Using Ratio Tables for Equivalent Rates
Using ratio tables for equivalent rates is a Grade 6 math skill in Big Ideas Math Advanced 1, Chapter 5: Ratios and Rates. Students fill in ratio tables to generate a set of equivalent rates by scaling up or down using multiplication or division, then use the table to solve problems such as finding distance at a constant speed for varying times.
Key Concepts
A ratio table organizes equivalent rates in columns, where each column represents the same rate relationship. To create a ratio table: find the unit rate by dividing, then multiply the unit rate by different values to generate equivalent rates systematically.
Common Questions
How do you use a ratio table to find equivalent rates?
Start with a known rate and multiply or divide both quantities by the same factor to generate new columns. For example, if the rate is 50 miles per hour, you can find rates for 2, 3, or 4 hours by multiplying: 100, 150, 200 miles.
What is an equivalent rate?
Equivalent rates represent the same ratio but with different numbers. For example, 2 miles per minute and 120 miles per hour are equivalent rates because they describe the same speed.
How do ratio tables relate to proportional reasoning?
Ratio tables show that proportional relationships maintain a constant ratio across all entries. Each column in the table represents an equivalent ratio, which is the foundation of proportional reasoning.
Where is this skill taught in Big Ideas Math Advanced 1?
Using ratio tables for equivalent rates is covered in Chapter 5: Ratios and Rates of Big Ideas Math Advanced 1, the Grade 6 math textbook.