Math Tasks With Multiple Solutions: An Example Of One and Why They Are Essential

By David Kwan

Try To Figure Out The Math Problem In Dan Meyer’s Video Below!!

How Dan Meyer’s Video Hooks You

A man receives a chocolate milk recipe from his aunt and goes about adding 4 scoops of chocolate to 1 cup of milk. Everything is going smoothly and then oops, he adds a fifth scoop of chocolate. Now, most people I know would either be thrilled or at worst indifferent about the prospect of an extra scoop of chocolate. After all, what is chocolate milk if not chocolaty? But Nana is different. She wants it her way and won’t take anything but. So now the man is probably sweating over how he can fix this problem and I can understand how he feels. In fact, I want to help him out. How can I help him fix his chocolate Frankenstein before Nana gets home?

Three Awesome Things Dan Did In 48 seconds

Dan Meyer, A Legend At Creating Math Tasks And Presumably The Man In The Video, Accomplishes Three Feats In Making The 48-Second Clip:

  • he invests students in solving a challenging math problem because his plight really hits home with them. Who hasn’t had a fastidious relative and felt their fiery wrath?
  • he gets students to independently recognize the problem; when students watch the problem they know what needs fixing.
  • And perhaps his most impressive feat is that he leaves the door open for students to produce their own solutions and defend them. There are many ways to fix his concoction and possible rationales for doing so:

-add any whole number of cups of milk and chocolate to preserve the ratio of the recipe (1:4)

-add 1/4 cup of milk (1.25:5)

-throw out half of the mix and add back a 1/2 cup of milk and 1 1/2 scoops of chocolate

-throw out the entire mix and start over

-if you want to preserve the original ratio, you can add 1/4 cup of milk, mix it, and then throw out 1/5 of the mix (credits to Evan)

Why Math Tasks With Multiple Solutions Are Important

Math tasks with multiple solutions like “Nana’s Chocolate Milk” are important because they encourage students to think more about how to solve a problem and less about whether their answers are correct. While we can focus class discussions on different student strategies, some students still shut down as soon as they know something is amiss, become unable to discuss strategy, and look towards their classmates for the answer. And over time, this practice of giving up personal responsibility becomes a mindset that will prevent students from attempting to solve anything.

But if students get to witness different solutions being used, then what is expected of them and their perceived roles change. Instead of being expected to find a single answer to a problem, they get to find their own. They are no longer passive observers, but potential leaders. Next time they are presented with a task, they will focus less on getting the right answer and more on creating one that makes sense to them. And while they will still look towards their classmates when it comes time to share out, they will be actively comparing their solutions rather than simply listening for one.

View full “Nana’s Chocolate Milk Task” here:

View other Three-Act Tasks by Dan Meyer here: