G.1 |
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
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G.1A |
Apply mathematics to problems arising in everyday life, society, and the workplace.
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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.
- TxCCRS:
- VII.D. Problem Solving and Reasoning – Real-world problem solving
- VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
- IX.A. Connections – Connections among the strands of mathematics
- IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
- IX.A.2. Connect mathematics to the study of other disciplines.
- IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
- IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
- IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
- IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
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G.1B |
Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
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Use
A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
- Problem-solving model
- Analyze given information
- Formulate a plan or strategy
- Determine a solution
- Justify the solution
- Evaluate the problem-solving process and the reasonableness of the solution
Note(s):
- The mathematical process standards may be applied to all content standards as appropriate.
- TxCCRS:
- I.B. Numeric Reasoning – Number sense and number concepts
- I.B.1. Use estimation to check for errors and reasonableness of solutions.
- V.A. Statistical Reasoning – Design a study
- V.A.1. Formulate a statistical question, plan an investigation, and collect data.
- VII.A. Problem Solving and Reasoning – Mathematical problem solving
- VII.A.1. Analyze given information.
- VII.A.2. Formulate a plan or strategy.
- VII.A.3. Determine a solution.
- VII.A.4. Justify the solution.
- VII.A.5. Evaluate the problem-solving process.
- VII.D. Problem Solving and Reasoning – Real-world problem solving
- VII.D.2. Evaluate the problem-solving process.
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G.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.
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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.
- TxCCRS:
- I.B. Numeric Reasoning – Number sense and number concepts
- I.B.1. Use estimation to check for errors and reasonableness of solutions.
- V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
- V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
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G.1D |
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
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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.
- TxCCRS:
- II.D. Algebraic Reasoning – Representing relationships
- II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
- II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
- VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
- VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
- VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
- VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
- VIII.B. Communication and Representation – Interpretation of mathematical work
- VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
- VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
- VIII.C. Communication and Representation – Presentation and representation of mathematical work
- VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
- VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
- VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
- IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
- IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
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G.1E |
Create and use representations to organize, record, and communicate mathematical ideas.
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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.
- TxCCRS:
- VIII.B. Communication and Representation – Interpretation of mathematical work
- VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
- VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
- VIII.C. Communication and Representation – Presentation and representation of mathematical work
- VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
- VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
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G.1F |
Analyze mathematical relationships to connect and communicate mathematical ideas.
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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 non-examples, patterns, etc.
- Current knowledge to new learning
Note(s):
- The mathematical process standards may be applied to all content standards as appropriate.
- TxCCRS:
- VII.A. Problem Solving and Reasoning – Mathematical problem solving
- VII.A.1. Analyze given information.
- VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
- VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
- VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
- VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
- VIII.B. Communication and Representation – Interpretation of mathematical work
- VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
- VIII.C. Communication and Representation – Presentation and representation of mathematical work
- VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
- VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
- VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
- IX.A. Connections – Connections among the strands of mathematics
- IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
- IX.A.2. Connect mathematics to the study of other disciplines.
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G.1G |
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
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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.
- TxCCRS:
- VII.A. Problem Solving and Reasoning – Mathematical problem solving
- VII.A.4. Justify the solution.
- VII.B. Problem Solving and Reasoning – Proportional reasoning
- VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
- VII.C. Problem Solving and Reasoning – Logical reasoning
- VII.C.1. Develop and evaluate convincing arguments.
- VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
- VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
- VIII.B. Communication and Representation – Interpretation of mathematical work
- VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
- VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
- VIII.C. Communication and Representation – Presentation and representation of mathematical work
- VIII. C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
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G.10 |
Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures. The student is expected to:
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G.10B |
Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change.
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Determine, Describe HOW CHANGES IN THE LINEAR DIMENSIONS OF A SHAPE AFFECT ITS PERIMETER, AREA, SURFACE AREA, OR VOLUME, INCLUDING PROPORTIONAL AND NON-PROPORTIONAL DIMENSIONAL CHANGE Including, but not limited to: - Verbal and written description
- Dimensional change
- Perimeter and circumference
- Area and surface area
- Volume
- Proportional change
- Two-dimensional proportional change – two dimensions multiplied by the same scale factor
- Three-dimensional proportional change – three dimensions multiplied by the same scale factor
- Non-proportional change
- Two-dimensional non-proportional change – either only one dimension multiplied by a scale factor or the two dimensions are multiplied by different scale factors
- Three-dimensional non-proportional change – either one and/or two dimensions multiplied by a scale factor or the three dimensions are multiplied by different scale factors
- Comparison of the effect of proportional and non-proportional dimensional change
- Emphasis on connections to units
- Dimension changes in real-world problem situations
Note(s):
- Grade Level(s)
- Grade 7 and 8 modeled the effect on linear and area measurements of dilated two-dimensional shapes.
- Various mathematical process standards will be applied to this student expectation as appropriate.
- TxCCRS
- I.C. Numeric Reasoning – Systems of measurement
- I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.
- III.A. Geometric and Spatial Reasoning – Figures and their properties
- III.A.2. Form and validate conjectures about one-, two-, and three-dimensional figures and their properties.
- III.B. Geometric and Spatial Reasoning – Transformations and symmetry
- III.B.1. Identify transformations and symmetries of figures.
- III.B.2. Use transformations to investigate congruence, similarity, and symmetries of figures.
- III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
- III.C.1. Make connections between geometry and algebraic equations.
- III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
- III.D.1. Find the perimeter and area of two-dimensional figures.
- III.D.2. Determine the surface area and volume of three-dimensional figures.
- III.D.3. Determine indirect measurements of geometric figures using a variety of methods.
- VII.A. Problem Solving and Reasoning – Mathematical problem solving
- VII.A.1. Analyze given information.
- VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
- VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
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G.11 |
Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures. The student is expected to:
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G.11A |
Apply the formula for the area of regular polygons to solve problems using appropriate units of measure.
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Apply
THE FORMULA FOR THE AREA OF REGULAR POLYGONS TO SOLVE PROBLEMS USING APPROPRIATE UNITS OF MEASURE
Including, but not limited to:
- Regular polygon – a convex polygon in which all sides are congruent (equilateral) and all angles are congruent (equiangular)
- Radius of a regular polygon – a segment that extends from the center of a regular polygon to a vertex. The radius of a regular polygon bisects the vertex angle to which it is drawn.
- Apothem – a segment that extends from the center of a regular polygon perpendicular to a side of the regular polygon. The apothem bisects the side of the regular polygon to which it is drawn.
- Formula for the area of regular polygons
- A =
aP where P represents the perimeter and a represents the apothem.
- Connection to area of a triangle: A =
bh
- Real-world problem situations involving area
- Emphasis on appropriate units of measure
Note(s):
- Grade Level(s)
- Previous grade levels used units, tools, and formulas to find the area of figures in problem situations.
- Previous grade levels introduced the language of regular polygons.
- Grade 7 determined the composite area of figures composed of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles.
- Geometry introduces a formula for the area of an n-sided polygon.
- Various mathematical process standards will be applied to this student expectation as appropriate.
- TxCCRS
- II.A. Algebraic Reasoning – Identifying expressions equations
- II.A.1. Explain the difference between expressions and equations.
- III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
- III.D.1. Find the perimeter and area of two-dimensional figures.
- VII.A. Problem Solving and Reasoning – Mathematical problem solving
- VII.A.3. Determine a solution.
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G.11B |
Determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure.
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Determine THE AREA OF COMPOSITE TWO-DIMENSIONAL FIGURES COMPRISED OF A COMBINATION OF TRIANGLES, PARALLELOGRAMS, TRAPEZOIDS, KITES, REGULAR POLYGONS, OR SECTORS OF CIRCLES TO SOLVE PROBLEMS USING APPROPRIATE UNITS OF MEASURE Including, but not limited to: - Composites of two-dimensional figures
- Triangles
- Parallelograms
- Trapezoids
- Kites
- Regular polygons
- Sectors of circles
- Applications to real-world situations
- Appropriate use of units of measure
Note(s):
- Grade Level(s)
- Previous grade levels used units, tools, and formulas to find the area of figures in problem situations.
- Previous grade levels introduced composites of two-dimensional figures.
- Geometry introduces kites, regular polygons, and sectors as shapes that can make up composite figures.
- Various mathematical process standards will be applied to this student expectation as appropriate.
- TxCCRS
- II.A. Algebraic Reasoning – Identifying expressions and equations
- II.A.1. Explain the difference between expressions and equations.
- III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
- III.D.1. Find the perimeter and area of two-dimensional figures.
- VII.A. Problem Solving and Reasoning – Mathematical problem solving
- VII.A.3. Determine a solution.
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G.11C |
Apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.
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Apply
THE FORMULAS FOR THE TOTAL AND LATERAL SURFACE AREA OF THREE-DIMENSIONAL FIGURES, INCLUDING PRISMS, PYRAMIDS, CONES, CYLINDERS, SPHERES, AND COMPOSITE FIGURES TO SOLVE PROBLEMS USING APPROPRIATE UNITS OF MEASURE
Including, but not limited to:
- Connections between formulas and models, including nets
- Formulas for lateral and total surface area
- Prisms
- Lateral surface area
- S = Perimeter of the base times the height
- S = Ph
- Total surface area
- S = Perimeter of the base times the height plus 2 times the area of the base
- S = Ph + 2B
- Pyramids
- Lateral surface area
- S =
times the perimeter of the base times the slant height
- S =
Pℓ
- Total surface area
- S =
times the perimeter of the base times the slant height plus the area of the base
- S =
Pℓ + B
- Cones
- Lateral surface area
- S = π times the radius times the slant height
- S = πrℓ
- Total surface area
- S = π times the radius times the slant height plus the area of the base
- S = πrℓ +πr2
- Cylinders
- Lateral surface area
- S = 2 times π times the radius times the height
- S = 2πrh
- Total surface area
- S = 2 times π times the radius times the height plus 2 times the area of the base
- S = 2πrh + 2πr2
- Spheres
- Total surface area
- S = 4 times π times the radius squared
- S = 4πr2
- Composite figures
- Applications to real-world situations
- Use of appropriate units of measure
Note(s):
- Grade Level(s)
- Previous grade levels used units, tools, and formulas to find area of figures in problem situations.
- Previous grade levels introduced the terminology of regular polygons.
- Grade 7 determined the surface area of pyramids and prisms using nets.
- Grade 8 connects previous knowledge of surface area and nets to the surface area formulas.
- Geometry introduces cones, pyramids, spheres, and composite figures to the surface area formulas.
- Various mathematical process standards will be applied to this student expectation as appropriate.
- TxCCRS
- II.A. Algebraic Reasoning – Identifying expressions and equations
- II.A.1. Explain the difference between expressions and equations.
- III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
- III.D.2. Determine the surface area and volume of three-dimensional figures.
- VII.A. Problem Solving and Reasoning – Mathematical problem solving
- VII.A.3. Determine a solution.
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G.11D |
Apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.
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Note(s):
- Grade Level(s)
- Grades 7 and 8 introduced determining and applying formulas to solve problems involving lateral and total surface area and volume of three-dimensional figures.
- Various mathematical process standards will be applied to this student expectation as appropriate.
- TxCCRS
- II.A. Algebraic Reasoning – Identifying expressions and equations
- II.A.1. Explain the difference between expressions and equations.
- III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
- III.D.2. Determine the surface area and volume of three-dimensional figures.
- VII.A. Problem Solving and Reasoning – Mathematical problem solving
- VII.A.3. Determine a solution.
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