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The Rates and proportional relationships exercise appears under the 8th grade (U.S.) Math Mission and Probability and statistics Math Mission. This exercise analyzes proportional rates in tables, graphs and equations.

## Types of Problems

There are two types of problems in this exercise:

1. Select the equations that work: This problem provides a word problem and several possible equations. The student is asked to select all of the possibilities from the list that would satisfy the conditions written in the problem.
2. Tell which has faster or slower rate: This problem provides two proportional relationships in either context, graphs, tables or equations. The student is asked to select which relationship has either the faster or slower rate of change.

## Strategies

Knowledge of the multiple representations of functions would help with this exercise.

1. A proportional relationship is of the form ${y=kx}$ for ${k}$ a constant.
2. The table form will always have a constant ratio when ${y}$ is divided by ${x}$ or vice versa.
3. The graph will always be a line through the origin.
4. The rate of proportionality (the ${k}$ from the equation) is the slope of the line. The faster rate means the steeper (or greater) slope.

## Real-life Applications

1. Data and statistics appear in news reports and in the media every day.
2. Many of the problems in this exercise could be viewed as real-life applications.
3. Statistics can be seen more frequently than calculus in every day life.
4. There are many applications of direct variation in business (revenue).
5. There are many applications of inverse variation in physics (gravitation).