Learning Standards for

Mathematics, Science, and Technology at Three Levels

 

 

Standard 1: Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

 

 

Standard 2: Students will access, generate, process, and transfer information using appropriate technologies.

 

Standard 3: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Standard 4: Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.

 

Standard 5: Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

 

Standard 6: Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

 

Standard 7: Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions.

 

Standard 1 ¾ Analysis, Inquiry, and Design

Elementary

Mathematical Analysis Scientific Inquiry

 

1. Abstraction and symbolic representation are used to communicate mathematically.

 

Students:

 

This is evident, for example, when students:

 

 

2. Deductive and inductive reasoning are used to reach mathematical conclusions.

 

Students:

 

 

3. Critical thinking skills are used in the solution of mathematical problems.

 

Students:

 

1. The central purpose of scientific inquiry is to develop explanations of natural phenomena in a continuing, creative process.

 

Students:

 

This is evident, for example, when students:

 

 

2. Beyond the use of reasoning and consensus, scientific inquiry involves the testing of proposed explanations involving the use of conventional techniques and procedures and usually requiring considerable ingenuity.

 

Students:

 

This is evident, for example, when students:

 

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

 

Engineering Design

 

3. The observations made while testing proposed explanations, when analyzed using conventional and invented methods, provide new insights into phenomena.

 

Students:

 

This is evident, for example, when students:

 

1. Engineering design is an iterative process involving modeling and optimization finding the best solution within given constraints which is used to develop technological solutions to problems within given constraints.

 

Students engage in the following steps in a design process:

 

This is evident, for example, when students:

 

 

Standard 1 ¾ Analysis, Inquiry, and Design

Intermediate

Mathematical Analysis Scientific Inquiry

 

1. Abstraction and symbolic representation are used to communicate mathematically.

 

Students:

 

 

2. Deductive and inductive reasoning are used to reach mathematical conclusions.

 

Students:

 

This is evident, for example, when students:

 

 

3. Critical thinking skills are used in the solution of mathematical problems.

 

Students:

 

1. The central purpose of scientific inquiry is to develop explanations of natural phenomena in a continuing, creative process.

 

Students:

 

This is evident, for example, when students:

 

 

2. Beyond the use of reasoning and consensus, scientific inquiry involves the testing of proposed explanations involving the use of conventional techniques and procedures and usually requiring considerable ingenuity.

 

Students:

 

This is evident, for example, when students:

 

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

 

Engineering Design

 

3. The observations made while testing proposed explanations, when analyzed using conventional and invented methods, provide new insights into phenomena.

 

Students:

 

This is evident, for example, when students:

 

 

1. Engineering design is an iterative process involving modeling and optimization finding the best solution within given constraints which is used to develop technological solutions to problems within given constraints.

 

Students engage in the following steps in a design process:

 

This is evident, for example, when students:

 

 

Standard 1 ¾ Analysis, Inquiry, and Design

Commencement

Mathematical Analysis Scientific Inquiry

 

1. Abstraction and symbolic representation are used to communicate mathematically.

 

Students:

 

 

2. Deductive and inductive reasoning are used to reach mathematical conclusions.

 

Students:

 

 

3. Critical thinking skills are used in the solution of mathematical problems.

 

Students:

 

1. The central purpose of scientific inquiry is to develop explanations of natural phenomena in a continuing, creative process.

 

Students:

 

This is evident, for example, when students:

 

 

2. Beyond the use of reasoning and consensus,

scientific inquiry involves the testing of proposed

explanations involving the use of conventional

techniques and procedures and usually requiring

considerable ingenuity.

 

Students:

 

This is evident, for example, when students:

.

 

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

 

Engineering Design

 

3. The observations made while testing proposed explanations, when analyzed using conventional and invented methods, provide new insights into phenomena.

 

Students:

 

This is evident, for example, when students:

 

1. Engineering design is an iterative process involving modeling and optimization finding the best solution within given constraints which is used to develop technological solutions to problems within given constraints.

 

Students engage in the following steps in a design process:

 

This is evident, for example, when students:

 

Standard 2 ¾ Information Systems

Elementary

Information Systems

 

1. Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning.

 

Students:

 

This is evident, for example, when students:

 

2. Knowledge of the impacts and limitations of information systems is essential to its effective and ethical use.

 

Students:

 

This is evident, for example, when students:

 

Students will access, generate, process, and transfer information using appropriate technologies.

 

3. Information technology can have positive and negative impacts on society, depending upon how it is used.

 

Students:

 

 

Standard 2 ¾ Information Systems

Intermediate

Information Systems

 

1. Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning.

 

Students:

 

This is evident, for example, when students:

 

2. Knowledge of the impacts and limitations of information systems is essential to its effective and ethical use.

 

Students:

 

Students will access, generate, process, and transfer information using appropriate technologies.

 

3. Information technology can have positive and negative impacts on society, depending upon how it is used.

 

Students:

 

 

Standard 2 ¾ Information Systems

Commencement

Information Systems

 

1. Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning.

 

Students:

 

This is evident, for example, when students:

 

2. Knowledge of the impacts and limitations of information systems is essential to its effective and ethical use.

 

Students:

 

This is evident, for example, when students:

 

Students will access, generate, process, and transfer information using appropriate technologies.

 

3. Information technology can have positive and negative impacts on society, depending upon how it is used.

 

Students:

 

Standard 3 ¾ Mathematics

Elementary

Mathematical Reasoning Number and Numeration

 

1. Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

 

Students:

 

This is evident, for example, when students:

 

2. Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.

 

Students:

 

This is evident, for example, when students:

 

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Operations Modeling/Multiple Representation

 

3. Students use mathematical operations and relationships among them to understand mathematics.

 

Students:

 

This is evident, for example, when students:

 

4. Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

 

Students:

 

This is evident, for example, when students:

 

Standard 3 ¾ Mathematics

Elementary

Measurement Uncertainty

 

5. Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.

 

Students:

 

This is evident, for example, when students:

6. Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.

 

Students:

 

This is evident, for example, when students:

 

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Patterns/Functions

 

7. Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

 

Students:

 

This is evident, for example, when students:

 

Standard 3 ¾ Mathematics

Intermediate

Mathematical Reasoning Number and Numeration

 

1. Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

 

Students:

 

This is evident, for example, when students:

 

 

2. Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.

 

Students:

 

This is evident, for example, when students:

1 = 3 = 25 = 0.25 = 25%

4 12 100

 

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Operations Modeling/Multiple Representation

 

3. Students use mathematical operations and relationships among them to understand mathematics.

 

Students:

 

This is evident, for example, when students:

4 5 3 2 4

 

 

4. Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

 

Students:

 

This is evident, for example, when students:

 

Standard 3 ¾ Mathematics

Intermediate

Measurement Uncertainty

 

5. Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.

 

Students:

 

This is evident, for example, when students:

 

 

6. Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.

 

Students:

 

This is evident, for example, when students:

 

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Patterns/Functions

 

7. Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

 

Students:

 

This is evident, for example, when students:

 

Standard 3 ¾ Mathematics

Commencement

Mathematical Reasoning Number and Numeration

 

1. Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

 

Students:

 

This is evident, for example, when students:

 

2. Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.

 

Students:

 

This is evident, for example, when students:

 

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Operations Modeling/Multiple Representation

 

3. Students use mathematical operations and relationships among them to understand mathematics.

 

Students:

 

This is evident, for example, when students:

 

 

4. Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

 

Students:

This is evident, for example, when students:

 

Standard 3 ¾ Mathematics

Commencement

Measurement Uncertainty

 

5. Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.

 

Students:

 

This is evident, for example, when students:

 

6. Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.

 

Students:

 

This is evident, for example, when students:

 

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Patterns/Functions

 

7. Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

 

Students:

 

This is evident, for example, when students:

 

Standard 3 ¾ Mathematics

Four year sequence in mathematics

Measurement Uncertainty

 

1. Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

 

Students:

 

This is evident, for example, when students:

 

 

2. Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.

 

Students:

 

This is evident, for example, when students:

 

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Operations Modeling/Multiple Representation

 

3. Students use mathematical operations and relationships among them to understand mathematics.

 

Students:

 

This is evident, for example, when students:

 

 

4. Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

 

Students:

 

This is evident, for example, when students:

 

Standard 3 ¾ Mathematics

Four year sequence in mathematics

Measurement Uncertainty

 

5. Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.

 

Students:

 

This is evident, for example, when students:

 

6. Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.

 

Students:

 

This is evident, for example, when students:

 

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

 

Patterns/Functions

 

7. Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

 

Students:

 

This is evident, for example, when students:

infinity.

 

 

Standard 4 ¾ Science

Elementary

Physical Setting

 

1. The Earth and celestial phenomena can be described by principles of relative motion and perspective.

 

Students:

 

This is evident, for example, when students:

 

2. Many of the phenomena that we observe on Earth involve interactions among components of air, water, and land.

Students:

 

This is evident, for example, when students:

 

 

3. Matter is made up of particles whose properties determine the observable characteristics of matter

and its reactivity.

 

Students:

 

This is evident, for example, when students:

 

4. Energy exists in many forms, and when these forms change energy is conserved.

 

Students:

 

This is evident, for example, when students:

 

5. Energy and matter interact through forces that result in changes in motion.

 

Students:

 

This is evident, for example, when students:

 

Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.

 

The Living Environment

 

1. Living things are both similar to and different from each other and nonliving things.

 

Students:

 

This is evident, for example, when students:

 

2. Organisms inherit genetic information in a variety of ways that result in continuity of structure and

function between parents and offspring.

 

Students:

 

This is evident, for example, when students:

 

3. Individual organisms and species change over time.

 

Students:

 

This is evident, for example, when students:

 

 

4. The continuity of life is sustained through reproduction and development.

 

Students:

 

This is evident, for example, when students:

 

5. Organisms maintain a dynamic equilibrium that sustains life.

 

Students:

 

This is evident, for example, when students:

 

6. Plants and animals depend on each other and their physical environment.

 

Students:

 

This is evident, for example, when students:

 

7. Human decisions and activities have had a profound impact on the physical and living environment.

 

Students:

 

This is evident, for example, when students:

 

Standard 4 ¾ Science

Intermediate

Physical Setting

 

1. The Earth and celestial phenomena can be described by principles of relative motion and perspective.

 

Students:

 

This is evident, for example, when students:

 

 

2. Many of the phenomena that we observe on Earth involve interactions among components of air, water, and land.

 

Students:

 

This is evident, for example, when students:

 

 

3. Matter is made up of particles whose properties determine the observable characteristics of matter

and its reactivity.

 

Students:

 

This is evident, for example, when students:

 

 

4. Energy exists in many forms, and when these forms change energy is conserved.

 

Students:

 

This is evident, for example, when students:

 

 

5. Energy and matter interact through forces that result in changes in motion.

 

Students:

 

This is evident, for example, when students:

 

Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.

 

The Living Environment

 

1. Living things are both similar to and different from each other and nonliving things.

 

Students:

 

This is evident, for example, when students:

 

2. Organisms inherit genetic information in a variety of ways that result in continuity of structure and function between parents and offspring.

 

Students:

 

This is evident, for example, when students:

 

3. Individual organisms and species change over time.

 

Students:

 

This is evident, for example, when students:

 

 

4. The continuity of life is sustained through reproduction and development.

 

Students:

 

This is evident, for example, when students:

 

5. Organisms maintain a dynamic equilibrium that sustains life.

 

Students:

 

This is evident, for example, when students:

 

6. Plants and animals depend on each other and their physical environment.

 

Students:

 

This is evident, for example, when students:

 

7. Human decisions and activities have had a profound impact on the physical and living environment.

 

Students:

describe the effects of environmental changes on humans and other populations.

 

This is evident, for example, when students:

 

Standard 4 ¾ Science

Commencement

Physical Setting

 

1. The Earth and celestial phenomena can be described by principles of relative motion and perspective.

 

Students:

 

This is evident, for example, when students:

 

2. Many of the phenomena that we observe on Earth involve interactions among components of air, water, and land.

 

Students:

 

This is evident, for example, when students:

 

3. Matter is made up of particles whose properties determine the observable characteristics of matter and its reactivity.

 

Students:

 

This is evident, for example, when students:

 

 

4. Energy exists in many forms, and when these forms change energy is conserved.

 

Students:

 

This is evident, for example, when students:

 

5. Energy and matter interact through forces that result in changes in motion.

 

Students:

 

This is evident, for example, when students:

 

Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.

 

The Living Environment

 

1. Living things are both similar to and different from each other and nonliving things.

 

Students:

 

2. Organisms inherit genetic information in a variety of ways that result in continuity of structure and function between parents and offspring.

 

Students:

 

This is evident, for example, when students:

 

3. Individual organisms and species change over time.

Students:

 

This is evident, for example, when students:

 

4. The continuity of life is sustained through reproduction and development.

 

Students:

 

This is evident, for example, when students:

 

 

5. Organisms maintain a dynamic equilibrium that sustains life.

 

Students:

 

This is evident, for example, when students:

 

6. Plants and animals depend on each other and their physical environment.

 

Students:

 

This is evident, for example, when students:

 

7. Human decisions and activities have had a profound impact on the physical and living environment.

 

Students:

 

This is evident, for example, when students:

 

Standard 5 ¾ Technology

Elementary

Engineering Design Tools, Resources, and Technological Process

 

1. Engineering design is an iterative process involving modeling and optimization used to develop technological solutions to problems within given constraints.

 

Students:

 

This is evident, for example, when students:

 

2. Technological tools, materials, and other resources should be selected on the basis of safety, cost, availability, appropriateness, and environmental impact; technological processes change energy, information, and material resources into more useful forms.

 

Students:

 

This is evident, for example, when students:

 

Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

 

Computer Technology Technological Systems

 

3. Computers, as tools for design, modeling, information processing, communication, and system control, have greatly increased human productivity and knowledge.

 

Students:

 

This is evident, for example, when students:

 

 

4. Technological systems are designed to achieve specific results and produce outputs, such as products,

structures, services, energy, or other systems.

 

Students:

 

This is evident, for example, when students:

 

Standard 5 ¾ Technology

Elementary

History and Evolution of Technology Impacts of Technology

 

5. Technology has been the driving force in the evolution of society from an agricultural to an industrial to an information base.

 

Students:

 

This is evident, for example, when students:

construct a model of an historical or future-oriented technological device or system and describe how it has contributed or might contribute to human progress.

 

6. Technology can have positive and negative impacts on individuals, society, and the environment and humans have the capability and responsibility to constrain or promote technological development.

 

Students:

 

This is evident, for example, when students:

 

Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

 

Management of Technology

 

7. Project management is essential to ensuring that technological endeavors are profitable and that products and systems are of high quality and built safely, on schedule, and within budget.

 

Students:

 

This is evident, for example, when students:

 

Standard 5 ¾ Technology

Intermediate

Engineering Design Tools, Resources, and Technological Process

 

1. Engineering design is an iterative process involving modeling and optimization used to develop technological solutions to problems within given constraints.

 

Students engage in the following steps in a design process:

 

This is evident, for example, when students:

 

2. Technological tools, materials, and other resources should be selected on the basis of safety, cost, r availability, appropriateness, and environmental impact; technological processes change energy, information, and material resources into more useful forms.

 

Students:

 

This is evident, for example, when students:

 

Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

 

Computer Technology Technological Systems

 

3. Computers, as tools for design, modeling, information processing, communication, and system control, have greatly increased human productivity and knowledge.

 

Students:

 

This is evident, for example, when students:

 

 

4. Technological systems are designed to achieve specific results and produce outputs, such as products,

structures, services, energy, or other systems.

 

Students:

 

This is evident, for example, when students:

 

Standard 5 ¾ Technology

Intermediate

History and Evolution of Technology Impacts of Technology

 

5. Technology has been the driving force in the evolution of society from an agricultural to an industrial to an information base.

 

Students:

 

This is evident, for example, when students:

 

6. Technology can have positive and negative impacts on individuals, society, and the environment and humans have the capability and responsibility to constrain or promote technological development.

 

Students:

 

This is evident, for example, when students:

 

Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

 

Management of Technology

 

7. Project management is essential to ensuring that technological endeavors are profitable and that products and systems are of high quality and built safely, on schedule, and within budget.

 

Students:

 

This is evident, for example, when students:

 

Standard 5 ¾ Technology

Commencement

Engineering Design Tools, Resources, and Technological Processes

 

1. Engineering design is an iterative process involving modeling and optimization used to develop technological solutions to problems within given constraints.

 

Students engage in the following steps in a design process:

 

This is evident, for example, when students:

 

2. Technological tools, materials, and other resources should be selected on the basis of safety, cost, availability, appropriateness, and environmental impact; technological processes change energy, information, and material resources into more useful forms.

 

Students:

 

This is evident, for example, when students:

 

Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

 

Computer Technology Technological Systems

 

3. Computers, as tools for design, modeling, information processing, communication, and system control, have greatly increased human productivity and knowledge.

 

Students:

 

This is evident, for example, when students:

 

 

4. Technological systems are designed to achieve specific results and produce outputs, such as products, structures, services, energy, or other systems.

 

Students:

 

This is evident, for example, when students:

 

Standard 5 ¾ Technology

Commencement

History and Evolution of Technology Impacts of Technology

 

5. Technology has been the driving force in the evolution of society from an agricultural to an industrial to an information base.

 

Students:

 

This is evident, for example, when students:

 

 

6. Technology can have positive and negative impacts on individuals, society, and the environment and humans have the capability and responsibility to constrain or promote technological development.

 

Students:

 

This is evident, for example, when students:

 

Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

 

Management of Technology

 

7. Project management is essential to ensuring that technological endeavors are profitable and that products and systems are of high quality and built safely, on schedule, and within budget.

 

Students:

 

This is evident, for example, when students:

 

 

Standard 6 ¾ Interconnectedness:

Common Themes Elementary

 

Systems Thinking Models

 

1. Through systems thinking, people can recognize the commonalities that exist among all systems and how parts of a system interrelate and combine to perform specific functions.

 

Students:

 

 

2. Models are simplified representations of objects, structures, or systems used in analysis, explanation, interpretation, or design.

 

Students:

 

This is evident, for example, when students:

 

Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

 

Magnitude and Scale Equilibrium and Stability

 

3. The grouping of magnitudes of size, time, frequency, and pressures or other units of measurement into a series of relative order provides a useful way to deal with the immense range and the changes in scale that affect the behavior and design of systems.

 

Students:

 

This is evident, for example, when students:

 

4. Equilibrium is a state of stability due either to a lack of changes (static equilibrium) or a balance between opposing forces (dynamic equilibrium).

 

Students:

 

This is evident, for example, when students:

 

 

Standard 6 ¾ Interconnectedness:

Common Themes Elementary

 

Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

 

Patterns of Change Optimization

 

5. Identifying patterns of change is necessary for making predictions about future behavior and conditions.

 

Students:

 

This is evident, for example, when students:

 

6. In order to arrive at the best solution that meets criteria within constraints, it is often necessary to make trade-offs.

 

Students:

 

This is evident, for example, when students:

 

Standard 6 ¾ Interconnectedness:

Common Themes Intermediate

 

Systems Thinking Models

 

1. Through systems thinking, people can recognize the commonalities that exist among all systems and how parts of a system interrelate and combine to perform specific functions.

 

Students:

 

This is evident, for example, when students:

2. Models are simplified representations of objects, structures, or systems used in analysis, explanation, interpretation, or design.

 

Students:

 

This is evident, for example, when students:

 

Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

 

Magnitude and Scale Equilibrium and Stability

 

3. The grouping of magnitudes of size, time, frequency, and pressures or other units of measurement into a series of relative order provides a useful way to deal with the immense range and the changes in scale that affect the behavior and design of systems.

 

Students:

 

This is evident, for example, when students:

 

4. Equilibrium is a state of stability due either to a lack of changes (static equilibrium) or a balance between opposing forces (dynamic equilibrium).

 

Students:

 

This is evident, for example, when students:

 

Standard 6 ¾ Interconnectedness:

Common Themes Intermediate

 

Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

 

Patterns of Change Optimization

 

5. Identifying patterns of change is necessary for making predictions about future behavior and conditions.

 

Students:

 

This is evident, for example, when students:

 

6. In order to arrive at the best solution that meets criteria within constraints, it is often necessary to make trade-offs.

 

Students:

 

This is evident, for example, when students:

 

Standard 6 ¾ Interconnectedness:

Common Themes Commencement

 

Systems Thinking Models

 

1. Through systems thinking, people can recognize the commonalities that exist among all systems and how parts of a system interrelate and combine to perform specific functions.

 

Students:

 

This is evident, for example, when students:

 

2. Models are simplified representations of objects, structures, or systems used in analysis, explanation, interpretation, or design.

 

Students:

 

This is evident, for example, when students:

 

Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

 

Magnitude and Scale Equilibrium and Stability

 

3. The grouping of magnitudes of size, time, frequency, and pressures or other units of measurement into a series of relative order provides a useful way to deal with the immense range and the changes in scale that affect the behavior and design of systems.

 

Students:

 

This is evident, for example, when students:

 

 

4. Equilibrium is a state of stability due either to a lack of changes (static equilibrium) or a balance between opposing forces (dynamic equilibrium).

 

Students:

 

This is evident, for example, when students:

 

Standard 6 ¾ Interconnectedness:

Common Themes Commencement

 

Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

 

Patterns of Change Optimization

 

5. Identifying patterns of change is necessary for making predictions about future behavior and conditions.

 

Students:

 

This is evident, for example, when students:

 

6. In order to arrive at the best solution that meets criteria within constraints, it is often necessary to make trade-offs.

 

Students:

 

This is evident, for example, when students:

 

Standard 7 ¾ Interdisciplinary

Problem Solving Elementary

 

Connections Strategies

 

1. The knowledge and skills of mathematics, science, and technology are used together to make informed decisions and solve problems, especially those relating to issues of science/technology/society, consumer decision making, design, and inquiry into phenomena.

 

Students:

 

This is evident, for example, when students:

 

 

2. Solving interdisciplinary problems involves a variety of skills and strategies, including effective work habits; gathering and processing information; generating and analyzing ideas; realizing ideas; making connections among the common themes of mathematics, science, and technology; and presenting results.

 

Students participate in an extended, culminating mathematics, science, and technology project. The project would require students to:

 

This is evident, for example, when students, addressing the issue of solid waste at the school in an interdisciplinary science/technology/society project:

 

Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions.

 

Skills and Strategies for Interdisciplinary Problem Solving

 

Working Effectively: Contributing to the work of a brainstorming group, laboratory partnership, cooperative learning group, or project team; planning procedures; identify and managing responsibilities of team members; and staying on task, whether working alone or as part of a group.

 

Gathering and Processing Information: Accessing information from printed media, electronic data bases, and community resources and using the information to develop a definition of the problem and to research possible solutions.

 

Generating and Analyzing Ideas: Developing ideas for proposed solutions, investigating ideas, collecting data, and showing relationships and patterns in the data.

 

Common Themes: Observing examples of common unifying themes, applying them to the problem, and using them to better understand the dimensions of the problem.

 

Realizing Ideas: Constructing components or models, arriving at a solution, and evaluating the result.

 

Presenting Results: Using a variety of media to present the solution and to communicate the results.

 

Standard 7 ¾ Interdisciplinary

Problem Solving Intermediate

 

Connections Strategies

 

1. The knowledge and skills of mathematics, science, and technology are used together to make informed decisions and solve problems, especially those relating to issues of science/technology/society, consumer decision making, design, and inquiry into phenomena.

 

Students:

 

This is evident, for example, when students:

 

2. Solving interdisciplinary problems involves a variety of skills and strategies, including effective work habits; gathering and processing information; generating and analyzing ideas; realizing ideas; making connections among the common themes of mathematics, science, and technology; and presenting results.

 

Students participate in an extended, culminating mathematics, science, and technology project. The project would require students to:

 

This is evident, for example, when students, addressing the issue of auto safety in an interdisciplinary science/technology/society project:

 

 

Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions.

 

Skills and Strategies for Interdisciplinary Problem Solving

 

Working Effectively: Contributing to the work of a brainstorming group, laboratory partnership, cooperative learning group, or project team; planning procedures; identify and managing responsibilities of team members; and staying on task, whether working alone or as part of a group.

 

Gathering and Processing Information: Accessing information from printed media, electronic data bases, and community resources and using the information to develop a definition of the problem and to research possible solutions.

 

Generating and Analyzing Ideas: Developing ideas for proposed solutions, investigating ideas, collecting data, and showing relationships and patterns in the data.

 

Common Themes: Observing examples of common unifying themes, applying them to the problem, and using them to better understand the dimensions of the problem.

 

Realizing Ideas: Constructing components or models, arriving at a solution, and evaluating the result.

 

Presenting Results: Using a variety of media to present the solution and to communicate the results.

 

Standard 7 ¾ Interdisciplinary

Problem Solving Commencement

 

Connections Strategies

 

1. The knowledge and skills of mathematics, science, and technology are used together to make informed decisions and solve problems, especially those relating to issues of science/technology/society, consumer decision making, design, and inquiry into phenomena.

 

Students:

 

This is evident, for example, when students:

 

 

2. Solving interdisciplinary problems involves a variety of skills and strategies, including effective work habits; gathering and processing information; generating and analyzing ideas; realizing ideas; making connections among the common themes of mathematics, science, and technology; and presenting results.

 

Students participate in an extended, culminating mathematics, science, and technology project. The project would require students to:

 

This is evident, for example, when students, addressing the issue of emergency preparedness in an interdisciplinary science/technology/society project:

 

 

Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions.

 

Skills and Strategies for Interdisciplinary Problem Solving

 

Working Effectively: Contributing to the work of a brainstorming group, laboratory partnership, cooperative learning group, or project team; planning procedures; identify and managing responsibilities of team members; and staying on task, whether working alone or as part of a group.

 

Gathering and Processing Information: Accessing information from printed media, electronic data bases, and community resources and using the information to develop a definition of the problem and to research possible solutions.

 

Generating and Analyzing Ideas: Developing ideas for proposed solutions, investigating ideas, collecting data, and showing relationships and patterns in the data.

 

Common Themes: Observing examples of common unifying themes, applying them to the problem, and using them to better understand the dimensions of the problem.

 

Realizing Ideas: Constructing components or models, arriving at a solution, and evaluating the result.

 

Presenting Results: Using a variety of media to present the solution and to communicate the results.