Using Ratio Tables for Systematic Comparison
Using ratio tables for systematic comparison is a Grade 6 math skill in Big Ideas Math Advanced 1, Chapter 5: Ratios and Rates. Students scale two different ratios to the same quantity in one column (finding a common value), then compare the other column values to determine which ratio is larger, cheaper, or faster.
Key Concepts
To compare ratios systematically, create ratio tables with equivalent ratios and find a common value in one column to directly compare the corresponding values in the other column. If ratio $a:b$ and ratio $c:d$ both have the same value for one quantity, compare the other quantities directly.
Common Questions
How do you use ratio tables to compare two ratios?
Build ratio tables for each ratio and scale them until one quantity is the same in both tables. Then compare the other quantity. For example, to compare for 4 oz vs for 7 oz, scale both to a common quantity (like 28 oz) and compare the total costs.
What is a unit rate and why is it useful for comparison?
A unit rate expresses a ratio per 1 unit (like cost per 1 item or miles per 1 hour). When comparing two ratios, converting both to unit rates makes comparison straightforward — the better deal has the lower unit price.
What real-world situations use ratio table comparisons?
Common comparisons include: finding the better price per unit, determining which car gets better gas mileage, deciding which recipe yields more servings per ingredient, or comparing speeds to find who arrives first.
Where is this skill taught in Big Ideas Math Advanced 1?
Using ratio tables for systematic comparison is covered in Chapter 5: Ratios and Rates of Big Ideas Math Advanced 1, the Grade 6 math textbook.