This article introduces a workshop in which teachers use ratios and integer sequences (e.g., the Fibonacci sequence) to make layered drinks. I love cooking, and I also love to make mocktails myself at home. As the article suggests, layered drinks can be made by using different amounts of sugar to achieve different drink densities. I tried a similar activity with my science class before to teach them about density, but I’ve never thought about analyzing the ratio of sugar mathematically by engaging with the concept of the Fibonacci sequence.
The workshop has two parts. Part One introduces the sugar ratios and density. The audience can compare the sweetness of two drinks by calculating the sugar ratio in each layer. The second part of the workshop explores how the monotonic sequence can be represented through the layers of the drink.
STOP 1: “Unlike most examples of food-based mathematical art, where the math is purely visual with no effect on the actual flavor and experience consuming the food [2, 4, 5], the math in our beverages is conveyed entirely by the ingredients and flavor.”
The activity contains two senses --- visual and taste. I think this is a very innovative idea since we don’t usually engage “taste” in learning, especially in math. By adding different amounts of sugar, students can tell that one beverage is sweeter than the other, so the ratio must be higher. This brings the abstract idea of ratio into real-life practice. I can make the connection to develop a bubble tea ordering question. In most stores, customers can request the sugar level of bubble tea. However, since the volumes of medium-sized and large-sized are different, the sugar content in each size must be different. If we want to maintain the same amount or the same ratio of sugar (i.e. 30%), how much sugar should we add? Many of my students love bubble tea, so I think they will be really interested in this question. Perhaps next time they order bubble tea, they will pause and think about it as well.
STOP 2: “Layered beverages are a particularly nice food to play with for this exercise. The layering caused by density is somewhat counterintuitive and can be a nice science lesson in addition to the math lesson described”.
I do agree that this activity works well for the science classes. Since I’ve tried a similar activity with my science class before, I attached some of the drinks I made earlier as the demo. Instead of focusing on the sugar level, I asked students to focus on the “state of matter” and “their density”. For example, in sparkling lemonade, the lemonade at the bottom is denser, while the sparkling water is lighter (because there are bubbles/gas), so it’s on top. Besides that, ice, as a solid, flows on top because it is less dense than liquid water. To develop on this idea, I’m thinking about whether we can also use a sequence with a different ratio of food colouring in water. This may be more accessible at the school lab and produce a clear observation.
Questions:
1. What other food-math connections idea do you have?
2. Instead of focusing on number sequences, can we develop some geometric food-math activities? i.e. different geometric shapes of cookies? Best way to cut and share a pizza?
Activity:
I’m really bad at paper folding. I remember when I was a kid, I was always the last one to finish the paper-folding activity in class (and sometimes I couldn’t even build the final product). I tried the instruction video listed in the doc. To be honest, it took me a long time to figure out how each part gets up and down ---- and I didn’t get it in the end. Instead of being stacked, I decided to try a different method and looked for other videos online. I found this one and it makes more sense to me!
https://youtu.be/9nBWJ3b8i5c?si=H3YFFmHWE6vrMSg5
This really made me wonder sometimes if students can’t do something, it is because they simply can’t do it, or because the instruction is not suitable for them. It also makes me doubt my personal skills. I’m really interested in and good at LEGO building, constructing IKEA furniture, and I majored in Physics so I always assume I’m good at “making things”. However, I always experience some challenges in Origami. I’m wondering if the difference is that Origami focuses more on flat 2D skills, while LEGO is more 3D with the visuals in more space. My final project is about transferring 2D nets to 3D models, so it may be a good idea to research deeper into why someone is more comfortable with 3D models than 2D.
I also asked my parents to try it. They said they tried but failed. One of the reasons is that the paper they used was too soft to fold. After a few rows, it was hard to recognize the pattern. This makes me wonder if we can use a pencil or pen to trace the pattern so it is more visual in the folding process.
I used food for a systems of equations activity with my FMP 10 class. We used double stuf and regular oreos and from the information on the packaging figured out how many calories are in just a cream filling or a single cookie wafer. It was a really good lesson and there was lots of talk about assumptions we need to make (is the double stuf actually double? how could we verify this?) I always bring in the different oreos and scales because everyone loves oreos, but it also gives a visual they can play with. Sometimes I will have students want to investigate mass also.
ReplyDeleteI really enjoyed reading about your layered drink activity. I’ve done density towers before with my Science 7 and 8 classes, but we always approached it strictly as a lab activity and never connected it to drinks or taste. I really liked your idea of also linking it to ratios. Using sweetness as a way to help students think about ratios and density at the same time seems like a really powerful connection. It would make the concept more tangible because students can actually taste the difference rather than only observing the layers visually.
ReplyDeleteYour post also reminded me of the only food-related lab I’ve really done with students, which was making ice cream in a baggie. We used it to explore changes of state and why adding salt to ice lowers the freezing point and helps the ice cream freeze faster. Like your example, it was a really memorable way for students to experience a scientific concept rather than just talk about it abstractly.
I can also relate to your experience with the origami activity. I struggle with paper folding as well! I still get confused when students talk about “hot dog fold” versus “hamburger fold.” Since I mostly teach older students, we don’t often do activities like this, but this week I happened to do an origami activity with a Grade 4 class. It really opened my eyes to how explicit the instructions need to be at every step. Something that seems obvious to an adult can actually be quite tricky for students when they’re trying to translate directions into folds.
Your idea about whether the challenge comes from the instructions rather than the learner is a really interesting question. It definitely made me reflect on how carefully we need to think about the way we explain and model hands-on tasks.
Hi Sunny,
ReplyDeleteI really enjoyed reading your post, especially your connection between math and taste through the layered drinks activity. The idea of engaging multiple senses, particularly taste, is such a powerful and often overlooked approach in mathematics learning. It really challenges the traditional view of math as purely abstract.
Your discussion of ratios, density, and even sequences like Fibonacci adds such depth to what could otherwise be seen as just a “fun” activity. I also found your point about the math actually impacting the experience (not just the visuals) really compelling. It makes the mathematics feel purposeful and embodied rather than decorative.