By Sunny Hu & Sukie Liu
Link to our presentation recording (Zoom recording): Recording
(Passcode: E5cb=J?3)
Link to our project handout: https://docs.google.com/document/d/1Rd_fGwEP3Jn0GVSfeA7LgSSL3TTCBNcn93IenWjvsDA/edit?usp=sharing
Link to our project slides: https://docs.google.com/presentation/d/19PKjZlaSiwAh-yv8yBW6UJCsy2vzECx12GoUEzOqDRY/edit?usp=sharing
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.
Contributors: Sunny Hu & Sukie Liu
Hi, everyone!
This is our draft project! We are working on a project of creating 3D paper models for the secondary math class geometry unit. We attached the project worksheet that students will use and our project slides.
Project Worksheet:
https://docs.google.com/document/d/1Rd_fGwEP3Jn0GVSfeA7LgSSL3TTCBNcn93IenWjvsDA/edit?usp=sharing
Slides for the project:
https://docs.google.com/presentation/d/19PKjZlaSiwAh-yv8yBW6UJCsy2vzECx12GoUEzOqDRY/edit?usp=sharing
Karaali, G. (2014). Can zombies write mathematical poetry? Mathematical poetry as a model for humanistic mathematics. Journal of Mathematics and the Arts, 8(1–2), 38–45. https://doi.org/10.1080/17513472.2014.926685
This article engaged with the author’s personal experiences to introduce how he started to connect his interests in math with poetry, which he was not very familiar with at first. Karaali got interested in the ideas introduced by the Humanistic Mathematics Network Journal (HMNJ) and stepped out of his comfort zone to explore how poetry in English can be connected with math. He believes that mathematics and poetry share the three most important ingredients of what makes us human: cognition, consciousness and creativity. Thus, he developed a course titled “Can Zombies Do Math” to encourage students attempt to write mathematical poems with creativity.
STOP 1: “In my native language, Turkish, sentence structure is quite different from that in English. Correct grammatical forms exist, though they are not as rigid as one might expect. The speaker may and will often move the main parts of speech around in order to make a statement, emphasize a point, underline a concept or simply to convey the spontaneity of the particular conversation… But with poetry, I could only hear my voice in Turkish. Mathematics was different. My mathematical language was definitely English…”
This is a really interesting point, and I resonated with it a lot as a second language speaker. Same as Karaali, I use English to do math a lot, but I’m more comfortable in writing or reading poems in my first language (which is Chinese). I’m wondering if there is a reason why people feel more attached to their first language in poems. Probably it is because of the culture? Or how familiar you are with the poetry styles when you were kids, since lullabies and songs are all different variations of poetry. Karaali mentions that grammar in Turkish is not as rigid as English, so you can change the order of words to form a sentence. I guess this gives people more flexibility and creativity in writing poems. I found Chinese grammar has a similar nature as well, where we can arrange different characters to make new words each time without affecting the grammar or meaning of the sentences. This really makes me wonder whether multilingual people have more ideas for exploring poems and make more innovative connections in mathematical poems from various perspectives.
STOP 2: “Referring to our students’ course work, we can inquire explicitly: what does it mean to be creative in the mathematics classroom? The answer will come rather easily to most teachers of mathematics: students can think of novel ways of approaching problems. But what is novel is most often simply some idea or technique that they have seen elsewhere, now taken and used out of that original context. A concept that is often considered in tandem with creativity is divergent thinking, which captures thinking processes that lead to multiple possibilities. So it is fundamental to creativity in general, and to creativity in the mathematics classroom in particular, to be flexible and open to many interpretations and approaches.”
When I first thought about being creative in math, I had the same idea as Karaali mentioned here: to have more approaches to solving problems means you are creative. However, Karaali argues a new idea: that students may use different approaches because they have seen or learned the questions elsewhere. This may not reflect the students’ creativity, as the idea may not be original. This aligns with his statement in ‘zombie-learning’ about following the rules without any human creativity, interpretation, or flexibility. Karaali introduces the concept of divergent thinking, which means generating more possibilities. I can tell he tries to link this idea to poem-writing, since writing is very personal, and the idea of a poem can only come from your own mind, which aligns with the use of divergent and creative thinking.
Questions:
1. How do you support English Learning students in your class to try the mathematical poem activity? How can you make the poem-writing activity fun but not too challenging for students?
2. In your opinion, what makes a poem a mathematical poem? Besides structuring the poem by numbers or sequences, what other ways can you think of? Can geometry, function and graph also be used as part of the poetry? If so, what would that look like?
Week 8 Activity
I’m not really good at poem-writing. Poetry was always the unit that caused me the most headaches when I was in high school. However, I’d like to challenge myself this time to try the Fib poems.
Similar to what Karaali experienced in his article, I came to Canada in grade 10 and studied most of the math in English, but my first language is Chinese. I am definitely more comfortable in reading or writing poems in Chinese. In the Chinese language, one word (character) is one syllable, so we never distinguish words and syllables. This makes it extremely hard for me to write English poems when I have to be aware of the differences and count syllables in words.
I really like the flexibility of the Fib poems, which can be counted as syllables per line, or words per line, or lines per stanza, or any other countable thing connected with the poem. This offers more creative ideas. You also don’t have to be perfect at English or poem-writing, since it is easier to start by counting the number of words.
Since I’m working on my project this week on 2D-to-3D models, I had the idea for a geometry-themed poem.
Geometry (count by the number of words: 1,1,2,3,5,8)
Point
Line
An angle
Forms a surface
Enclose edges of a figure
New dimension is formed to create more possibilities
Element (count by the number of words: 1,1,2,3,5,8)
I
Am
An Element
Starts with H
Have one proton, no neutrons
Lightest element in the world—who am I
