Unit Plan + 3 Lessons (Draft)

 Link to the Unit Plan Draft

Group Curricular Micro-Teaching Reflection

 Reflection

Our lesson was on linear regression from FOM 12, and we focused on an interactive activity-based learning for the students. It was my first time going through the FOM 12 curriculum, and I noticed that many topics are different from what is covered in PC 12. 

As we worked our way through the lesson into the worksheet activity, each of us (without making a group decision beforehand) walked around making sure students were on task, asking them questions, giving assistance if students were unsure of the task, and keeping them engaged. It was fantastic that we all knew what to do and how to be present in the classroom during the activity, despite the lack of practice time we had. 

After reading through the peer-assessments, some improvements we can make for next time would be:

• Including additional scaffoldings for clear worksheet instructions: This could be written on the worksheet or verbally communicated before assigning the worksheet questions

• Explain instructions before distributing worksheet: A student mentioned that a couple of students missed instructions because they had their attention on the worksheet in front of them.

• Lesson run-through before lesson: We did not have enough time to do a full run-through of our lesson. Despite most of it being organized and smooth, there were areas where we could definitely improve and gave advice to each other if we went over what we were going to say in the lesson.

Self-/Peer-Assessments

Group Curricular Micro-Teaching Lesson Plan

Group members: Yuki, Ross, Katarina

Subject and Grade Level: FOM 12

Curriculum Big Idea: Modelling data requires an understanding of a variety of functions

Curriculum Competencies: Reasoning and modelling, Connecting and reflecting

Curriculum content: Regression analysis

Learning objectives: Students should understand what a line of best fit is, know how to choose the function that yields the best fit, and think about what the error is

Materials: Whiteboard markers (for teacher explanations on board), calculators (Desmos), worksheet

Teacher	Student	Assessment	Timing
(Set up) Co-teachers hand out activity worksheets.	Students offer what functions they are familiar with Ask the class to use their hands to show what those functions look like	(Accessing prior knowledge)  Setting the stage and asking students what functions they remember learning in previous units or grades.  Note: We will have been studying linear, quadratics, exponential, logarithmic, and sinusoidal functions throughout the year	3 min
(Matching Activity) Teacher asks students to have a look at the dataset and match the type of function to the dataset. The matching activity will be done as a think-pair-share.	Students match on their own, discuss with partner, and then share as a class (Think-pair-share)	Teachers check in with groups, ask them to describe their thinking, see if there are any functions that are challenging to match	6 min (1 min think, 2 min pair, 3 min share) Note: move on to class-share if pair discussions start to  drift off topic
(Error activity) The teacher asks students to have a look at the three sets of fits on one of the dataset from the matching activity. Discuss with partners: which fit do you think is the ‘best fit’? Could you provide a measure of which one is best? (Could do TPS but it might be hard with time)	Students work in pairs to think about which fit is best, and measure error (in a non-sophisticated way).	Teachers check in with groups, ask them to describe their thinking, see if students are recognizing that the best fit is connected to how large the error is. Use an exit ticket to check understanding – Which fit they think is best and why?	4 min
Teacher introduces Pearson correlation coefficient as a measure of error	Students listen		2 min

Extension: Factorial Function

Earlier in the year (likely) they will have done a unit on combinatorics. Note that we do not have a function y=x! because we know it only works with integers. But if we put for example (0.5)! into a calculator we do get a result. 

• Have students use desmos to plot y=n! for integers n = [0,6]

• Use function regressions they have practiced to see how close you can fit the curve and the various values of R^2. Try plugging in (7,7!) and calculate the error, as well as different non-whole numbered inputs.

If short on time, we will not introduce Pearson’s correlation coefficient and end with the exit ticket. 

Micro-teaching Reflection

Self- and Peer-evaluations

    A big idea I learned from this activity is that it's very easy to get myself engaged in teaching the content because we chose a topic that we are passionate and have knowledge in. This made me realize how important it is to have passion and solid knowledge in what you are teaching (whether it's teaching/training a skill at work and tutoring academic subjects, to explaining someone about the details of some breaking news), to be an effective instructor for your audience. If I'm not having a fun time talking about something, how would it be possible to keep the students engaged in what I say? Not everything teachers teach is "fun" (like certain historical events, since those should be treated in a respectful manner), but the significance of being able to show how much we care and think it's meaningful will reach the audience. In the math context, this definitely reaffirmed my values as a teacher, on the importance of mastery while creating a positive learning environment for all students. 

    My micro-teaching lesson went smoothly, having enough time to go through the key slides and information needed to complete the assignment at the end. I think the layout of the lesson was very clear, especially because I took the time at the start to go over the lesson objective and learning objectives with the students. While teaching, I noticed that all of my students were very engaged in the content. With this, I made the choice to allocate more time to the end-of-class activity. The choice to make this change ended up being successful, even though I made the decision on the spot. I'm happy that I was able to make flexible decisions as I saw how the students were doing. 

    One thing I should work on is my voice projection, especially when we have many groups talking at the same time. I've always had a hard time adjusting my volume to the adequate loudness of the environment, since I either speak very very loud in a large room to teach karate, or I talk softer with my friends in a smaller group setting. I hope I can practice this during our other teaching opportunities in the program or during the upcoming short practicum. Something that I could have added to my lesson was another very small check-in question or activity. This could've been a short Check-Your-Understanding question mid-lesson to connect with students and see if they are on the right track with the material. Even if I didn't have to use this check-in question, I could have added a slide just in case I had students who were struggling to understand the lesson. 

Micro-teaching Lesson Plan

 

Math Art Project (Group Response)

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.

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. 

Note: We will post a picture of the complete class tessellation tomorrow

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.

Math Art Project (Individual Response)

    This math art project with my group was a great start for me to think about how we can relate art pieces to math concepts and mathematical thinking. With the variety of choices off of the site provided by Susan, we were able to choose an art that we personally like and want to recreate, as well as seeing if the mathematical ideas behind the work is understandable for our level. By researching various ways to recreate our artwork, we came across many unique origami tessellation designs that range from simple to complex folds. When I played around with the Spread Hex Tessellation I made, I tried to incorporate my own folds and designs, which didn't end up symmetric and looked slightly off, so I had to stick to the original spread hex design. If I had more time to learn and discover more designs, I could have been able to make one that is unique to me and our group that is not on youtube or any origami textbooks!

    In the future, I would definitely want to incorporate these art projects as part of a couple of units in the curriculum so the students can develop creative thinking within a math class. Math is not all about algebra and graphs and problem solving, but it is seen in many designs around us. Everyone's interactive activity can be building blocks to any future hands-on activity that I can do with younger grades, leading to fun brain breaks and group activities. It will be a valuable learning experience for the students to shift gears from equations on paper to visually appealing artwork, opening up pathways in math education that it's not always the marks and test scores that hold meaning in math. Similar to what our group faced, the students will also have lots of freedom when selecting their artwork, and promotes personalization of the artwork. However, we must take into consideration that any interactive activity or project should have some connection to our curriculum, and be careful with time management so that students have enough lesson days to complete the curriculum in school. When certain activity instructions are difficult (like folding a flower with origami), it can be hard to have students pay close attention to the details and could end up having students give up or dislike the topic because it is "too hard and too time consuming" for them.

    I personally had so much fun being the student and doing the activity, while also being the teacher to help lead the activity. These opportunities are valuable since we get to see what it's like to learn crafts without prior knowledge, which helps with understanding frustration and satisfaction.