Thinking with mathematical models
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Thinking with mathematical models
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Enrichment Activities
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Objectives of this Unit
| Build and analyze mathematical models | Fit a line to experimental data |
| Identify the variables of interest in a situation | Conduct experiments to gather data about how variables are related |
Vocabulary
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Equation Model | An equation that describes the relationship between two variables. In this unit, you fit graph models to data points, and then, when possible, you use your graph models to find equation models. An equation model allows you to make predictions about values between and beyond the values in a set of data. |
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Fulcrum | The balance point of a teeter-totter or balance scale. In order for a teeter-totter to balance, the product of the weight and distance on one side must equal the product of the weight and distance on the other side of the fulcrum. |
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Graph Model | A straight line or curve that represents a mathematical relationship. If the data you plot show a trend, you can draw a graph model that fits the pattern of change in the data. A graph model allows you to make predictions about values between and beyond the values in a set of data. |
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Inverse Relationship | A nonlinear relationship in which the product of two variables is constant. In an inverse relationship, the values of one variable decrease as the values of the other variable increase. |
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Linear Relationship | A relationship in which there is a constant rate of change between two variables. A linear relationship can be represented by a straight line graph and by an equation in the form y=mx+b. In the equation, m is the slope of the line, and b is the y-intercept. |
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Mathematical Model | A mathematical representation, such as a graph or an equation, of the relationship in a set of data. |
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Relationship | An association between two variables. A relationship can be represented in a graph, in a table, or with an equation. |