# PH.2 a-b - Mathematical Relationships

The student will investigate and understand how to analyze and interpret data. Key concepts include

a)  a description of a physical problem is translated into a mathematical statement in order to find a solution; and

b)  relationships between physical quantities are determined using the shape of a curve passing through experimentally obtained data.

Bloom's Levels:  Analyze; Understand

### BIG IDEAS

• I can determine how steep a roof must be so that snow is able to slide off.
• I can determine the impact a steep hill has on the average and instantaneous speed of a runner.

### UNDERSTANDING THE STANDARD

The concepts developed in this standard include the following:

• Mathematics is a tool used to model and describe phenomena.
• Graphing and dimensional analysis are used to reveal relationships and other important features of data.
• Predictions are made from trends based on the data.
• The shape of the curve fit to experimentally obtained data is used to determine the relationship of the plotted quantities.
• All experimental data do not follow a linear relationship.
• The area under the curve of experimentally obtained data is used to determine related physical quantities.
• Physical phenomena or events can often be described in mathematical terms (as an equation or inequality).

### ESSENTIALS

In order to meet this standard, it is expected that students will

a-b) recognize linear and nonlinear relationships from graphed data.

where appropriate, draw a straight line through a set of experimental data points and determine the slope and/or area under the curve.

### KEY VOCABULARY

Updated: Dec 01, 2017