Question: Joe has a bag of red, blue, and yellow marbles. For every three red marbles, he has five blue marbles and two yellow marbles. If he has 18 red marbles, how many blue marbles does he have? How many yellow marbles does he have?
Students are often taught to solve a proportion problem such as this by setting up equal ratios, something like shown below. However, I find that my students struggle with this approach. Especially when these questions are first introduced, the process is too abstract, which causes them to lose track of which value represents what.
This year, I’ve adopted a more concrete approach using a diagramming model, and we’ve had a lot more success. See the slides below for steps.
Now try applying the same concept to a more complicated question:
Question 2: Ani is making bouquets of lilies, daisies, and ferns. For every two lilies, she wants to use five daisies and four stems of ferns. If she has twenty-seven daisies, twenty-five ferns, and twelve lilies, how many bouquets can she make? How many lilies, daisies, and ferns will she have left over?
Click here to see the solution.