Mini lesson plan

 

Date: Sep 30th	Title: Master Golf Rules with PGA Standards
Lesson duration	15min
Big Ideas, Competencies, and Content	Introduce Golf rules with PGA standards Scoring terms and meanings
Learning Objectives   (SWBAT … The student will  be able to…)	Understand the game design and key scoring terms. Be able to watch a golf competition and engage with it from their own point of view
	PROCEDURE
Elements of the lesson	Estimated Time	What the teacher says/does	What the students do	Material
Introduction	3min	“Have you ever seen golf on TV or in movies? What did you notice? “	Small discussion with other people	slides
Body Activities	5min	Introduce the essential rules of golf How scores work in golf	Can come up with different questions	slides
Body Activity	5min	Scoring terms and meanings	Can come up with different questions	slides
Closure	2min	Exit ticket Giving a few true/false questions for students to answer	Think, pair, share	slides
Student Assessment	-	Self-assessment Peer reviews	Self-assessment Peer reviews
Plan "B"		Talk about some real-life experience and hold discussions

The Locker Problem

 

Post at 12:07am… 

I have sense it might be related to factors but I can’t find the final pattern of it…..

Math Art Project Personal Write-ups

At the beginning of this project, I was doubtful about whether we could successfully recreate Eric Gjerde’s tessellation, since the intricate folds and layered symmetry appeared very complex. However, after searching on YouTube and finding a tutorial, I realized that by carefully following the guided steps we could reproduce the structure and even make our own slightly revised version. Through this process, I noticed that the mathematics behind Gjerde’s original hexagon tessellation relies heavily on 120° rotational symmetry, hexagonal tiling, and repeating twist folds that interlock seamlessly across the plane. In contrast, when we worked on a variation using square paper, the underlying mathematics shifted: instead of hexagonal tiling, the design emphasized 90° rotations, reflective symmetry across axes, and the layering of concentric shapes. This contrast highlighted how different polygons produce different geometric constraints and patterns, even when applying the same origami techniques like pleat intersections and twist folds. 

For me, this showed that origami tessellations are not only artistic but also deeply mathematical, demonstrating concepts such as symmetry groups, angle measures, and tiling properties in a tangible form. I found this process to be an approachable teaching tool, since the folding steps naturally illustrate how abstract mathematical ideas connect to real-life problem solving and hands-on creativity.

Math Art Project Group Write-ups

Group members: Damanjit, Elvie, Helin, Yuki

Original Artwork and Artist: Flowering Grid by Eric Gjerde by Tejom Patel

After our group collectively chose this artwork as our project topic, we faced a big issue of not having resources that lets us perfectly remake the original artwork. The artist, Tejom Patel, had creatively expanded their flower tessellation (based on Eric Gjerde’s work), by adding different folds to produce a new, unique piece. We started off attempting to perfectly mimic Patel’s art. However, due to our lack of knowledge on how the folds and designs work, we had to start off by choosing a design that had guides and tutorials. This was the Spread Hex Tessellation.

Similar to the original artwork, we kept the idea of hexagons and reflectional symmetry, but folded a tessellation where the hexagons overlap and pile up.

 

 Similar to the original artwork, we kept the idea of hexagons and reflectional symmetry, but folded a tessellation where the hexagons overlap and pile up. 

Here is the link to the video tutorial of the spread hex tessellation: 

https://youtu.be/3BTu2Hih39A?si=jRJpq3Fw6cG6oauz 

Through our research phase, we came across Eric Gjerde’s book Origami Tessellations: Awe-Inspiring Geometric Designs. This resource provided detailed folding tutorials for many origami tessellations built from triangles, squares, and hexagons, and also explained key techniques such as Pleat Intersections, Triangle Twist, Square Twist, and Hexagon Twist. With this reference, we gained a deeper understanding when looking back at our own work, and it also gave us the idea to design an activity more suitable for a short classroom session.

Our interactive activity with the class was a hands-on origami activity where each student folds their own piece of flower that will then combine to create a big multi-piece flower tessellation. Since abstract origami tessellations take a long time to fold, we designed it such that all prep is done (fold lines created beforehand) and students are to follow instructions while helping each other to collectively create one piece of art with the class. 

Here is the link to the origami flower we made in class:

https://youtube.com/shorts/tQMteMhp1Dk?si=Hxtkz7Yhg_-RoIt7 

In addition to experimenting with hexagon-based tessellations, our group created a variation called the Layered Compass, which is folded from square paper rather than a hexagonal grid. This shift gave us a chance to explore the mathematical flexibility of tessellation design. Whereas hexagons naturally lend themselves to 120° rotational symmetries and interlocking flower-like patterns, the square base highlights 90° rotations, reflections, and layered symmetry. By adapting the same folding principles—pleats, twists, and repeating units—to a different polygonal foundation, we were able to compare how tiling properties change with shape and how symmetry groups are expressed through origami art. Using square paper also made the process more accessible, since it is a common format and easier for classroom folding activities. Through this variation, we not only made the project our own but also deepened our appreciation of tessellations as a versatile mathematical art form that can be reinvented through creative folding choices.

Here is the instruction of the easy version floral origami tessellation!!

 

Flip it over here!!!

Ta-Da~~ Done!

My favourite and least favourite math teacher

Thinking back on my learning experience, I’m grateful that I didn’t encounter many unprofessional teachers who negatively impacted my education. Before college, I studied in China and also took the national college entrance exam which is also called Gao Kao. In elementary school, I was not a “science person,” and math was my biggest nightmare. Back then, I often wished math could disappear from my life and kept questioning why we needed to study it at all. I had zero interest in the subject, and perhaps my math teacher was one of the reasons. She was a young lady with short hair and simple glasses. I still remember how afraid I felt in her class, especially of being called up to solve problems on the blackboard. Each time she responded with her impatient “unbelievable look”  when students gave the wrong answer. I barely hear appraise words from her even when we got the correct answer. From then, I lost interest and motivation in studying math and I really thought I was too dumb to understand. 

However, things changed in middle school. I had a new math teacher who was caring and supportive, and he made math engaging in ways I had never imagined. He explained concepts so clearly that they became interesting and easier to understand. By connecting the content with real-life examples, he made math much more approachable. His classes were always full of creativity; he introduced various activities and different types of assignments that allowed us to practice and develop a deeper understanding. In his class, I learned not only the concepts themselves but also how to think critically about problems. Even when I struggled with certain concepts and received a low score on a midterm, he remained patient and encouraged me to visit his office hours, where he walked me through the correct solution step by step.

As a teacher, the responsibility is not only to teach knowledge but also to cultivate ways of thinking and problem-solving skills. A good teacher focuses on how students are growing, rather than on how low their starting point might be. Being a good teacher also means creating a supportive environment, showing patience, and inspiring curiosity so that students feel encouraged to take risks in their learning. I hope to be a teacher like my middle school math teacher—to follow his example and make small but meaningful positive impacts on my students.

What is meant by “Curriculum”

 “What schools do not teach may be as important as what they do teach.” I gained new insight into the idea of the null curriculum through this article. While schools can explicitly teach the content outlined in the BC curriculum, students’ ability to generate their own thoughts around specific ideas cannot simply be taught directly. Thinking is one of the most productive abilities for individuals, and when combined with the BC curriculum, it allows us to foster this ability alongside subject content. I believe this is also why inquiry-based classrooms are encouraged and why we need to teach students how to learn, not just limit them to mathematics concepts.

Moreover, teaching should not be reduced to mere techniques. In today’s world, where knowledge is so easily accessible through AI and the internet, or even through books, the role of a teacher must go beyond delivering information; it’s important for us to differentiate ourselves with “teaching robots.” Education can occur outside of school, but within schools the hidden curriculum is especially powerful: students learn not only knowledge, but also authority, competition, and social norms. Through collaboration, reflection, and effective assessment, students can experience meaningful interpersonal growth.

Finally, curriculum should be seen as a fundamental tool that helps us create a structure for the totality of experiences students encounter in school. As Eisner emphasizes, these experiences are not shaped by the explicit curriculum alone but also by the hidden and null curricula working together. When we combine all three curriculum, it is way easier to create richer learning opportunities that prepare students not only for academic success but also for life beyond the classroom.

Reflection on “instrumental understanding & relational understanding”

 When I read the part about students aiming for instrumental understanding while teachers are eager to teach relationally, it made me think about how I was taught mathematics in middle school. At that time, math felt like a subject where I had to memorize a lot of formulas and apply them to different questions. It was “useful” for solving problems and getting the correct answers, and it also helped me build confidence, just as Skemp mentions. However, when I think back, I realize I didn’t really understand why I was using those formulas. Compared to instrumental understanding, teaching should focus on delivering content in a way that helps students develop relational understanding within a bigger context, ultimately improving their problem-solving skills. Getting the correct answer can bring quick success, but it shouldn’t be the final goal.

Reading further, I found Skemp’s point that the advantages of relational mathematics make it easier to remember. Based on my own experience, this is true. For example, when learning a new language, reciting well-organized sentences and vocabulary provides a strong starting point. It is much faster to understand the meaning first before memorizing mechanically. At this point, I stopped and realized that Skemp is not simply arguing that instrumental understanding is “wrong” or that relational understanding is always “better.” In my opinion, finding a balance between these two types of understanding is crucial for teachers. Instrumental methods can provide students with quick wins and confidence, while relational approaches ensure that their knowledge is meaningful and lasting.