Math and Science Integration

The STEM that Bridges!

Math/Science Integration

Science  Technology  Engineering  Mathematics

Goals and Objectives

Integrated Curriculum

Blueprint for Learning

Classroom Resources

Benchmarks for  Integrated Curriculum

3-5  BENCHMARKS

A. Systems

 By the end of 5th grade, students should know that: 1.       In something that consists of many parts, the parts usually influence one another. 2.       Something may not work as well (or at all) if a part of it is missing, broken, worn out, mismatched, or misconnected.

B. Models

 By the end of 5th grade, students should know that: 1.       Seeing how a model works after changes are made to it may suggest how the real thing would work if the same were done to it. 2.       Geometric figures, number sequences, graphs, diagrams, sketches, number lines, maps, and stories can be used to represent objects, events, and processes in the real world, although such representations can never be exact in every detail.

C. Constancy and Change

 By the end of 5th grade, students should know that: 1.       Some features of things may stay the same even when other features change. 2.       Things change in steady, repetitive, or irregular ways or sometimes in more than one way at the same time.

D. Scale

 By the end of 5th grade, students should know that: 1.       Almost anything has limits on how big or small it can be. 2.       Finding out what the biggest and the smallest possible values of something are is often as revealing as knowing what the usual value is.

C. Mathematical Inquiry

 By the end of 5th grade, students should know that: 1.       Numbers and shapes and operations on them help to describe and predict things about the world around us. 2.       In using mathematics, choices have to be made about what operations will give the best results.

A. Technology and Science

 By the end of 5th grade, students should know that: 1.       Throughout all of history, people everywhere have invented and used tools. 2.       In earlier times, the accumulated information and techniques of each generation of workers were taught on the job directly to the next generation of workers. Today, the knowledge base for technology can be found as well in libraries of print and electronic resources and is often taught in the classroom. 3.       Measuring instruments can be used to gather accurate information for making scientific comparisons of objects and events and for designing and constructing things that will work properly. 4.       Technology extends the ability of people to change the world: to cut, shape, or put together materials; to move things from one place to another; and to reach farther with their hands, voices, senses, and minds.

6-8  BENCHMARKS

A. Patterns and Relationships

 By the end of 8th grade, students should know that: 1.       Usually there is no one right way to solve a mathematical problem; different methods have different advantages and disadvantages. 2.       Logical connections can be found between different parts of mathematics.

B. Mathematics, Science, and Technology

 By the end of 8th grade, students should know that: 1.       Mathematics is helpful in almost every kind of human endeavor—from laying bricks to prescribing medicine or drawing a face. In particular, mathematics has contributed to progress in science and technology for thousands of years and still continues to do so.

C. Mathematical Inquiry

 By the end of 8th grade, students should know that: 1.       Mathematicians often represent things with abstract ideas, such as numbers or perfectly straight lines, and then work with those ideas alone. 2.       When mathematicians use logical rules to work with representations of things, the results may or may not be valid for the things themselves.

A. Systems

 By the end of 8th grade, students should know that: 1.       A system can include processes as well as things. 2.       Thinking about things as systems means looking for how every part relates to others. 3.       Any system is usually connected to other systems, both internally and externally.

B. Models

 By the end of 8th grade, students should know that: 1.       Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly, or that are too vast to be changed deliberately, or that are potentially dangerous. 2.       Mathematical models can be displayed on a computer and then modified to see what happens. 3.       Different models can be used to represent the same thing.

C. Constancy and Change

 By the end of 8th grade, students should know that: 1.       Physical and biological systems tend to change until they become stable and then remain that way unless their surroundings change. 2.       A system may stay the same because nothing is happening or because things are happening but exactly counterbalance one another. 3.       Many systems contain feedback mechanisms that serve to keep changes within specified limits. 4.       Symbolic equations can be used to summarize how the quantity of something changes over time or in response to other changes. 5.       Symmetry (or the lack of it) may determine properties of many objects, from molecules and crystals to organisms and designed structures. 6.       Cycles, such as the seasons or body temperature, can be described by their cycle length or frequency, what their highest and lowest values are, and when these values occur.

D. Scale

 By the end of 8th grade, students should know that: 1.       Properties of systems that depend on volume, such as capacity and weight, change out of proportion to properties that depend on area, such as strength or surface processes. 2.       As the complexity of any system increases, gaining an understanding of it depends increasingly on summaries, such as averages and ranges, and on descriptions of typical examples of that system.

A. Technology and Science

 By the end of 8th grade, students should know that: 1.       In earlier times, the accumulated information and techniques of each generation of workers were taught on the job directly to the next generation of workers. 2.       Technology is essential to science for such purposes as access to outer space and other remote locations, sample collection and treatment, measurement, data collection and storage, computation, and communication of information. 3.       Engineers, architects, and others who engage in design and technology use scientific knowledge to solve practical problems.

9-12  BENCHMARKS

A. Systems

 By the end of 12th grade, students should know that: 1.       A system usually has some properties that are different from those of its parts, but appear because of the interaction of those parts. 2.       Understanding how things work and designing solutions to problems of almost any kind can be facilitated by systems analysis. 3.       The successful operation of a designed system usually involves feedback. 4.       Even in some very simple systems, it may not always be possible to predict accurately the result of changing some part or connection.

B. Models

 By the end of 12th grade, students should know that: 1.       The basic idea of mathematical modeling is to find a mathematical relationship that behaves in the same ways as the objects or processes under investigation. 2.       Computers have greatly improved the power and use of mathematical models by performing computations that are very long, very complicated, or repetitive. 3.       The usefulness of a model can be tested by comparing its predictions to actual observations in the real world.

C. Constancy and Change

 By the end of 12th grade, students should know that: 1.       A system in equilibrium may return to the same state of equilibrium if the disturbances it experiences are small. 2.       Along with the theory of atoms, the concept of the conservation of matter led to revolutionary advances in chemical science. 3.       Things can change in detail but remain the same in general (the players change, but the team remains; cells are replaced, but the organism remains). 4.       Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change. 5.       In many physical, biological, and social systems, changes in one direction tend to produce opposing (but somewhat delayed) influences, leading to repetitive cycles of behavior. 6.       In evolutionary change, the present arises from the materials and forms of the past, more or less gradually, and in ways that can be explained. 7.       Most systems above the molecular level involve so many parts and forces and are so sensitive to tiny differences in conditions that their precise behavior is unpredictable, even if all the rules for change are known.

D. Scale

 By the end of 12th grade, students should know that: 1.       Representing large numbers in terms of powers of ten makes it easier to think about them and to compare things that are greatly different. 2.       Because different properties are not affected to the same degree by changes in scale, large changes in scale typically change the way that things work in physical, biological, or social systems. 3.       As the number of parts of a system increases, the number of possible interactions between pairs of parts increases much more rapidly.

A. Patterns and Relationships

 By the end of 12th grade, students should know that: 1.       Mathematics is the study of any patterns or relationships, whereas natural science is concerned only with those patterns that are relevant to the observable world. 2.       As in other sciences, simplicity is one of the highest values in mathematics. 3.       Theories and applications in mathematical work influence each other. 4.       New mathematics continues to be invented, and connections between different parts of mathematics continue to be found.

B. Mathematics, Science, and Technology

 By the end of 12th grade, students should know that: 1.       Mathematical modeling aids in technological design by simulating how a proposed system would theoretically behave. 2.       Mathematics and science as enterprises share many values and features: belief in order, ideals of honesty and openness, the importance of criticism by colleagues, and the essential role played by imagination. 3.       Mathematics provides a precise language for science and technology—to describe objects and events, to characterize relationships between variables, and to argue logically. 4.       Developments in science or technology often stimulate innovations in mathematics by presenting new kinds of problems to be solved. 5.       Developments in mathematics often stimulate innovations in science and technology.

C. Mathematical Inquiry

 By the end of 12th grade, students should know that: 1.       Some work in mathematics is much like a game mathematicians choose an interesting set of rules and then play according to those rules to see what can happen. 2.       Much of the work of mathematicians involves a modeling cycle, which consists of three steps: (1) using abstractions to represent things or ideas, (2) manipulating the abstractions according to some logical rules, and (3) checking how well the results match the original things or ideas.

A. Technology and Science

 By the end of 12th grade, students should know that: 1.       Technological problems often create a demand for new scientific knowledge, and new technologies make it possible for scientists to extend their research in new ways or to undertake entirely new lines of research. 2.       Mathematics, creativity, logic and originality are all needed to improve technology. 3.       Technology usually affects society more directly than science because it solves practical problems and serves human needs (and may create new problems and needs).

NATIONAL SCIENCE EDUCATION STANDARDS

From Chapter 6, download all of the standards for K-4, 5-8 and 9-12 related to this topic.  Enter below.

K-4  STANDARDS

CONTENT STANDARD A:
As a result of activities in grades K-4, all students should develop

·         Abilities necessary to do scientific inquiry

5-8  STANDARDS

CONTENT STANDARD A:
As a result of activities in grades 5-8, all students should develop

·         Abilities necessary to do scientific inquiry

9-12  STANDARDS

CONTENT STANDARD A: As a result of activities in grades 9-12, all students should develop

·         Abilities necessary to do scientific inquiry

PROGRAM STANDARD A:
All elements of the K-12 science program must be consistent with the other National Science Education Standards and with one another and developed within and across grade levels to meet a clearly stated set of goals.

·         In an effective science program, a set of clear goals and expectations for students must be used to guide the design, implementation, and assessment of all elements of the science program.

·         Curriculum frameworks should be used to guide the selection and development of units and courses of study.

·         Teaching practices need to be consistent with the goals and curriculum frameworks.

·         Assessment policies and practices should be aligned with the goals, student expectations, and curriculum frameworks.

·         Support systems and formal and informal expectations of teachers must be aligned with the goals, student expectations and curriculum frameworks.

·         Responsibility needs to be clearly defined for determining, supporting, maintaining, and upgrading all elements of the science program.

CONTENT CLARIFICATION BUILDER
Related Content Knowledge

SCIENCE FOR ALL AMERICANS

1. Science for All Americans is based on the belief that the science-literate person is one who is aware that science, mathematics, and technology are interdependent human enterprises with strengths and limitations; understands key concepts and principles of science; is familiar with the natural world and recognizes both its diversity and unity; and uses scientific knowledge and scientific ways of thinking for individual and social purposes.

### Chapter 11: COMMON THEMES

Some important themes pervade science, mathematics, and technology and appear over and over again, whether we are looking at an ancient civilization, the human body, or a comet. They are ideas that transcend disciplinary boundaries and prove fruitful in explanation, in theory, in observation, and in design.

It is the union of science, mathematics, and technology that forms the scientific endeavor and that makes it so successful. Although each of these human enterprises has a character and history of its own, each is dependent on and reinforces the others

• Science provides mathematics with interesting problems to investigate, and mathematics provides science with powerful tools to use in analyzing data. Often, abstract patterns that have been studied for their own sake by mathematicians have turned out much later to be very useful in science. Science and mathematics are both trying to discover general patterns and relationships, and in this sense they are part of the same endeavor.
• Mathematics is the chief language of science. The symbolic language of mathematics has turned out to be extremely valuable for expressing scientific ideas unambiguously.
• Mathematics and science have many features in common. These include a belief in understandable order; an interplay of imagination and rigorous logic; ideals of honesty and openness; the critical importance of peer criticism; the value placed on being the first to make a key discovery; being international in scope; and even, with the development of powerful electronic computers, being able to use technology to open up new fields of investigation.
• Mathematics and technology have also developed a fruitful relationship with each other. The mathematics of connections and logical chains, for example, has contributed greatly to the design of computer hardware and programming techniques. Mathematics also contributes more generally to engineering, as in describing complex systems whose behavior can then be simulated by computer. In those simulations, design features and operating conditions can be varied as a means of finding optimum designs. For its part, computer technology has opened up whole new areas in mathematics, even in the very nature of proof, and it also continues to help solve previously daunting problems.

2.

BENCHMARKS FOR SCIENCE LITERACY

(ESSAY)

1. Which Benchmarks address the topic you targeted for instruction? COMMON THEMES

2 Some powerful ideas often used by mathematicians, scientists, and engineers are not the intellectual property of any one field or discipline. Indeed, notions of system, scale, change and constancy, and models have important applications in business and finance, education, law, government and politics, and other domains, as well as in mathematics, science, and technology. These common themes are really ways of thinking rather than theories or discoveries. (Energy also represents a prominent tool for thinking in science and technology, but because it is part of the content of science, it is not included here as a theme.) Science for All Americans recommends what all students should know about those themes, and the benchmarks in the four sections below suggest how student understanding of them should grow over the school years. Although the context of both Science for All Americans and Benchmarks is mainly science, mathematics, and technology, other contexts are identified here to emphasize the general usefulness of these themes. 3. Copy and paste the information below and remove any unrelated material.

MATHEMATICS

#### Data Analysis and Probability

 Instructional programs from prekindergarten through grade 12 should enable all students to-- formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them; select and use appropriate statistical methods to analyze data; develop and evaluate inferences and predictions that are based on data; understand and apply basic concepts of probability.

#### Connections

 Instructional programs from prekindergarten through grade 12 should enable all students to-- recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect and build on one another to produce a coherent whole; recognize and apply mathematics in contexts outside of mathematics.

What are the Mathematics Standards that a student could meet by completing t

his unit?

> Go to Mathematics Standards…

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