces)
 6 edges
 4 vertices
 Area – the measurement attribute that describes the number of square units a figure or region covers
 Area is a twodimensional square unit measure.
 Positive rational number side lengths
 Surface Area
 Lateral surface area – the sum of all the lateral surface areas of a figure; the number of square units needed to cover the lateral view (area excluding the base(s) of a threedimensional figure)
 Total surface area – the sum of all the surface areas of a figure; the number of square units needed to cover all of the surfaces (bases and lateral area)
 Net – a twodimensional model or drawing that can be folded into a threedimensional solid
Note(s):
 Grade Level(s):
 Grade 6 determined solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
 Grade 8 will use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 I. Numeric Reasoning
 III.C. Geometric Reasoning – Connections between geometry and other mathematical content strands
 IV. Measurement Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections
