I am not sure who to thank first, Robert Kaplinsky or Dan Meyer… If it were not for Robert Kaplinsky, I would not have come across a tweet of excited anticipation to try Dan Meyer’s ratio lesson entitled Nana’s Chocolate Milk. If it weren’t for Dan Meyer, there would be no such lesson. What can I say, both mathematically inclined gentlemen have my gratitude.
I have been talking about ratios with students for as long as I have been in the middle school grades. In my, oh my gosh, I can’t believe I used to teach math that way years, I would simply teach students how to find an equivalent fraction by scaling up or down by the same factor. Perhaps, as an aside, I would mention real-world tie ins like, recipes, but I really could have done so much more. In Dan’s lesson, he delivers the conceptual gift of ratios with ease through the power of chocolate milk.
In his three act task, Dan “accidentally” puts in an extra scoop of chocolate into a glass of milk, even though he knows that Nana’s preferred chocolate milk beverage has a 4:1 ratio of chocolate powder scoops to cups of milk. He asks the simple question, how can he fix the situation?
The students were invested as soon as they saw the video clip. They could all relate to accidentally putting too much of an ingredient in something. For some, it was to much milk in cereal, for others, it was accidentally over-measuring a tablespoon of vanilla in a batch of cookies. The point is, the Mathematical Practice Standard of abstraction and quantitative reasoning was in sharp focus here.
When students were challenged with how to fix it, some students immediately suggested to spill it out and start again. Although, definitely a solution, that option was not deemed an economical option, and the double number line was presented. As I walked around the room and heard students debating each other about how to change the milk and/or chocolate amounts with keeping the Nana-preferred ratio in tact, I noticed the mathematical conversations were appropriately everywhere. Some students immediately thought to double the amount of milk and add three additional scoops, and then put the remaining chocolate milk aside in the fridge for the next day. Others didn’t think that another cup of milk would fit in the glass (part of act 2) and asked if fractions were okay. Some had not quite understood the ratio concepts by their responses, which was addressed in the closing thanks to the anticipation model touted by both Graham Fletcher and Robert Kaplinsky. The point is, there was rich, robust conversation about ratios through the relatable chocolate milk scenario.
When students were told that the glass could not fit 2 cups of liquid, students wondered how much liquid displacement occurred with the powder to see if adding an additional ¼ or ½ cup would be a more appropriate answer. I wasn’t sure the first class had understood the idea of ratios, so I used Dan’s sequel on Nana’s eggs. It was clear that the lesson was powerfully effective as they all came up with correct solutions keeping the egg to flour ratio intact immediately. Every, single, student… I have always been a huge fan of cooking, baking, and math. How fun it was to watch the concept of food make a beautiful day in the math classroom!
The lesson link is here: Nana’s Chocolate Milk