6th Grade Math

Ratios, proportions, and algebraic thinking for sixth grade students.

Advanced Topics

Working with Proportional Relationships

Proportional Relationships in Action

When two quantities increase or decrease at the same rate, they have a proportional relationship. This means if one doubles, so does the other!

How to Identify

Check if the ratio stays the same as the numbers get bigger or smaller.

Using Tables and Graphs

Tables can help you see how numbers change together. On a graph, proportional relationships make a straight line through the origin (0,0).

Formula for Proportionality

If y is proportional to x, you can write:

\[ y = kx \]

where k is the constant of proportionality.

Real-World Examples

Proportional relationships help with things like recipes, maps, and unit conversions.

Key Formula

\[y = kx\]

Examples

  • If a car travels at a constant speed, the distance and time are proportional.

  • If you earn $8 per hour, your total money earned is proportional to the hours you work.

In a Nutshell

A proportional relationship means two things always change at the same rate.

Key Terms

Constant of Proportionality
The fixed number (k) in a proportional relationship.
Direct Variation
Another name for a proportional relationship.