Ratios and Rates 4 (#MSMathChat)

I was thinking that analyzing a different candy could also make for a fun way to discuss ratios and begin to think about why they matter.

Let’s say each student in the class receives a bag of M&Ms. Before opening them, I might ask the students if they think that the ratio of colors is the same in every bag. Do you think they should be the same? Why or why not?

Have students open their bags and come up with a compound ratio showing how all their colors are related. Compare these ratios across all the bags in the class. To be honest, I have no idea what you’ll find. My gut says you’ll see that the ratio of colors varies per bag. I do wonder if there might be some generally consistency to the ratio though. For example, I doubt you’ll randomly find a bag that’s all or mostly red.

If the ratio of colors isn’t the same in all bags, think about why. Think about a factory and why different ratios of each color are ending up in each bag. What’s going on when the candies are packaged that results in different ratios?

Think about it if they did all have the same ratio. Think about what that factory would look like to ensure this ratio is maintained. Do you think there is an economic reason why they are or are not all the same ratio in each bag? What other factors could affect it?

Can you think of products (not just food) that ensure some kind of a consistent ratio and products that do not? Here are some examples off the top of my head:

  • Soda cases generally have a consistent ratio – Basically the ratio is 0 to whatever flavor is labeled on the box. We generally don’t have random flavors of soda in a box.
  • An 8-pack of markers has a consistent ratio of 1:1:1:1:1:1:1:1 because you get one of each color.
  • I would hazard a guess that packs of multi-color balloons do not have the same ratio of colors from package to package. Or maybe they do. In order to be a multi-color pack, they probably have to guarantee some variability in color. You wouldn’t want to be the person who ends up with 1 green, 1 blue, and 9 red balloons. Maybe they do have a consistent ratio. Or maybe it’s just roughly consistent somehow. Hmm, I wonder.
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