STANDARDS MET BY THE FLOW RATES MODEL
National Science Education Standards
Content Standard 
Description 
Unifying Concepts and Processes 
All students should develop understanding and abilities aligned with the following concepts and processes:  Systems, order, and organization
 Evidence, models, and explanation
 Constancy, change, and measurement
 Evolution and equilibrium
 Form and function

Science as Inquiry 
All students should develop: Abilities necessary to do scientific inquiry
 Identify questions and concepts that guide scientific investigations
 Design and conduct scientific investigations
 Use technology and mathematics to improve investigations and communications
 Formulate and revise scientific explanations and models using logic and evidence
 Recognize and analyze alternative explanations and models
 Communicate and defend a scientific argument
 Understandings about scientific inquiry

AAAS Benchmarks
Topic 
Description 
1BScientific Inquiry 
Hypotheses are widely used in science for choosing what data to pay attention to and what additional data to seek, and for guiding the interpretation of data (both new and previously available). 
2BMathematics, Science, and Technology 
Mathematics provides a precise language for science and technology  to describe objects and events, to characterize relationships between variables, and to argue logically. 
9BSymbolic Relationships 
In some cases, the more of something there is, the more rapidly it may change. 
Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works. The usefulness of a mathematical model for predicting may be limited by uncertainties in measurements, by neglect of some important influences, or by requiring too much computation. 
11ASystems 
Understanding how things work and designing solutions to problems of almost any kind can be facilitated by systems analysis. In defining a system, it is important to specify its boundaries and subsystems, and identify what its input and its output are expected to be. 
The successful operation of a designed system usually involves feedback. The feedback of output from some parts of a system to input of other parts can be used to encourage what is going on in a system, discourage it, or reduce its discrepancy from some desired value. The stability of a system can be greater when it includes appropriate feedback mechanisms. 
11BModels 
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. A mathematical model may give insight about how something really works or may fit observations very well without any intuitive meaning. 
Computers have greatly improved the power and use of mathematical models by performing calculations that are very long, very complicated, or repetitive. Therefore computers can show the consequences of applying complex rules or of changing the rules. The graphic capabilities of computers make them useful in the design and testing of devices and structures and in the simulation of complicated processes 
The usefulness of a model can be tested by comparing its predictions to actual observations in the real world. But a close match does not necessarily mean that the model is the only "true" model or the only one that would work. 
11CConstancy and Change 
Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change. 
Maryland Core Learning Goals in Science
Goal/Expectation 
Description 
Goal 1 
The student will demonstrate ways of thinking and acting inherent in the practice of science. The student will use the language and instruments of science to collect, organize, interpret, calculate, and communicate information. 
1.2 
The student will pose scientific questions and suggest experimental approaches to provide answers to questions. 
1.4 
The student will demonstrate that data analysis is a vital aspect of the process of scientific inquiry and communication. 
1.5 
The student will use appropriate methods for communicating in writing and orally the processes and results of scientific investigation. 
1.6 
The student will use mathematical processes. 
National Council of Teachers of Mathematics Standards
Expectation 
Description 
Mathematical Models 
All students should be able to use mathematical models to
represent and understand
quantitative relationships: Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships
 Use symbolic expressions, including iterative and
recursive forms, to represent relationships arising
from various contexts
 Draw reasonable conclusions about a situation being
modeled

Analysis of Change 
All students should be able to: Analyze change in various
contexts

Approximate and interpret rates of change from
graphical and numerical data

Problem Solving 
All students should be able to solve real world problems:
Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on the process of mathematical problem solving

Maryland Core Learning Goals in Mathematics
Goal/Expectation 
Description 
Goal 1 
The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and realworld problems using patterns, functions, and algebra. 
1.1 
The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology. 
1.2 
The student will model and interpret realworld situations using the language of mathematics and appropriate technology. 
Goal 3 
The student will demonstrate the ability to apply probability and statistical methods for representing and interpreting data and communicating results, using technology when needed. 
3.2 
The student will apply the basic concepts of statistics and probability to predict possible outcomes of realworld situations. 
