Week 8: Fibre Arts, Culinary Arts and Fashion Art

Summary, Applications and Overall Reflection:

Hawkley, A. (2015) Exploring ratio and sequences with mathematically layered beverages.

Thank you, Maria, for allowing us to switch. =D I loved reading this article as I teach density to the students and building density towers is one of my favourite labs! In my classroom I just finished a cooking class that looked at fractions and ratios, and I thought this paper was a brilliant way to approach the lesson using drinkable products rather than food!

Adjusting the ratio of sugar to water changes the density of the liquid. The more sugar (greater sweetness), the more dense the liquid.  In Hawksley (2015) article, she explores the idea of the Fibonacci-like sequences, like Lucas numbers, by adjusting three key ingredients of lemonade: lemon juice, simply syrup and water. Essentially, the intensity of the drink would increase exponentially (p. 521) as you go down the layers of the drink. 

For a more simplistic approach, this could also work with fractions sequences for younger grades (I work with grade 6, so this would be a fantastic link to our unit in math and science). By creating a total volume of 1/2 cup, you could create different concentrations of solutions by adjusting the lemon juice, sugar and water. Note, when making the drink, always start with the sweetest or more dense layer!

I tried making it but I forgot about buying food colouring, I only had three. And they weren't such great colours! So I couldn't complete the entire Fibonacci sequence. But, the layers do show up!

Applications:
(Sorry - I may go into a scientific rant here) There are other ways to integrate mathematical concepts. 

• Comparing decimal values: Varying densities and concentration levels could allow students to make observations about how decimals work. For example, starting with pure water at 1.00g/mL and comparing that to other syrups such as honey (1.44g/ml), corn syrup, maple syrup etc. 

• Graphing: This could be a great data set to teach students how to graph, for example compare the % of sugar to water ratio and density (g/mL). This is actually an application to canning goods because the concentration of sugar affects the quality of the fruits (Vitz et al., 2021)

• Temperature also affects density! Water is most dense at 4OC. So changing temperature and determining density would be another way to explore this concept. 

ACTIVITY (Shoelaces):

I didn’t have any clean shoes so tried doing the lace activity using a holed pencil container. The issue was that there were 6 holes that were aligned, and I had to improvise and use 2 interior holes as the ‘7th’. My first go made me realize how important it is to align the laces upward or downward. In the video, this wasn’t as apparent, because you can only see the lines connecting the dots. I realized depending on the direction it made a significant differences in how the final look would appear.

Figure 1 (left): Lace attempt 1, where the starting strand pointed inwards and the resulting longer points ended up being inwards.
Figure 2 (right) Lace attempt 2, where the starting strand pointed outwards, resulting in the longer points directed outwards.

Figure 3 (left): I thought I did a different design than Attempt 2, but it ended up looking very similar! Again, because you can’t see the inside design, the outward design looked the same.
Figure 4 (right): I tried one of the more crazy designs and found it hard to follow. 

One of the issues was also to figure out how to end up with the strands outward.

Overall Reflection:

From my engagement, I was drawn to the links with culinary foods. For the orbifold patterns, I was surprised that there were 17 different types of wallpaper patterns. I love interior design, so looking at sequencing and design from an aesthetic perspective would be engaging! 

Additional Sources

Vitz. E., Moore, Justin Shorb, Xavier Prat-Resina, Tim Wendorff, E. V., John W., & Hahn, A. (2021, July 12). Sugar Solution Density. Chemical Education Digital Library (ChemEd DL). https://chem.libretexts.org/@go/page/49969