One batch of a certain shade of purple paint is made by mixing 3 pails of blue paint with 2 pails of red paint.

A. Complete the following ratio table:

B. What patterns do you notice in the rows and columns? How would the entries in the nth column of the table be related to the entries in the 1st column of the table?

C. Create a diagram of this ratio with Fraction Bars. How can you use your diagram to find how many pails of red paint you will need if you have 24 pails of blue paint and want to make the same shade of purple described above?

D. Use a double number line to show equivalent paint ratios for the shade of purple in this problem. What are some advantages and limitations of double number lines?

Adapted from: Mathematics for Elementary Teachers, Sybilla Beckmann, 2nd ed., 2008.