Reflection on the Reading:
Exploring Ratios and
Sequences with Mathematically Layered Beverages by Andrea Johanna
Hawksley
As I delved into Andrea Johanna Hawksley's exploration of
teaching ratios and sequences through layered beverages, I was captivated by
the innovative approach to blending math with culinary delight. Two prominent
stops in this reading stood out to me, offering unique insights into the
intersection of mathematics and food.
The first notable stop is the introduction of simple
two-layered beverages, a clever tool to enhance comfort with fractions and
ratios. The author seamlessly integrates mathematics into cooking, highlighting
the strict ratios in recipes and emphasizing the importance of understanding
fractions. The example of expressing sweetness as a ratio between layers—3:5,
for instance—creates a tangible link between the abstract world of numbers and
the delicious experience of consuming layered drinks.
The second stop takes me into exploring sequences using
beverages with many layers. The limitation that each layer must be less dense
than the previous one narrows down the feasible sequences, introducing a
fascinating challenge. The author introduces sequences like the Fibonacci
sequence, demonstrating how the layers' proportions can mirror the sequence's
mathematical properties. Creating a Fibonacci lemonade, where the intensity of
flavors increases exponentially, adds a delightful twist to the exploration.
These stops underscore the dynamic relationship between
mathematics and the sensory experience of consuming layered beverages. The
interactive nature of the workshop engages participants in hands-on
calculations, transforming the often abstract and challenging concept of
fractions into a practical, enjoyable exercise. The layered drinks not only
serve as visual aids but also as tangible representations of mathematical
principles.
Now, turning to potential questions:
- Can
you think of other mathematical concepts that could be effectively taught
through food, similar to the approach described in the reading?
- How might these concepts be translated
into a hands-on, enjoyable learning experience?
Andrea Hawksley (Bridges 2015) Exploring ratios and
sequences with mathematically layered beverages
Activity
Reflection on Personal Exploration:
Miura Ori Origami and Mathematically-Interesting Shoe
Lacing
Embarking on the journey of trying out Miura Ori Origami and
exploring mathematically interesting ways of lacing shoes has been a
fascinating and eye-opening experience. Though seemingly unrelated, both
activities offered a unique perspective on the interconnectedness of
mathematics with everyday objects and artistic creations.
Miura Ori Origami: Unraveling Mathematical Beauty
Attempting the Miura Ori Origami technique, as demonstrated
by Uyen Nguyen, was a delightful immersion into the world of mathematical
elegance embedded in fashion design. The step-by-step video instructions (B)
unveiled a mesmerizing sequence of folds that transformed a flat piece of paper
into a three-dimensional masterpiece. The recurring patterns of triangles and
parallelograms became apparent, showcasing the precision and symmetry inherent
in the origami art form.
What struck me the most was the mathematical precision
required to achieve the final result. The interconnected folds carefully
considered angles, proportions, and geometric relationships. It was a reminder
that even in the seemingly free-flowing world of art and design, mathematics
plays a pivotal role in creating order and structure.
Shoe Lacing: Tying the Knot
with Numbers
Shifting gears to the world of shoelaces, I delved into the
Mathologer video, uncovering the intricate mathematics behind different lacing
patterns. Before this exploration, I never thought much about the mathematical
aspects of something as mundane as shoe laces. The video opened my eyes to the
complexity and diversity of lacing techniques, each with its unique
mathematical properties.
The revelation that the popular criss-cross and zig-zag
lacing patterns are not just aesthetic choices but have mathematical
underpinnings was intriguing. The emphasis on tight lacing and the connection
to mathematical concepts, such as the contribution of each eyelet and the rapid
increase in possibilities with more eyelets, showcased the intricate
relationship between mathematics and seemingly unrelated daily activities.
In conclusion, both activities underscored the omnipresence
of mathematics in our lives, whether in the meticulous folds of an origami
creation or the efficient lacing of shoes. These experiences have heightened my
appreciation for the beauty and functionality that mathematics brings to even
the most ordinary aspects of our daily routines.
Questions to ponder:
- Consider
incorporating mathematical concepts into art forms or routine activities.
How do you think this integration could enhance learning experiences and
make mathematical ideas more accessible and engaging for a broader
audience?
Miura Ori - Traditionelle Miura-Faltung
https://www.youtube.com/watch?app=desktop&v=EEGmnKKKhrk
What is the best way to lace your shoes? Dream proof.
https://www.youtube.com/watch?v=CSw3Wqoim5M
Hi Tony,
ReplyDeleteThe layered drinks with many layers had me thinking… Each layer must be less dense than the previous one so I wonder if there would be any tangible difference when consuming each layer. Would the drinker be able to feel the change in density as they drank through the layers? Just something to think about!
The first mathematical concept that comes to mind with food is fractions (as demonstrated in the paper you read). I’ve used cutting apples to demonstrate an intro to fractions for my Grade 3 students (the first time they have to learn fractions). We’ve used Skittles to work out fractions of amounts, counting the different colours. Another way that I think food can be used is in graphing. If I think back to Week 2, I used Rockets and graphed the colours in the package with my students. This was an engaging way to tackle collecting and analyzing data and bonus… they got to eat the data at the end!
The need for precision when doing Origami was especially apparent when completing a simple paper airplane with my students. Many were over-folding which then affected the next fold in the sequence. They got frustrated! Who knew a six step design could be so challenging!
I watched part of the Mathologer video as well but didn’t have time to experiment with my shoes. It was eye opening just how many ways it is possible to tie shoes!
Great final question! I think the beauty of incorporating mathematics and the arts in Grade 2 is the hands-on aspect of it. Most of my students would much rather be ‘doing’ something to demonstrate a concept instead of writing about it - mathematics and arts is engaging! It also allows my students who cannot explain their understanding through written products to show me what they know through ‘doing’. I know there still needs to be a balance but especially for my struggling learners, ‘doing’ the math through art allows them to feel successful.