Identifying proportional relationships

Identifying proportional relationships
Description
Exercise Name:	Identifying proportional relationships
Math Missions:	7th grade (U.S.) Math Mission
Types of Problems:	3

The Identifying proportional relationships exercise appears under the 7th grade (U.S.) Math Mission. This exercise introduces has several problems that attempt to help the user better understand direct variation.

Types of Problems

There are three types of problem in this exercise:

1. Determine if the relationship is proportional: This problem provides a given graph, chart or word problem and asks the user to determine whether they relationship is proportional or not. The answer is given in a multiple choice format.

   

   Determine if the relationship is proportional

2. Fill in missing information and determine if the relationship is proportional: This problem provides information and a partially filled in chart, or T-table. The user is asked to complete the missing information and determine if the relationship is proportional.

   

   Fill in missing information and determine if the relationship is proportional

3. Create graph and determine if the relationship is proportional: This problem has a grid on which the user is asked to create a graph representing some information. In addition, users are asked to determine if the given relationship is proportional or not.

   

   Create graph and determine if relationship is proportional

Strategies

This concept is almost identical to direct variation, so knowledge of direct variation will assist with doing these problems correctly.

1. It is said that ${k}$ varies directly with ${x}$ if ${y=kx}$, or equivalently if ${{\frac {y}{x}}=k}$ for a constant ${k}$.
2. A proportional relationship must go through the origin so determining if a relationship is proportional can be done very quickly with a graph.
3. To increase speed, find the ratio of output to input in two cases. In a proportional relationship these will be identical.

Real-life Applications

1. Businesses can use proportions to figure out how much money they will earn if they sell more products.