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:
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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.

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:
 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 problemsolving process.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.2. Evaluate the problemsolving process.

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:
 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.

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:
 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

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:
 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.

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:
 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.

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:
 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.

7.6 
Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is expected to:


7.6A 
Represent sample spaces for simple and compound events using lists and tree diagrams.
Supporting Standard

Represent
SAMPLE SPACES FOR SIMPLE AND COMPOUND EVENTS USING LISTS AND TREE DIAGRAMS
Including, but not limited to:
 Event – a probable situation or condition
 Outcome – the result of an action or event
 Mutually exclusive events – events that cannot happen at the same time
 Simple event – a set or subset of outcomes from a single action or activity where the outcomes cannot be subdivided (e.g., flipping a coin (heads or tails), rolling of a number cube (a specific number when rolled, odd or even, prime or composite), spinning a spinner for a particular color or number, etc.)
 Compound events – a set of outcomes from a combination of actions or activities where the outcomes can be subdivided (e.g., flipping a coin and rolling a number cube, drawing tiles out of a bag and spinning a spinner, etc.)
 Independent events – the outcome from one action or activity does not affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Dependent events – the outcome from one action or activity may affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Sample space – a set of all possible outcomes of one or more events
 Various representations of sample space for simple and compound events
 Lists
 Tree diagrams
 Tables
 Fundamental Counting Principle – if one event has a possible outcomes and a second independent event has b possible outcomes, then there are a • b total possible outcomes for the two events together
 This principle can be applied to determine the sample space for more than two events.
 Connections between various representations
Note(s):
 Grade Level(s):
 Grade 7 introduces representing sample spaces for simple and compound events using lists and tree diagrams.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 IV.A. Probabilistic Reasoning – Counting principles
 IV.A.1. Determine the nature and the number of elements in a finite sample space.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.

7.6B 
Select and use different simulations to represent simple and compound events with and without technology.

Select, Use
DIFFERENT SIMULATIONS TO REPRESENT SIMPLE AND COMPOUND EVENTS WITH AND WITHOUT TECHNOLOGY
Including, but not limited to:
 Event – a probable situation or condition
 Outcome – the result of an action or event
 Simple event – a set or subset of outcomes from a single action or activity where the outcomes cannot be subdivided (e.g., flipping a coin (heads or tails), rolling of a number cube (a specific number when rolled, odd or even, prime or composite), spinning a spinner for a particular color or number, etc.)
 Compound events – a set of outcomes from a combination of actions or activities where the outcomes can be subdivided (e.g., flipping a coin and rolling a number cube, drawing tiles out of a bag and spinning a spinner, etc.)
 Independent events – the outcome from one action or activity does not affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Dependent events – the outcome from one action or activity may affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Sample space – a set of all possible outcomes of one or more events
 Simulation – an experiment or model used to test the outcomes of an event
 Developing a design for a simulation
 Appropriate methods to simulate simple and compound events
 With technology
 Calculator
 Computer model
 Random number generators
 Without technology
 Spinners (even and uneven sections)
 Color tiles
 Twocolor counters
 Coins
 Deck of cards
 Marbles
 Number cubes
Note(s):
 Grade Level(s):
 Grade 7 introduces selecting and using different simulations to represent simple and compound events with and without technology.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IV.C. Probabilistic Reasoning – Measurement involving probability
 IV.C.1. Use probability to make informed decisions.

7.6C 
Make predictions and determine solutions using experimental data for simple and compound events.
Supporting Standard

Predict, Determine
SOLUTIONS USING EXPERIMENTAL DATA FOR SIMPLE AND COMPOUND EVENTS
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
 Percents
 Event – a probable situation or condition
 Outcome – the result of an action or event
 Mutually exclusive events – events that cannot happen at the same time
 Experimental data – the data collected or observed from the outcomes of an experiment
 Various types of experiments
 Representation of experimental data as a fraction, decimal, or percent
 Data should be used for experimental probabilities, and sample spaces should be used for theoretical probabilities.
 Simple event – a set or subset of outcomes from a single action or activity where the outcomes cannot be subdivided (e.g., flipping a coin (heads or tails), rolling of a number cube (a specific number when rolled, odd or even, prime or composite), spinning a spinner for a particular color or number, etc.)
 Compound events – a set of outcomes from a combination of actions or activities where the outcomes can be subdivided (e.g., flipping a coin and rolling a number cube, drawing tiles out of a bag and spinning a spinner, etc.)
 Independent events – the outcome from one action or activity does not affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Dependent events – the outcome from one action or activity may affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Proportional reasoning to make predictions using experimental data
Note(s):
 Grade Level(s):
 Grade 7 introduces making predictions and determining solutions using experimental data for simple and compound events.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IV.B. Probabilistic Reasoning – Computation and interpretation of probabilities
 IV.B.1. Compute and interpret the probability of an event and its complement.
 IV.B.2. Compute and interpret the probability of conditional and compound events.
 IV.C. Probabilistic Reasoning – Measurement involving probability
 IV.C.1. Use probability to make informed decisions.
 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.

7.6D 
Make predictions and determine solutions using theoretical probability for simple and compound events.
Supporting Standard

Predict, Determine
SOLUTIONS USING THEORETICAL PROBABILITY FOR SIMPLE AND COMPOUND EVENTS
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
 Percents
 Event – a probable situation or condition
 Outcome – the result of an action or event
 Mutually exclusive events – events that cannot happen at the same time
 Sample space – a set of all possible outcomes of one or more events
 Probability – a ratio between the number of desired outcomes to the total possible outcomes, 0 ≤ p ≤ 1
 Probability =
 Notation for probability
 The closer a probability of an outcome is to 1, the more likely the outcome will occur; whereas, the closer a probability of an outcome is to 0, the less likely the outcome will occur.
 Theoretical probability – the likelihood of an event occurring predicted by using formulas and mathematical calculations without conducting an experiment
 Various types of theoretical experiments
 Representation of theoretical probability as a fraction, decimal, or percent
 Sample spaces should be used for theoretical probabilities, and data should be used for experimental probabilities.
 Simple event – a set or subset of outcomes from a single action or activity where the outcomes cannot be subdivided (e.g., flipping a coin (heads or tails), rolling of a number cube (a specific number when rolled, odd or even, prime or composite), spinning a spinner for a particular color or number, etc.)
 Compound events – a set of outcomes from a combination of actions or activities where the outcomes can be subdivided (e.g., flipping a coin and rolling a number cube, drawing tiles out of a bag and spinning a spinner, etc.)
 Independent events – the outcome from one action or activity does not affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Dependent events – the outcome from one action or activity may affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Proportional reasoning to make predictions using theoretical probability
Note(s):
 Grade Level(s):
 Grade 7 introduces making predictions and determining solutions using theoretical probability for simple and compound events.
 Geometry will identify whether two events are independent and compute the probability of the two events occurring together with or without replacement.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IV.B. Probabilistic Reasoning – Computation and interpretation of probabilities
 IV.B.1. Compute and interpret the probability of an event and its complement.
 IV.B.2. Compute and interpret the probability of conditional and compound events.
 IV.C. Probabilistic Reasoning – Measurement involving probability
 IV.C.1. Use probability to make informed decisions.
 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.

7.6E 
Find the probabilities of a simple event and its complement and describe the relationship between the two.
Supporting Standard

Find
THE PROBABILITIES OF A SIMPLE EVENT AND ITS COMPLEMENT AND DESCRIBE THE RELATIONSHIP BETWEEN THE TWO
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
 Percents
 Event – a probable situation or condition
 Outcome – the result of an action or event
 Sample space – a set of all possible outcomes of one or more events
 Probability – a ratio between the number of desired outcomes to the total possible outcomes, 0 ≤ p ≤ 1
 Probability =
 Notation for probability
 The closer a probability of an outcome is to 1, the more likely the outcome will occur; whereas, the closer a probability of an outcome is to 0, the less likely the outcome will occur.
 Various types of simple experiments
 Simple event – a set or subset of outcomes from a single action or activity where the outcomes cannot be subdivided (e.g., flipping a coin (heads or tails), rolling of a number cube (a specific number when rolled, odd or even, prime or composite), spinning a spinner for a particular color or number, etc.)
 Complement of an event – the probability of the nonoccurrence of a desired outcome
 The complement can be addressed by determining the probability of an event and subtracting that probability from 1 or by using the sample space to eliminate the possible outcomes of a given event and determining the probability of the remaining outcomes of the given event.
 The outcomes of a simple event and its complement complete the sample space.
 Representation of probability and complements as a fraction, decimal, or percent
 Relationship between a simple event and its complement expressed as a ratio or numerical expression.
 The sum of the probability of a simple event and its complement will always be 1.
Note(s):
 Grade Level(s):
 Grade 7 introduces finding the probabilities of a simple event and its complement and describing the relationship between the two.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IV.B. Probabilistic Reasoning – Computation and interpretation of probabilities
 IV.B.1. Compute and interpret the probability of an event and its complement.
 IV.B.2. Compute and interpret the probability of conditional and compound events.
 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.

7.6F 
Use data from a random sample to make inferences about a population.

Use
DATA FROM A RANDOM SAMPLE TO MAKE INFERENCES ABOUT A POPULATION
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
 Percents
 Data – information that is collected about people, events, or objects
 Inference – a conclusion or prediction based on data
 Population – total collection of persons, objects, or items of interest
 Sample – a subset of the population selected in order to make inferences about the entire population
 Random sample – a subset of the population selected without bias in order to make inferences about the entire population
 Random samples are more likely to contain data that can be used to make predictions about a whole population.
 Data from a random sample given or collected in various forms
 Verbal
 Tabular (vertical/horizontal)
 Graphical
 Inferences based on random sample
 Qualitative – a broad subjective description (e.g., the probability of an event occurring is certain, more likely, not likely, equally likely, or impossible.)
 Quantitative – a narrowed objective description associated with a quantity (e.g., the probability of selecting a consonant from the word EXPERIMENT is 1.5 times as likely as selecting a vowel from the same word, etc.)
 The size of a sample influences the strength of the inference about the population.
 The larger the sample, the stronger the inference about the population.
 The smaller the sample, the weaker the inference about the population.
 Proportional reasoning from data in a random sample to make inferences about the population
Note(s):
 Grade Level(s):
 Grade 7 introduces using data from random samples to make inferences about a population.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IV.C. Probabilistic Reasoning – Measurement involving probability
 IV.C.1. Use probability to make informed decisions.
 V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
 V.C.3. Make predictions using summary statistics.
 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.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

7.6H 
Solve problems using qualitative and quantitative predictions and comparisons from simple experiments.
Readiness Standard

Solve
PROBLEMS USING QUALITATIVE AND QUANTITATIVE PREDICTIONS AND COMPARISONS FROM SIMPLE EXPERIMENTS
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
 Percents
 Event – a probable situation or condition
 Outcome – the result of an action or event
 Sample space – a set of all possible outcomes of one or more events
 Probability – a ratio between the number of desired outcomes to the total possible outcomes, 0 ≤ p ≤ 1
 Probability =
 Notation for probability
 The closer a probability of an outcome is to 1, the more likely the outcome will occur; whereas, the closer a probability of an outcome is to 0, the less likely the outcome will occur.
 Simple experiment – an experiment with one simple event
 Various types of simple experiments
 Theoretical data – the possible outcomes of an event without conducting an experiment
 Experimental data – the data collected or observed from the outcomes of an experiment
 Predictions and comparisons
 Qualitative – a broad subjective description (e.g., the probability of an event occurring is certain, more likely, not likely, equally likely, or impossible.)
 Quantitative – a narrowed objective description associated with a quantity (e.g., the probability of selecting a consonant from the word EXPERIMENT is 1.5 times as likely as selecting a vowel from the same word, etc.)
 Proportional reasoning to make predictions and comparisons from simple experiments
Note(s):
 Grade Level(s):
 Grade 7 introduces solving problems using qualitative and quantitative predictions and comparisons from simple experiments.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IV.C. Probabilistic Reasoning – Measurement involving probability
 IV.C.1. Use probability to make informed decisions.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.3. Determine a solution.

7.6I 
Determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces.
Readiness Standard

Determine
EXPERIMENTAL AND THEORETICAL PROBABILITIES RELATED TO SIMPLE AND COMPOUND EVENTS USING DATA AND SAMPLE SPACES
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
 Percents
 Event – a probable situation or condition
 Outcome – the result of an action or event
 Mutually exclusive events – events that cannot happen at the same time
 Sample space – a set of all possible outcomes of one or more events
 Various representations of sample space
 Lists
 Tree diagrams
 Tables
 Fundamental Counting Principle – if one event has a possible outcomes and a second independent event has b possible outcomes, then there are a • b total possible outcomes for the two events together
 This principle can be applied to determine the sample space for more than two events.
 Probability – a ratio between the number of desired outcomes to the total possible outcomes, 0 ≤ p ≤ 1
 Probability =
 Notation for probability
 The closer a probability of an outcome is to 1, the more likely the outcome will occur; whereas, the closer a probability of an outcome is to 0, the less likely the outcome will occur.
 Theoretical probability – the likelihood of an event occurring predicted by using formulas and mathematical calculations without conducting an experiment
 Sample spaces should be used for theoretical probabilities, and data should be used for experimental probabilities.
 Experimental probability – the likelihood of an event occurring from the outcomes of an experiment
 Data should be used for experimental probabilities, and sample spaces should be used for theoretical probabilities,
 Various types of experiments
 Representation of probability as a fraction, decimal, or percent
 Complement of an event – the probability of the nonoccurrence of a desired outcome
 The outcomes of an event and its complement complete the sample space.
 Relationship between an event and its complement expressed as a ratio or numerical expression
 The sum of the probability of an event and its complement will always be 1.
 Relationship between theoretical and experimental probability
 Law of large numbers – as the number of trials in an experiment increases, the experimental probability of an event approaches the theoretical probability of the same event, meaning the difference between the experimental and theoretical probability will be closer to zero
 Simple event – a set or subset of outcomes from a single action or activity where the outcomes cannot be subdivided (e.g., flipping a coin (heads or tails), rolling of a number cube (a specific number when rolled, odd or even, prime or composite), spinning a spinner for a particular color or number, etc.)
 Compound events – a set of outcomes from a combination of actions or activities where the outcomes can be subdivided (e.g., flipping a coin and rolling a number cube, drawing tiles out of a bag and spinning a spinner, etc.)
 Independent events – the outcome from one action or activity does not affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
 Dependent events – the outcome from one action or activity may affect the probability of the outcome(s) of any subsequent action(s) or activity(s); usually involves compound events
Note(s):
 Grade Level(s):
 Grade 7 introduces determining experimental and theoretical probabilities related to simple and compound events using data and sample spaces.
 Geometry will determine probabilities based on area to solve contextual problems.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IV.B. Probabilistic Reasoning – Computation and interpretation of probabilities
 IV.B.1. Compute and interpret the probability of an event and its complement.
 IV.B.2. Compute and interpret the probability of conditional and compound events.
 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.
